The media and politicians often tell us something like “Last period’s” result was the worst in “n” periods. Example: Last year’s murder rate was the highest in ten years. They then go on to lament how things have degenerated and to blame someone.
By itself, this kind of statement conveys no useful information about the message topic.
Suppose the underlying murder rate is constant. Due to random fluctuations, each year’s realized murder rate will be different. No matter how large is the highest realized murder rate to date and how small the lowest murder rate to date, the highest and lowest will be surpassed over time. The probability that the media and politicians will jump on this when it occurs is about 1.
Given a murder rate so high that it its probability of being realized in a year is only 10%, then it ought to be realized about once in ten years. The probability that the media and politicians will jump on this when it occurs is about 1. Assuming independence, the probability of not seeing such a high murder rate in ten years is 35%, i.e., there is a probability of 65% of seeing at least one year in a ten year period with such a high murder rate.
Moral: That the media and politicians make a big deal of unusually good or bad outcomes is something that often can be chalked up to either an agenda or ignorance. In either case, it says more about the person than the message topic.
One important probability is the probability that something has changed (good or bad), given that the media and politicians deliver their message. Since it is about equally likely that the media and politicians will deliver their message whether or not there has been an underlying change in circumstances, the fact that they deliver their message conveys approximately no information.
Wednesday, June 28, 2006
Tradeoffs: Humvee armor
Life is about tradeoffs. Much of what you see in the media and from politicians ignores the tradeoffs. That is one reason why you can’t trust either.
From time to time, this blog will suggest some of the tradeoffs on important issues (and some not important ones) that ought to be considered.
Here is an example.
There was a lot of initial criticism from the media and politicians about Humvees having inadequate armor.
The more armor, the less chance of the occupants being killed from enemy action. On the other hand, armor makes the vehicle less stable and the more chance there is of the occupants (and bystanders) being killed from accidents involving loss of control (e.g., rollovers). Since the percentage of time Humvee driving is in combat conditions is low, there seems a reasonable chance that the overall Humvee related fatality rate is increased by adding armor.
I have no idea what the net effect has been. But the initial media and political focus on one side of the issue was misleading. Some of the media addressed the tradeoff later, with nothing like the initial misleading exposure. Politicians have yet to provide balance.
Here is a link to an article on the topic. I have no idea what the net effect has been. But the initial media and political focus on one side of the issue was misleading.
Go to article
From time to time, this blog will suggest some of the tradeoffs on important issues (and some not important ones) that ought to be considered.
Here is an example.
There was a lot of initial criticism from the media and politicians about Humvees having inadequate armor.
The more armor, the less chance of the occupants being killed from enemy action. On the other hand, armor makes the vehicle less stable and the more chance there is of the occupants (and bystanders) being killed from accidents involving loss of control (e.g., rollovers). Since the percentage of time Humvee driving is in combat conditions is low, there seems a reasonable chance that the overall Humvee related fatality rate is increased by adding armor.
I have no idea what the net effect has been. But the initial media and political focus on one side of the issue was misleading. Some of the media addressed the tradeoff later, with nothing like the initial misleading exposure. Politicians have yet to provide balance.
Here is a link to an article on the topic. I have no idea what the net effect has been. But the initial media and political focus on one side of the issue was misleading.
Go to article
Monday, June 26, 2006
Stealing from your fellow citizens
Being a Florida resident, I just received this email letter from my Senator, Bill Nelson.
This is an example of how Government rewards people for making poor decisions.
Hurricanes are anticipated in Florida. If Floridians were not confident that the rest of the country would be required to reimburse them for much of their hurricane damage, Floridians, faced with the real costs of living in Florida, would build stronger infrastructure, stronger homes, etc. Just as important, they would build less in dangerous areas, like on the Ocean or the Gulf.
Subsidizing Floridians for known events distorts the economy in a way such that it is possible to readjust production so that everyone is better off (technically, the subsidy ensures that equilibrium is not Pareto-optimum).
It is jus plain dumb (but thanks for your money, anyway).
At this point you are probably nodding your head in agreement and ridiculing Government. But the real problem is that Bill Nelson gets elected in return for bribes like this.
As Pogo said, we have met the enemy and he is us.
Even worse, see if you can think up a set of “rules” for Government that would induce individuals, in and out of Government, to behave in the kind of efficient (Pareto-optimal?) manner we all claim we want to see. Don't forget to assume that everyone acts in their own self interest (in the economics vocabulary, marginal, not general analysis).
I conjecture that no such set of rules exists.
Here is the letter.
June 26, 2006
“Dear Floridian,I am pleased to report that Congress has authorized $5.2 billion for disaster relief to Florida and other states hit by hurricanes last year. The funding is included in the Iraq war funding supplemental bill.
These federal funds are especially important to communities in the Panhandle that were hit hard by Hurricane Dennis. Although previous Federal disaster relief excluded damage caused by this storm, this new funding will help all communities damaged by storms last year, including Dennis, Rita, Katrina, and Wilma.
The relief will come in the form of disaster Community Development Block Grants (CDBGs), with the Department of Housing and Urban Development dispersing the funds among eligible states, and states then allocating the money to counties and municipalities. CDBG funds are often used for long-term recovery efforts, housing and business assistance, infrastructure reconstruction, mitigation efforts, and public services.
The following counties are eligible for the funds: Bay, Brevard, Broward, Calhoun, Charlotte, Collier, DeSoto, Dixie, Escambia, Franklin, Gadsden, Glades, Gulf, Hardee, Hendry, Highlands, Holmes, Indian River, Jackson, Jefferson, Lee, Leon, Levy, Liberty, Martin, Miami-Dade, Monroe, Okaloosa, Okeechobee, Osceola, Palm Beach, Polk, Santa Rosa, Sarasota, St. Lucie, Taylor, Wakulla, Walton, and Washington.
Sincerely,
Bill Nelson
U.S. Senator”
This is an example of how Government rewards people for making poor decisions.
Hurricanes are anticipated in Florida. If Floridians were not confident that the rest of the country would be required to reimburse them for much of their hurricane damage, Floridians, faced with the real costs of living in Florida, would build stronger infrastructure, stronger homes, etc. Just as important, they would build less in dangerous areas, like on the Ocean or the Gulf.
Subsidizing Floridians for known events distorts the economy in a way such that it is possible to readjust production so that everyone is better off (technically, the subsidy ensures that equilibrium is not Pareto-optimum).
It is jus plain dumb (but thanks for your money, anyway).
At this point you are probably nodding your head in agreement and ridiculing Government. But the real problem is that Bill Nelson gets elected in return for bribes like this.
As Pogo said, we have met the enemy and he is us.
Even worse, see if you can think up a set of “rules” for Government that would induce individuals, in and out of Government, to behave in the kind of efficient (Pareto-optimal?) manner we all claim we want to see. Don't forget to assume that everyone acts in their own self interest (in the economics vocabulary, marginal, not general analysis).
I conjecture that no such set of rules exists.
Here is the letter.
June 26, 2006
“Dear Floridian,I am pleased to report that Congress has authorized $5.2 billion for disaster relief to Florida and other states hit by hurricanes last year. The funding is included in the Iraq war funding supplemental bill.
These federal funds are especially important to communities in the Panhandle that were hit hard by Hurricane Dennis. Although previous Federal disaster relief excluded damage caused by this storm, this new funding will help all communities damaged by storms last year, including Dennis, Rita, Katrina, and Wilma.
The relief will come in the form of disaster Community Development Block Grants (CDBGs), with the Department of Housing and Urban Development dispersing the funds among eligible states, and states then allocating the money to counties and municipalities. CDBG funds are often used for long-term recovery efforts, housing and business assistance, infrastructure reconstruction, mitigation efforts, and public services.
The following counties are eligible for the funds: Bay, Brevard, Broward, Calhoun, Charlotte, Collier, DeSoto, Dixie, Escambia, Franklin, Gadsden, Glades, Gulf, Hardee, Hendry, Highlands, Holmes, Indian River, Jackson, Jefferson, Lee, Leon, Levy, Liberty, Martin, Miami-Dade, Monroe, Okaloosa, Okeechobee, Osceola, Palm Beach, Polk, Santa Rosa, Sarasota, St. Lucie, Taylor, Wakulla, Walton, and Washington.
Sincerely,
Bill Nelson
U.S. Senator”
Sunday, June 25, 2006
The New York Times’s overblown OxyContin abuse story
Here is a link to a STATS article “The New York Times' Other WMD Problem”. It discusses another example of the NYT’s poor quality control.
The NYT is not trustworthy.
Here are some excerpts from the STATS article.
“In short, the Sentinel wildly over-estimated the number of people it claimed had died from overdoses of oxycodone (the active ingredient in OxyContin) by failing to scrutinize state law enforcement data. Most of those who died turned out to have consumed, in addition to OxyContin, a cocktail of illegal drugs.”
“Still, at least the Sentinel apologized and corrected the record. No such correction or apology has ever issued from the New York Times for taking a leading role in prompting the idea that OxyContin was a weapon of mass destruction in the nation's heartland.”
““Heck, we already know it’s pretty epidemic down here,” Capt. Minor Allen of the Hazard Police Department in southeastern Kentucky told Times readers in 2001 (“Cancer Painkillers Pose New Abuse Threat” by Francis X. Clines with Barry Meier, Feb 9.) “Abuse of this drug has become unbelievable in the last year, with probably 85 to 90 percent of our field work now related to oxys,” he continued. “We find them carrying pill pushers that are sold in drugstores to help elderly people swallow their prescriptions.””
“Unfortunately, the Times placed far too much trust in the numbers being thrown out by law enforcement and legal sources — as did other news organizations, especially television, which covered Operation Oxyfest like children covering candy.”
“As the Washington Post’s television critic Tom Shales wrote in Electronic Media just a few weeks after OxyContin abuse dominated February sweeps (March 26, 2001),”
““there is no hard evidence that OxyContin played a key role in 59 Kentuckians keeling over. David Jones, an official with the Kentucky State Medical Examiner’s Office, looked into the claim and wrote a letter to Purdue Pharma: ‘I am unaware of any reliable data in Kentucky that proves OxyContin is causing a lot of deaths. In the State M.E. Office, we are seeing an increase in the number of deaths from ingesting several different prescription drugs and mixing them with alcohol. OxyContin is sometimes one of these drugs.’”
“For confirmation, the Free Times turned to David W. Jones, executive director of the Kentucky State Medical Examiner’s office. He asserts that ‘as far as deaths go, I’ve heard different numbers in different places at different times; I have no idea where these people are getting their facts and figures.’ While he stresses that not every drug-related death is necessarily reported to his office, according to his data there were 27 oxycodone-related deaths in the entire state in 2000…”
““…Two of the 27 victims, he explains were found to have both oxycodone and alcohol in their bodies, with death caused by the interaction of two nervous system depressants. What’s more, 23 others had a head-spinning multiplicity of other drugs in their systems, including highly potent prescription painkillers such as Diludad and Fentanyl, as well as powerful illegal drugs like cocaine and heroin. In the final analysis, Jones reveals, only two of the 27 fatalities can be shown to have been due to the effects of oxycodone alone – not just two in eastern Kentucky, two in the entire state.””
The NYT is not trustworthy.
Here are some excerpts from the STATS article.
“In short, the Sentinel wildly over-estimated the number of people it claimed had died from overdoses of oxycodone (the active ingredient in OxyContin) by failing to scrutinize state law enforcement data. Most of those who died turned out to have consumed, in addition to OxyContin, a cocktail of illegal drugs.”
“Still, at least the Sentinel apologized and corrected the record. No such correction or apology has ever issued from the New York Times for taking a leading role in prompting the idea that OxyContin was a weapon of mass destruction in the nation's heartland.”
““Heck, we already know it’s pretty epidemic down here,” Capt. Minor Allen of the Hazard Police Department in southeastern Kentucky told Times readers in 2001 (“Cancer Painkillers Pose New Abuse Threat” by Francis X. Clines with Barry Meier, Feb 9.) “Abuse of this drug has become unbelievable in the last year, with probably 85 to 90 percent of our field work now related to oxys,” he continued. “We find them carrying pill pushers that are sold in drugstores to help elderly people swallow their prescriptions.””
“Unfortunately, the Times placed far too much trust in the numbers being thrown out by law enforcement and legal sources — as did other news organizations, especially television, which covered Operation Oxyfest like children covering candy.”
“As the Washington Post’s television critic Tom Shales wrote in Electronic Media just a few weeks after OxyContin abuse dominated February sweeps (March 26, 2001),”
““there is no hard evidence that OxyContin played a key role in 59 Kentuckians keeling over. David Jones, an official with the Kentucky State Medical Examiner’s Office, looked into the claim and wrote a letter to Purdue Pharma: ‘I am unaware of any reliable data in Kentucky that proves OxyContin is causing a lot of deaths. In the State M.E. Office, we are seeing an increase in the number of deaths from ingesting several different prescription drugs and mixing them with alcohol. OxyContin is sometimes one of these drugs.’”
“For confirmation, the Free Times turned to David W. Jones, executive director of the Kentucky State Medical Examiner’s office. He asserts that ‘as far as deaths go, I’ve heard different numbers in different places at different times; I have no idea where these people are getting their facts and figures.’ While he stresses that not every drug-related death is necessarily reported to his office, according to his data there were 27 oxycodone-related deaths in the entire state in 2000…”
““…Two of the 27 victims, he explains were found to have both oxycodone and alcohol in their bodies, with death caused by the interaction of two nervous system depressants. What’s more, 23 others had a head-spinning multiplicity of other drugs in their systems, including highly potent prescription painkillers such as Diludad and Fentanyl, as well as powerful illegal drugs like cocaine and heroin. In the final analysis, Jones reveals, only two of the 27 fatalities can be shown to have been due to the effects of oxycodone alone – not just two in eastern Kentucky, two in the entire state.””
Saturday, June 24, 2006
Richard Feynman's Douglas Robb Memorial Lectures
Thanks to my friend Neal Hitzig for directing me to this link.
http://www.vega.org.uk/video/subseries/8
Here is some information from the website.
A set of four priceless archival recordings from the University of Auckland (New Zealand) of the outstanding Nobel prize-winning physicist Richard Feynman - arguably the greatest science lecturer ever. Although the recording is of modest technical quality the exceptional personal style and unique delivery shine through.
A gentle lead-in to the subject, Feynman starts by discussing photons and their properties.
http://www.vega.org.uk/video/programme/45
What are reflection and transmission, and how do they work?
http://www.vega.org.uk/video/programme/46
Feynman diagrams and the intricacies of particle interaction.
http://www.vega.org.uk/video/programme/47
What does it mean, and where is it all leading?
http://www.vega.org.uk/video/programme/48
http://www.vega.org.uk/video/subseries/8
Here is some information from the website.
A set of four priceless archival recordings from the University of Auckland (New Zealand) of the outstanding Nobel prize-winning physicist Richard Feynman - arguably the greatest science lecturer ever. Although the recording is of modest technical quality the exceptional personal style and unique delivery shine through.
A gentle lead-in to the subject, Feynman starts by discussing photons and their properties.
http://www.vega.org.uk/video/programme/45
What are reflection and transmission, and how do they work?
http://www.vega.org.uk/video/programme/46
Feynman diagrams and the intricacies of particle interaction.
http://www.vega.org.uk/video/programme/47
What does it mean, and where is it all leading?
http://www.vega.org.uk/video/programme/48
Friday, June 23, 2006
A Week At The Gym
This was sent to me by a longtime friend, retired, of course.
For my sixty fifth birthday this year, my wife (the dear) purchased a week of personal training at the local health club for me. Although I am still in great shape since playing on my college football team 45 years ago, Idecided it would be a good idea to go ahead and give it a try.
I called the club and made my reservations with a personal trainer named Belinda, who identified herself as a 26-year-old aerobics instructor and model for athletic clothing and swim wear. My wife seemed pleased with my enthusiasm to get started!
The club encouraged me to keep a diary to chart my progress . . .
Dear Diary:
MONDAY:
Started my day at 6:00 a.m.Tough to get out of bed, but found it was well worth it when I arrived atthe health club to find Belinda waiting for me.She is something of a Greek goddess - with blond hair, dancing eyes anddazzling white smile.
Woo Hoo!!
Belinda gave me a tour and showed me the machines. She took my pulse after five minutes on the treadmill. She was alarmed that my pulse was so fast, but I attribute it to standing next to her in her Lycra aerobic outfit.
I enjoyed watching the skillful way in which she conducted her aerobics class after my workout today. Very inspiring! Belinda was encouraging as I did my sit-ups, although my gut was already aching from holding it in the whole time she was around. This is going to bea FANTASTIC week!!
TUESDAY
I drank a whole pot of coffee, but I finally made it out the door.
Belinda made me lie on my back and push a heavy iron bar into the air when she put weights on it! My legs were a little wobbly on the treadmill, but I made the full mile. Belinda's rewarding smile made it all worthwhile. I feel GREAT!!
It's a whole new life for me.
WEDNESDAY
The only way I can brush my teeth is by laying on the toothbrush on the counter and moving my mouth back and forth over it. I believe I have a hernia in both pectorals. Driving was OK as long as I didn't try to steer or stop. I parked on top of a GEO in the club parking lot.
Belinda was impatient with me, insisting that my screams bothered other clubmembers. Her voice is a little too perky for early in the morning and when she scolds, she gets this nasal whine that is VERY annoying.
My chest hurt when I got on the treadmill, so Belinda put me on the stairmonster. Why the hell would anyone invent a machine to simulate an activity rendered obsolete by elevators? Belinda told me it would help me get in shape and enjoy life. She said some other shit too.
THURSDAY
Belinda was waiting for me with her vampire-like teeth exposed as her thin, cruel lips were pulled back in a full snarl. I couldn't help being a half an hour late, it took me that long to tie my shoes.
Belinda took me to work out with dumbbells. When she was not looking, I ran and hid in the men's room. She sent Lars to find me. Then, as punishment, she put me on the rowing machine -- which I sank.
FRIDAY
I hate that bitch Belinda more than any human being has ever hated any other human being in the history of the world. Stupid, skinny, anemic little cheerleader. If there was a part of my body I could move without unbearable pain, I wouldbeat her with it.
Belinda wanted me to work on my triceps. I don't have any triceps! And if you don't want dents in the floor, don't hand me the M----- f-----barbells or anything that weighs more than a sandwich.
The treadmill flung me off and I landed on a health and nutrition teacher. Why couldn't it have been someone softer, like the drama coach or the Choir director?
SATURDAY
Belinda left a message on my answering machine in her grating, shrilly voice wondering why I did not show up today. Just hearing her made me want to smash the machine with my planner. However, I lacked the strength to even use the TV remote and ended up catching eleven straight hours of the Weather Channel.
SUNDAY
I'm having the Church van pick me up for services today so I can go and thank GOD that this week is over. I will also pray that next year my wife (the bitch) will choose a gift for me that is fun -- like a root canal or a vasectomy.
For my sixty fifth birthday this year, my wife (the dear) purchased a week of personal training at the local health club for me. Although I am still in great shape since playing on my college football team 45 years ago, Idecided it would be a good idea to go ahead and give it a try.
I called the club and made my reservations with a personal trainer named Belinda, who identified herself as a 26-year-old aerobics instructor and model for athletic clothing and swim wear. My wife seemed pleased with my enthusiasm to get started!
The club encouraged me to keep a diary to chart my progress . . .
Dear Diary:
MONDAY:
Started my day at 6:00 a.m.Tough to get out of bed, but found it was well worth it when I arrived atthe health club to find Belinda waiting for me.She is something of a Greek goddess - with blond hair, dancing eyes anddazzling white smile.
Woo Hoo!!
Belinda gave me a tour and showed me the machines. She took my pulse after five minutes on the treadmill. She was alarmed that my pulse was so fast, but I attribute it to standing next to her in her Lycra aerobic outfit.
I enjoyed watching the skillful way in which she conducted her aerobics class after my workout today. Very inspiring! Belinda was encouraging as I did my sit-ups, although my gut was already aching from holding it in the whole time she was around. This is going to bea FANTASTIC week!!
TUESDAY
I drank a whole pot of coffee, but I finally made it out the door.
Belinda made me lie on my back and push a heavy iron bar into the air when she put weights on it! My legs were a little wobbly on the treadmill, but I made the full mile. Belinda's rewarding smile made it all worthwhile. I feel GREAT!!
It's a whole new life for me.
WEDNESDAY
The only way I can brush my teeth is by laying on the toothbrush on the counter and moving my mouth back and forth over it. I believe I have a hernia in both pectorals. Driving was OK as long as I didn't try to steer or stop. I parked on top of a GEO in the club parking lot.
Belinda was impatient with me, insisting that my screams bothered other clubmembers. Her voice is a little too perky for early in the morning and when she scolds, she gets this nasal whine that is VERY annoying.
My chest hurt when I got on the treadmill, so Belinda put me on the stairmonster. Why the hell would anyone invent a machine to simulate an activity rendered obsolete by elevators? Belinda told me it would help me get in shape and enjoy life. She said some other shit too.
THURSDAY
Belinda was waiting for me with her vampire-like teeth exposed as her thin, cruel lips were pulled back in a full snarl. I couldn't help being a half an hour late, it took me that long to tie my shoes.
Belinda took me to work out with dumbbells. When she was not looking, I ran and hid in the men's room. She sent Lars to find me. Then, as punishment, she put me on the rowing machine -- which I sank.
FRIDAY
I hate that bitch Belinda more than any human being has ever hated any other human being in the history of the world. Stupid, skinny, anemic little cheerleader. If there was a part of my body I could move without unbearable pain, I wouldbeat her with it.
Belinda wanted me to work on my triceps. I don't have any triceps! And if you don't want dents in the floor, don't hand me the M----- f-----barbells or anything that weighs more than a sandwich.
The treadmill flung me off and I landed on a health and nutrition teacher. Why couldn't it have been someone softer, like the drama coach or the Choir director?
SATURDAY
Belinda left a message on my answering machine in her grating, shrilly voice wondering why I did not show up today. Just hearing her made me want to smash the machine with my planner. However, I lacked the strength to even use the TV remote and ended up catching eleven straight hours of the Weather Channel.
SUNDAY
I'm having the Church van pick me up for services today so I can go and thank GOD that this week is over. I will also pray that next year my wife (the bitch) will choose a gift for me that is fun -- like a root canal or a vasectomy.
Saturday, June 17, 2006
Corn-ethanol for cars?
Here is another example of how Government meddling with the economy reduces the standard of living.
If two products or processes accomplish a job and one is cheaper, then replacing the cheaper one with the more expensive one reduces the standard of living.
According to the Wall Street Journal and others, Government’s subsidizing and/or forcing corn-ethanol use in cars increases the cost per mile of driving. It also increases oil demand, since it requires more than a gallon of oil to produce a gallon of corn-ethanol and the latter has less energy per gallon.
By increasing oil demand, it increases the price of oil and the price of all products that use oil in the production or delivery process.
Why is it so easy for Government to mess up the economy like this? Because too many voters either vote their own immediate interests (e.g., farmers) or fail to understand the issues.
The problem is not Government. The problem is us.
The Wall Street Journal’s editorial can be found here “An Energy Field of Dreams”.
Here are some excerpts.
“We'd say the world had gone mad, except that this is a fairly typical case study in how political meddling distorts energy markets. Weary of high gas prices, drivers can be forgiven for desiring a "miracle" fuel that is allegedly cheap and clean. But the corn farmers, ethanol producers, politicians and environmentalists who have promoted the new ethanol mania have no excuse for peddling misinformation.”
“We have nothing against corn-based ethanol per se, assuming it competes in the market on the same basis as other fuels. Ethanol's problem is that it is expensive to make and provides far fewer miles per gallon than gasoline. So its supporters have worked the political system to subsidize ethanol, and more recently to force Americans to buy it.”
“U.S. taxpayers today pay twice for ethanol: once in crop subsidies to corn farmers and again in a 51-cent subsidy for every gallon of ethanol. Without such a subsidy, ethanol simply wouldn't be cost competitive with gasoline. Then last year, Congress went further and passed a new ethanol mandate, requiring drivers to use at least 7.5 billion gallons annually by 2012.”
“Sorry. The most widely cited research on this subject comes from Cornell's David Pimental and Berkeley's Ted Patzek. They've found that it takes more than a gallon of fossil fuel to make one gallon of ethanol--29% more. That's because it takes enormous amounts of fossil-fuel energy to grow corn (using fertilizer and irrigation), to transport the crops and then to turn that corn into ethanol. The Saudis ought to love the stuff.”
If two products or processes accomplish a job and one is cheaper, then replacing the cheaper one with the more expensive one reduces the standard of living.
According to the Wall Street Journal and others, Government’s subsidizing and/or forcing corn-ethanol use in cars increases the cost per mile of driving. It also increases oil demand, since it requires more than a gallon of oil to produce a gallon of corn-ethanol and the latter has less energy per gallon.
By increasing oil demand, it increases the price of oil and the price of all products that use oil in the production or delivery process.
Why is it so easy for Government to mess up the economy like this? Because too many voters either vote their own immediate interests (e.g., farmers) or fail to understand the issues.
The problem is not Government. The problem is us.
The Wall Street Journal’s editorial can be found here “An Energy Field of Dreams”.
Here are some excerpts.
“We'd say the world had gone mad, except that this is a fairly typical case study in how political meddling distorts energy markets. Weary of high gas prices, drivers can be forgiven for desiring a "miracle" fuel that is allegedly cheap and clean. But the corn farmers, ethanol producers, politicians and environmentalists who have promoted the new ethanol mania have no excuse for peddling misinformation.”
“We have nothing against corn-based ethanol per se, assuming it competes in the market on the same basis as other fuels. Ethanol's problem is that it is expensive to make and provides far fewer miles per gallon than gasoline. So its supporters have worked the political system to subsidize ethanol, and more recently to force Americans to buy it.”
“U.S. taxpayers today pay twice for ethanol: once in crop subsidies to corn farmers and again in a 51-cent subsidy for every gallon of ethanol. Without such a subsidy, ethanol simply wouldn't be cost competitive with gasoline. Then last year, Congress went further and passed a new ethanol mandate, requiring drivers to use at least 7.5 billion gallons annually by 2012.”
“Sorry. The most widely cited research on this subject comes from Cornell's David Pimental and Berkeley's Ted Patzek. They've found that it takes more than a gallon of fossil fuel to make one gallon of ethanol--29% more. That's because it takes enormous amounts of fossil-fuel energy to grow corn (using fertilizer and irrigation), to transport the crops and then to turn that corn into ethanol. The Saudis ought to love the stuff.”
Thursday, June 15, 2006
Money flows into and out of the stock market
Does money flow into or out of the stock market (the secondary market)? Don’t dollars of stock purchased always equals dollars of stock sold? So, how can there be a net dollar flow into or out of the stock market?
Wednesday, June 14, 2006
Al Gore and Global Warming
My friend James Kitler, trained as an engineer sent me a website article that debunks Al Gore’s “The Inconvenient Truth”.
Here is an excerpt to convey the flavor.
“"Scientists have an independent obligation to respect and present the truth as they see it," Al Gore sensibly asserts in his film "An Inconvenient Truth", showing at Cumberland 4 Cinemas in Toronto since Jun 2. With that outlook in mind, what do world climate experts actually think about the science of his movie? "
“Professor Bob Carter of the Marine Geophysical Laboratory at James Cook University, in Australia gives what, for many Canadians, is a surprising assessment: "Gore's circumstantial arguments are so weak that they are pathetic. It is simply incredible that they, and his film, are commanding public attention."”
It goes on from there.
Stanford University has a Solar Center that has lots of good stuff on global warming. There is an interesting chart on the first page that suggests that climate is by far most correlated with solar activity. Looking at it makes you a skeptic with respect to Al Gore, although one chart is not a proof. On the other hand, having listened to Al Gore before, I have got to wonder how he could track down the truth even if he wanted to.
Looking down the links on Stanford University’s site, I found one quoting some researchers. Here are a couple of quotes.
“But the Earth is warming up, you say. Well, the evidence for that is very skimpy and not supported by an overwhelming quantity and quality of facts, as well as by the poor quality of surface temperature recordings.”
“Aside from the design- and human errors that may and do creep in when setting up instrumentation and taking readings, the readings are affected by the heat island effect generated in urban areas. The heat-island effect is substantial, measurable in communities of 250 or more residents, increasing over time as energy consumption and population density increase, and cannot be ignored. Determining accurate correction factors for individual areas in which temperature readings are taken in uncharacteristic hot-spots becomes difficult and even impossible if no corresponding records of readings exist for the surrounding rural areas, and as more and more weather stations in rural areas are being taken out of service.”
“However, for a number of years now, temperature measurements have been made via balloons and, in an even more thorough and comprehensive fashion, via satellites. The records established by those means show no or at worst only almost imperceptible global warming. Of course, those records are unbiased by human error and undistorted by the fact that temperature readings taken in urban areas are affected by the heat-island effects of the cities in which many are taken and that taint the results of global averaging of global temperature records.”
“What do they tell us about the highly-advertised claims of the world's climate alarmists relative to warming-induced droughts and floods?....”
“Climate alarmists claim that global warming will bring extremes of both floods and droughts to the world, and that the earth is now warmer than it has been in the entire past millennium. If these two claims were correct, we should clearly be seeing wet and dry periods that exceed the worst of the past half-millennium or more. In this extensive and well-calibrated record from the United States, however, we don't. Ergo, something is rotten in more than Denmark.”
“Curiously, and the Kyoto-hype advocates must surely be interested in that (or are they?), the record for the Sargasso Sea shows that the current sea-surface temperature is about half a degree Celsius below the average for the last 3000 years. Moreover, although the sea-surface temperature has recently increased somewhat but not quite reached the 3000-year average, it is rising in perfect synchronicity with the record of solar activity. It has done so before and will do so again.”
“Just as there were times in the past where it was much colder than it is now, so there were times when our globe was much warmer. The last period of a considerably warmer climate was during the Medieval Optimum, just before the Little Ice Age set in out of which we are climbing just now.”
“Superstitions, in spite of many voices of reason, brought about the witch hunts as the climate turned colder during the Little Ice Age. (See the paper by historian Wolfgang Behringer: Climatic Change and Witch-Hunting: The Impact of the Little Ice Age on Mentalities) Superstitions, in spite of many voices of reason, bring us now the witch hunts promoted by the proponents of the Kyoto accord. Such is the power of propaganda.”
There are lots more interesting links.
I am not a climate expert. But, being a Bayesian, I note that alarmists have seldom been right in the past and exhibit a characteristic behavior that does not instill confidence in me. So, my bet is that disaster is not imminent.
Even if global warming is an imminent problem, my preferred solution is fewer people. Smaller families, anyone?
Here is an excerpt to convey the flavor.
“"Scientists have an independent obligation to respect and present the truth as they see it," Al Gore sensibly asserts in his film "An Inconvenient Truth", showing at Cumberland 4 Cinemas in Toronto since Jun 2. With that outlook in mind, what do world climate experts actually think about the science of his movie? "
“Professor Bob Carter of the Marine Geophysical Laboratory at James Cook University, in Australia gives what, for many Canadians, is a surprising assessment: "Gore's circumstantial arguments are so weak that they are pathetic. It is simply incredible that they, and his film, are commanding public attention."”
It goes on from there.
Stanford University has a Solar Center that has lots of good stuff on global warming. There is an interesting chart on the first page that suggests that climate is by far most correlated with solar activity. Looking at it makes you a skeptic with respect to Al Gore, although one chart is not a proof. On the other hand, having listened to Al Gore before, I have got to wonder how he could track down the truth even if he wanted to.
Looking down the links on Stanford University’s site, I found one quoting some researchers. Here are a couple of quotes.
“But the Earth is warming up, you say. Well, the evidence for that is very skimpy and not supported by an overwhelming quantity and quality of facts, as well as by the poor quality of surface temperature recordings.”
“Aside from the design- and human errors that may and do creep in when setting up instrumentation and taking readings, the readings are affected by the heat island effect generated in urban areas. The heat-island effect is substantial, measurable in communities of 250 or more residents, increasing over time as energy consumption and population density increase, and cannot be ignored. Determining accurate correction factors for individual areas in which temperature readings are taken in uncharacteristic hot-spots becomes difficult and even impossible if no corresponding records of readings exist for the surrounding rural areas, and as more and more weather stations in rural areas are being taken out of service.”
“However, for a number of years now, temperature measurements have been made via balloons and, in an even more thorough and comprehensive fashion, via satellites. The records established by those means show no or at worst only almost imperceptible global warming. Of course, those records are unbiased by human error and undistorted by the fact that temperature readings taken in urban areas are affected by the heat-island effects of the cities in which many are taken and that taint the results of global averaging of global temperature records.”
“What do they tell us about the highly-advertised claims of the world's climate alarmists relative to warming-induced droughts and floods?....”
“Climate alarmists claim that global warming will bring extremes of both floods and droughts to the world, and that the earth is now warmer than it has been in the entire past millennium. If these two claims were correct, we should clearly be seeing wet and dry periods that exceed the worst of the past half-millennium or more. In this extensive and well-calibrated record from the United States, however, we don't. Ergo, something is rotten in more than Denmark.”
“Curiously, and the Kyoto-hype advocates must surely be interested in that (or are they?), the record for the Sargasso Sea shows that the current sea-surface temperature is about half a degree Celsius below the average for the last 3000 years. Moreover, although the sea-surface temperature has recently increased somewhat but not quite reached the 3000-year average, it is rising in perfect synchronicity with the record of solar activity. It has done so before and will do so again.”
“Just as there were times in the past where it was much colder than it is now, so there were times when our globe was much warmer. The last period of a considerably warmer climate was during the Medieval Optimum, just before the Little Ice Age set in out of which we are climbing just now.”
“Superstitions, in spite of many voices of reason, brought about the witch hunts as the climate turned colder during the Little Ice Age. (See the paper by historian Wolfgang Behringer: Climatic Change and Witch-Hunting: The Impact of the Little Ice Age on Mentalities) Superstitions, in spite of many voices of reason, bring us now the witch hunts promoted by the proponents of the Kyoto accord. Such is the power of propaganda.”
There are lots more interesting links.
I am not a climate expert. But, being a Bayesian, I note that alarmists have seldom been right in the past and exhibit a characteristic behavior that does not instill confidence in me. So, my bet is that disaster is not imminent.
Even if global warming is an imminent problem, my preferred solution is fewer people. Smaller families, anyone?
Tuesday, June 13, 2006
The New York Times Gives Me A Quick Laugh
Logging on to the NYT’s web site and the Sunday Magazine section, I noticed an article by Niall Ferguson (no relation). The website noted the title,
“Reason to Worry”,
along with the verbal bait
“Why you could be excused for feeling a little uneasy about the collapse in household savings, the rise in home-mortgage debt, a large and growing trade deficit and the fact that Asian countries hold so many U.S. treasuries. Go to Article”
I laughed because I am not worried about debt owed foreigners by the US. I figure if we owe somebody else something, as a country, they have to be careful of us, not the other way around.
Then I scanned the article. The writing is creative. How can you not appreciate this kind of language.
“Think of the economy of the United States as a dinosaur — one of those huge herbivores whose bulk shook the ground. A brachiosaur. A brontosaur. A diplodocus. Like them, the U.S. economy is mind-bogglingly enormous — two and a half times as big as the next largest economy in the world and almost as large as that of the six other members of the Group of Seven combined. The catch is that it has to consume almost incessantly to sustain its great heft.”
“Contrary to what we used to believe, leviathans like the diplodocus were not exactly sloths. It is now thought that they had the strength to stand on their hind legs in order to reach food at the top of trees. They may even have been able to run rather than merely plod. But it seems reasonable to assume that their reaction times were slow; it was a very long way from the diplodocus's tail to its brain. If a predator sank its fangs into that tail, it might have taken the diplodocus a few moments to feel the pain.”
“The big question about the dinosaurs is, of course, What caused their extinction? Why were so many species unable to evolve in response to environmental changes? The most common explanation is that a very sudden event, like a meteor's impact, gave the dinosaurs too little time to evolve and provided smaller and more dynamic life forms with an opportunity to take over.”
“An analogous question for economists is whether the United States is capable of evolving out of its present excessive indebtedness. Or could the global economic environment change so drastically as to threaten, if not extinction, then at least decline relative to smaller, more dynamic economies?”
No kidding, metaphor has become analysis.
Did I read right? “decline relative to smaller, more dynamic economies?” Isn’t that always going on? After all, if Microsoft goes up 1% and Widgets goes up 2%, then isn’t Microsoft declining relative to Widgets? A disaster in the making. Sheer genius.
At the bottom of the first page of the article, you see that Niall Ferguson is Laurence A. Tisch professor of history at Harvard University and the author of "Colossus: The Rise and Fall of the American Empire." Well, I guess that the American Empire will eventually fall. Probably the whole Universe, too, if I can believe Kaku. I’m just not so sure it’s as imminent as Prof. Ferguson makes out.
I continued scanning the article and found this nugget.
“As a result, there has been an immense rise in foreign ownership of American securities of all kinds, but especially government bonds. Foreign ownership of the U.S. federal debt passed the halfway mark in June 2004. About a third of corporate bonds are now in foreign hands, as is more than 13 percent of the U.S. stock market. One analyst has half-seriously calculated that at the current rate of foreign accumulation, the last U.S. Treasury held by an American will be purchased by the People's Bank of China on Feb. 9, 2012.”
Let’s see. Doesn’t this conclusion follow if the percentage of foreign owner ship of US debt increases, no matter by how little, and we forecast a continuation? Better yet, let’s do Prof. Ferguson one better and find, of all the possible period lengths ending with the most recent data, the period length with the biggest average daily increase in the percentage of foreign ownership of US debt. Let’s extend that. Maybe we can move doomsday a lot closer than 2012.
I am willing to bet Prof. Ferguson $1 million that on 1/1/2013, Some US debt will be owned by US citizens. Heck, I’ll even make it 12/31/2013.
I’m all for selling a lot more debt to the Chinese and using the proceeds to buy Chinese consumer goods. Of course, my strategy would be to default on the debt when the Chinese wise up. If third world countries are any guide, perhaps the UN would pay off our debt to the Chinese for us.
Next, I found this:
“So what's the catch? A sudden increase in the dollar price of American imports could stoke inflation in the United States. There is already some patchy evidence of an upturn in inflation. Whichever measure you use, prices are certainly rising at a faster rate now than they were two years ago, . . .”
Have you ever noticed that no matter which way an economic variable goes, someone says it is a disaster? From “patchy evidence” in either direction comes disaster. Actually, assuming prices are up faster more recently than two years ago, is this a statistically significant change? Does it make disaster really likely, sort of likely, or are we just seeing the normal random crud?
I sympathize with Ferguson’s concern over all the mortgage debt and that a lot of it is in ARMs. I think some of us are setting themselves up for hard times (there I go playing fortune teller). But, to tell you the truth, if this disaster happens, I expect to sit back and enjoy the fun. Nor do I think it will end the American Empire. I wonder. Would it be worse than the Great Depression? Now there was a real disaster, and look where we are now.
“Reason to Worry”,
along with the verbal bait
“Why you could be excused for feeling a little uneasy about the collapse in household savings, the rise in home-mortgage debt, a large and growing trade deficit and the fact that Asian countries hold so many U.S. treasuries. Go to Article”
I laughed because I am not worried about debt owed foreigners by the US. I figure if we owe somebody else something, as a country, they have to be careful of us, not the other way around.
Then I scanned the article. The writing is creative. How can you not appreciate this kind of language.
“Think of the economy of the United States as a dinosaur — one of those huge herbivores whose bulk shook the ground. A brachiosaur. A brontosaur. A diplodocus. Like them, the U.S. economy is mind-bogglingly enormous — two and a half times as big as the next largest economy in the world and almost as large as that of the six other members of the Group of Seven combined. The catch is that it has to consume almost incessantly to sustain its great heft.”
“Contrary to what we used to believe, leviathans like the diplodocus were not exactly sloths. It is now thought that they had the strength to stand on their hind legs in order to reach food at the top of trees. They may even have been able to run rather than merely plod. But it seems reasonable to assume that their reaction times were slow; it was a very long way from the diplodocus's tail to its brain. If a predator sank its fangs into that tail, it might have taken the diplodocus a few moments to feel the pain.”
“The big question about the dinosaurs is, of course, What caused their extinction? Why were so many species unable to evolve in response to environmental changes? The most common explanation is that a very sudden event, like a meteor's impact, gave the dinosaurs too little time to evolve and provided smaller and more dynamic life forms with an opportunity to take over.”
“An analogous question for economists is whether the United States is capable of evolving out of its present excessive indebtedness. Or could the global economic environment change so drastically as to threaten, if not extinction, then at least decline relative to smaller, more dynamic economies?”
No kidding, metaphor has become analysis.
Did I read right? “decline relative to smaller, more dynamic economies?” Isn’t that always going on? After all, if Microsoft goes up 1% and Widgets goes up 2%, then isn’t Microsoft declining relative to Widgets? A disaster in the making. Sheer genius.
At the bottom of the first page of the article, you see that Niall Ferguson is Laurence A. Tisch professor of history at Harvard University and the author of "Colossus: The Rise and Fall of the American Empire." Well, I guess that the American Empire will eventually fall. Probably the whole Universe, too, if I can believe Kaku. I’m just not so sure it’s as imminent as Prof. Ferguson makes out.
I continued scanning the article and found this nugget.
“As a result, there has been an immense rise in foreign ownership of American securities of all kinds, but especially government bonds. Foreign ownership of the U.S. federal debt passed the halfway mark in June 2004. About a third of corporate bonds are now in foreign hands, as is more than 13 percent of the U.S. stock market. One analyst has half-seriously calculated that at the current rate of foreign accumulation, the last U.S. Treasury held by an American will be purchased by the People's Bank of China on Feb. 9, 2012.”
Let’s see. Doesn’t this conclusion follow if the percentage of foreign owner ship of US debt increases, no matter by how little, and we forecast a continuation? Better yet, let’s do Prof. Ferguson one better and find, of all the possible period lengths ending with the most recent data, the period length with the biggest average daily increase in the percentage of foreign ownership of US debt. Let’s extend that. Maybe we can move doomsday a lot closer than 2012.
I am willing to bet Prof. Ferguson $1 million that on 1/1/2013, Some US debt will be owned by US citizens. Heck, I’ll even make it 12/31/2013.
I’m all for selling a lot more debt to the Chinese and using the proceeds to buy Chinese consumer goods. Of course, my strategy would be to default on the debt when the Chinese wise up. If third world countries are any guide, perhaps the UN would pay off our debt to the Chinese for us.
Next, I found this:
“So what's the catch? A sudden increase in the dollar price of American imports could stoke inflation in the United States. There is already some patchy evidence of an upturn in inflation. Whichever measure you use, prices are certainly rising at a faster rate now than they were two years ago, . . .”
Have you ever noticed that no matter which way an economic variable goes, someone says it is a disaster? From “patchy evidence” in either direction comes disaster. Actually, assuming prices are up faster more recently than two years ago, is this a statistically significant change? Does it make disaster really likely, sort of likely, or are we just seeing the normal random crud?
I sympathize with Ferguson’s concern over all the mortgage debt and that a lot of it is in ARMs. I think some of us are setting themselves up for hard times (there I go playing fortune teller). But, to tell you the truth, if this disaster happens, I expect to sit back and enjoy the fun. Nor do I think it will end the American Empire. I wonder. Would it be worse than the Great Depression? Now there was a real disaster, and look where we are now.
Sunday, June 11, 2006
Has the New York Times Ever Heard of Quality Control?
Byron Calame, the NYT’s Public Editor has a great piece on a NYT story about an alleged standing room “seat” to be put on the Airbus A380. The piece is “Landing on Page 1 With Hardly a Wary Eye”.
Here are some excerpts from Byron’s article describe the issue.
“As the old journalism platitude goes, "If your mother says she loves you, check it out." And when there's a story that's likely to make readers go "Wow!," it should be checked twice.”
“But such a story still made its way to The Times's front page last month while hardly meeting a skeptical eye — despite crossing the path of a passel of editors at all levels, including those who run the paper.”
“The Wow! in the April 25 story was a standing-room-only "seat" for airline passengers. An attention-grabbing illustration depicted a standing passenger leaning back against a nearly vertical board and held in place by restraints. The headline couldn't have been clearer: "One Day, That Economy Ticket May Buy You a Place to Stand." And the article explained that Airbus, the giant aircraft maker, "has been quietly pitching" the idea to Asian airlines.”
“It turns out this account was wrong. Airbus had abandoned the idea no later than 2004. There was no proof that the idea had been pitched to any Asian airlines.”
“The problems didn't stop there. Despite an immediate public denial by Airbus, the stand-up seat idea stood uncorrected for a week.”
Here is the telltale comment from Associate Managing Editor Chuck Strum.
“The news desk, where experienced editors do a final read of most Page 1 articles each night, had only "routine questions" about the article, said Chuck Strum, an associate managing editor. "The news desk treated this piece as a light feature," he said. "It was a thin piece and seemed harmless enough."”
“"In general," Mr. Strum said in defense of the news desk, "we don't assume that the various ... desks submit articles in which the central premise is wrong."”
In other words, Mr. Strum is admitting that there is no effective quality control at the NYT because the premises underlying quality control are not recognized by the NYT staff, right up to the top.
There is an old adage in the Quality Control fraternity, and it is accurate. When Quality Control reports to production, there is no quality control. The NYT is even worse. Byron Calame could be viewed as the NYT Quality Control Department. However, he doesn’t have any authority. In effect, the NYT’s Quality Control Department exists in a vacuum.
Not too surprising, considering the NYT’s accuracy.
Personally, I have never read an accurate NYT article on a topic I had first hand knowledge of.
Here are some excerpts from Byron’s article describe the issue.
“As the old journalism platitude goes, "If your mother says she loves you, check it out." And when there's a story that's likely to make readers go "Wow!," it should be checked twice.”
“But such a story still made its way to The Times's front page last month while hardly meeting a skeptical eye — despite crossing the path of a passel of editors at all levels, including those who run the paper.”
“The Wow! in the April 25 story was a standing-room-only "seat" for airline passengers. An attention-grabbing illustration depicted a standing passenger leaning back against a nearly vertical board and held in place by restraints. The headline couldn't have been clearer: "One Day, That Economy Ticket May Buy You a Place to Stand." And the article explained that Airbus, the giant aircraft maker, "has been quietly pitching" the idea to Asian airlines.”
“It turns out this account was wrong. Airbus had abandoned the idea no later than 2004. There was no proof that the idea had been pitched to any Asian airlines.”
“The problems didn't stop there. Despite an immediate public denial by Airbus, the stand-up seat idea stood uncorrected for a week.”
Here is the telltale comment from Associate Managing Editor Chuck Strum.
“The news desk, where experienced editors do a final read of most Page 1 articles each night, had only "routine questions" about the article, said Chuck Strum, an associate managing editor. "The news desk treated this piece as a light feature," he said. "It was a thin piece and seemed harmless enough."”
“"In general," Mr. Strum said in defense of the news desk, "we don't assume that the various ... desks submit articles in which the central premise is wrong."”
In other words, Mr. Strum is admitting that there is no effective quality control at the NYT because the premises underlying quality control are not recognized by the NYT staff, right up to the top.
There is an old adage in the Quality Control fraternity, and it is accurate. When Quality Control reports to production, there is no quality control. The NYT is even worse. Byron Calame could be viewed as the NYT Quality Control Department. However, he doesn’t have any authority. In effect, the NYT’s Quality Control Department exists in a vacuum.
Not too surprising, considering the NYT’s accuracy.
Personally, I have never read an accurate NYT article on a topic I had first hand knowledge of.
Saturday, June 10, 2006
The New York Times Statistical Intuition About Stocks Is Not Good
Jeff Sommer's recent article in the New York Times, "Fear of Inflation Prompts Big Losses in Stocks" makes a big deal about the recent one-week decline of 3.2% in the Dow Jones Industrials. But if you think about it, it is not particularly unusual.
Roughly, the DJI has a mean weekly return of about zero. Its annual standard deviation of return is about 15%, more or less. Assuming weekly returns are independent as an approximation, a 15% annual volatility corresponds to a 2.08% weekly volatility. A weekly return of -3.2% is only 1.54 standard deviations from the mean.
Assuming normality, the probability of a result 1.54 standard deviations below the mean or worse is 6.2%. This sounds pretty low, but Mr. Sommer did not pick this week at random. He scoured recent history for the worst week and found that it was the worst since about a year ago.
The real question is how likely is at least one weekly decline of at 3.2% or worse in a year.
Roughly this size negative return or worse should occur about three times a year (0.062*52=3.2). In fact, the probability that it would occur at least one week a year is about (1-(1-0.062)^52)=0.964, or about 96.4%.
Something that is expected to happen at least once a year with probability 96.4% is not unusual.
It is tempting to blame Mr. Somer for either incompetence or grand standing. However, we should remember that journalists and reporters are trained as journalists and reporters, and cannot be expected to understand useful things (note the grand standing :-)).
Roughly, the DJI has a mean weekly return of about zero. Its annual standard deviation of return is about 15%, more or less. Assuming weekly returns are independent as an approximation, a 15% annual volatility corresponds to a 2.08% weekly volatility. A weekly return of -3.2% is only 1.54 standard deviations from the mean.
Assuming normality, the probability of a result 1.54 standard deviations below the mean or worse is 6.2%. This sounds pretty low, but Mr. Sommer did not pick this week at random. He scoured recent history for the worst week and found that it was the worst since about a year ago.
The real question is how likely is at least one weekly decline of at 3.2% or worse in a year.
Roughly this size negative return or worse should occur about three times a year (0.062*52=3.2). In fact, the probability that it would occur at least one week a year is about (1-(1-0.062)^52)=0.964, or about 96.4%.
Something that is expected to happen at least once a year with probability 96.4% is not unusual.
It is tempting to blame Mr. Somer for either incompetence or grand standing. However, we should remember that journalists and reporters are trained as journalists and reporters, and cannot be expected to understand useful things (note the grand standing :-)).
Infinity Is Not What It Seems
I have always appreciated the power of mathematics but, unfortunately, am not very good at it. Of course, in life all you have to know to succeed is a few more pages in the math book than the next guy.
One thing that impressed me was the notion that there was more than one "infinity". Like most people, I understood infinity to be connected with the number of positive integers. But on various occassions, things seemed not so clear.
One problem is how to determine when two sets of things have the same number of elements (those of you who know math will have to excuse my loose language). The example I use is to think of two sets of things in two separate bags. Suppose I draw one item from one bag and match it to one item from the other bag and I never run out of things in one bag before I run out of things in the other bag. Well, I think that is a good way to define the number of things in the two bags as the same.
So, is the number of positive integers less than the number of positive and negative integers? The above rule for determining the answer shows that the number of positive integers is the same as the number of positive and negative integers. All you have to do is start counting the positive and negative integers using only the positive integers. The correspondence goes like this 1 goes with 1, 2 goes with -1, 3 goes with 2, 4 goes with -2, and so on. It is clear that the positive integers will never run out and every positive and negative integer will have a unique positive integer assigned to it. Yes, Virginia, twice the number of positive integers is the same as once the number of positive integers.
Oy.
It gets worse. Consider the points in the plane characterized by two integers, such as (3,5). Do the number of these points in the infinite plane exceed the number of positive integers? Not if we can count them systematically with the positive integers. And we can. Start at (0,1) on the x axis and go to (1,1), then (0,1), then to (-1,1), then to (-1,0), then to (-1,-1), then to (0,-1), then to (1,-1). We have used the positive integers from 1 to 8 to go in a "circle" around the origin. Next move outward to (0,2) and complete the next largest circle. Clearly we will never run out of the positive integers but will end up counting every pair of positive and negative integers.
We would ordinarily think of the number of pairs of positive and negative integers as infinity times infinity. But this exercise shows that our suspected infinity times infinity is just infinity.
So, if we define ordinary infinity as the number of positive integers, is that what we are stuck with. It seems not, because we can find a bag with so many elements that they cannot be counted with the positive integers. The example I am thinking of is the set of infinite decimals lying between 0 an 1 (inclusive).
The classic approach to showing that this set cannot be counted with the positive integers is to first assume that it has been counted and a two column table has been laid out with the positive integers in the first column and the corresponding infinite decimals in the second column. Next, consider the following infinite decimal. Its first digit differs from the first digit of the first infinite decimal. Its second digit differs from the second digit of the second inifinite decimal, and so on. clearly this is a new infinite decimal that nowhere appear in column two of our table. This contradicts the initial assumption that a correspondence between the positive integers and the infinite decimals between 0 and 1 had been achieved.
We ran out of positive integers before we ran out of infinte decimals between 0 and 1.
The number of infinite decimals exceeds the number of positive integers.
Oy, again.
Here are some links on the topic. Don't ask me to explain them.
http://en.wikipedia.org/wiki/Transfinite_number
http://mathworld.wolfram.com/TransfiniteNumber.html
http://mathworld.wolfram.com/Aleph-0.html
http://mathworld.wolfram.com/Aleph-0.html
One thing that impressed me was the notion that there was more than one "infinity". Like most people, I understood infinity to be connected with the number of positive integers. But on various occassions, things seemed not so clear.
One problem is how to determine when two sets of things have the same number of elements (those of you who know math will have to excuse my loose language). The example I use is to think of two sets of things in two separate bags. Suppose I draw one item from one bag and match it to one item from the other bag and I never run out of things in one bag before I run out of things in the other bag. Well, I think that is a good way to define the number of things in the two bags as the same.
So, is the number of positive integers less than the number of positive and negative integers? The above rule for determining the answer shows that the number of positive integers is the same as the number of positive and negative integers. All you have to do is start counting the positive and negative integers using only the positive integers. The correspondence goes like this 1 goes with 1, 2 goes with -1, 3 goes with 2, 4 goes with -2, and so on. It is clear that the positive integers will never run out and every positive and negative integer will have a unique positive integer assigned to it. Yes, Virginia, twice the number of positive integers is the same as once the number of positive integers.
Oy.
It gets worse. Consider the points in the plane characterized by two integers, such as (3,5). Do the number of these points in the infinite plane exceed the number of positive integers? Not if we can count them systematically with the positive integers. And we can. Start at (0,1) on the x axis and go to (1,1), then (0,1), then to (-1,1), then to (-1,0), then to (-1,-1), then to (0,-1), then to (1,-1). We have used the positive integers from 1 to 8 to go in a "circle" around the origin. Next move outward to (0,2) and complete the next largest circle. Clearly we will never run out of the positive integers but will end up counting every pair of positive and negative integers.
We would ordinarily think of the number of pairs of positive and negative integers as infinity times infinity. But this exercise shows that our suspected infinity times infinity is just infinity.
So, if we define ordinary infinity as the number of positive integers, is that what we are stuck with. It seems not, because we can find a bag with so many elements that they cannot be counted with the positive integers. The example I am thinking of is the set of infinite decimals lying between 0 an 1 (inclusive).
The classic approach to showing that this set cannot be counted with the positive integers is to first assume that it has been counted and a two column table has been laid out with the positive integers in the first column and the corresponding infinite decimals in the second column. Next, consider the following infinite decimal. Its first digit differs from the first digit of the first infinite decimal. Its second digit differs from the second digit of the second inifinite decimal, and so on. clearly this is a new infinite decimal that nowhere appear in column two of our table. This contradicts the initial assumption that a correspondence between the positive integers and the infinite decimals between 0 and 1 had been achieved.
We ran out of positive integers before we ran out of infinte decimals between 0 and 1.
The number of infinite decimals exceeds the number of positive integers.
Oy, again.
Here are some links on the topic. Don't ask me to explain them.
http://en.wikipedia.org/wiki/Transfinite_number
http://mathworld.wolfram.com/TransfiniteNumber.html
http://mathworld.wolfram.com/Aleph-0.html
http://mathworld.wolfram.com/Aleph-0.html
Free Will
What could free will mean?
If we know someone, doesn't that mean that we know something about their personality, i.e., how they are likely to behave in various circumstances? Doesn't that imply a degree of predictability? To the extent behavior is predictable, doesn't that mean that it follows rules? If so, doesn't having an identifiable personality imply some lack of free will?
If predictablity is the antithesis of free will, and what else could it be, wouldn't free will have to manifest itself by unpredictability?
If someone exhibited free will, wouldn't their behavior be random? Doesn't this imply behavior that is unrelated to circumstances? If so, free will would seem to imply remarkably unproductive behavior with no survival value.
Perhaps free will is an illusion.
That is not to say that conciousness is an illusion. Conciousness and free will are entirely different things.
If we know someone, doesn't that mean that we know something about their personality, i.e., how they are likely to behave in various circumstances? Doesn't that imply a degree of predictability? To the extent behavior is predictable, doesn't that mean that it follows rules? If so, doesn't having an identifiable personality imply some lack of free will?
If rational behavior is something to strive for, doesn't that imply predictability, hence a lack of free will?
If someone exhibited free will, wouldn't their behavior be random? Doesn't this imply behavior that is unrelated to circumstances? If so, free will would seem to imply remarkably unproductive behavior with no survival value.
Perhaps free will is an illusion.
That is not to say that conciousness is an illusion. Conciousness and free will are entirely different things.
Friday, June 09, 2006
An Apparent Paradox
In the previous post, I noted that a stock's long-term return is approximately its expected return less one-half its variance of return. This applies to portfolios, too.
Consider a stock market made up of stocks that all have the same expected return and the same variance of return. Then each stock has the same long-term return, approximately equal to its expected return less one-half its variance of return.
Now consider a portfolio of these stocks. The portfolio's expected return is the same as each stock's expected return. But, due to diversification, the portfolio's variance of return is less than each stock's variance of return. Consequently, the portfolio's long-term return exceeds that of the stocks.
Apparently, a portfolio's long-term return can be greater than the long-term returns of its stocks!
Consider a stock market made up of stocks that all have the same expected return and the same variance of return. Then each stock has the same long-term return, approximately equal to its expected return less one-half its variance of return.
Now consider a portfolio of these stocks. The portfolio's expected return is the same as each stock's expected return. But, due to diversification, the portfolio's variance of return is less than each stock's variance of return. Consequently, the portfolio's long-term return exceeds that of the stocks.
Apparently, a portfolio's long-term return can be greater than the long-term returns of its stocks!
Long-term return is not expected return
Most investment professionals are familiar with expected return and variance of return. Through the CFA program and in their MBA courses, they have learned about the mean-variance efficient frontier and the single period Capital Asset Pricing Model. But they haven't learned that long-term return is not expected return, and is usually considerably less.
Suppose that a stock has a 50/50 chance of going up by a factor of 1.5 or down by a factor of 0.9. Then the expected return is (0.5 x 1.5 + 0.5 x 0.9) - 1 = 0.20, or 20%. Most professional investors figure that this also is the stock's long-term return. But, here is the way to see that it is not.
Just as the percentage of tails in coin flipping approaches 50% over time, the percentage of the time the stock will go up approaches 50% over time. In other words, the typical two-period long-term result must be one up and one down. This implies that $1.00 invested in the stock will, in a typical two periods, either grow by a factor of 1.5 and then decline by a factor of 0.9 or decline by a factor of 0.9 and then grow by a factor of 1.5. Either way, the typical two-period terminal value of $1.00 is (1.2 x 0.9) = $1.35, which implies a per period long-term return of 16.2%. This is a less than 20% per period.
Just to make things interesting, consider what happens if the up factor is 2.0 and the down factor is 0.4. The expected return is still 20% per period. But now the typical two period terminal wealth of a $1.00 investment is (2.0x 0.4) = $0.8. Now the per period long-term return is -10.6%. This is a lot less than 20% per period.
Evidently, long-term return is always less than expected return and the difference is large to the extent the variance is large. In fact, long-term return is approximately expected return less one-half variance of return.
One reason why leveraged investments are so dangerous is because, ultimately, leverage increases variance of return a lot faster than it increases expected return.
Moral: Leverage and volatility are dangerous.
Suppose that a stock has a 50/50 chance of going up by a factor of 1.5 or down by a factor of 0.9. Then the expected return is (0.5 x 1.5 + 0.5 x 0.9) - 1 = 0.20, or 20%. Most professional investors figure that this also is the stock's long-term return. But, here is the way to see that it is not.
Just as the percentage of tails in coin flipping approaches 50% over time, the percentage of the time the stock will go up approaches 50% over time. In other words, the typical two-period long-term result must be one up and one down. This implies that $1.00 invested in the stock will, in a typical two periods, either grow by a factor of 1.5 and then decline by a factor of 0.9 or decline by a factor of 0.9 and then grow by a factor of 1.5. Either way, the typical two-period terminal value of $1.00 is (1.2 x 0.9) = $1.35, which implies a per period long-term return of 16.2%. This is a less than 20% per period.
Just to make things interesting, consider what happens if the up factor is 2.0 and the down factor is 0.4. The expected return is still 20% per period. But now the typical two period terminal wealth of a $1.00 investment is (2.0x 0.4) = $0.8. Now the per period long-term return is -10.6%. This is a lot less than 20% per period.
Evidently, long-term return is always less than expected return and the difference is large to the extent the variance is large. In fact, long-term return is approximately expected return less one-half variance of return.
One reason why leveraged investments are so dangerous is because, ultimately, leverage increases variance of return a lot faster than it increases expected return.
Moral: Leverage and volatility are dangerous.
Thinking About The Stock Market (written about 2000)
Well over one hundred years ago, Charles MacKay published a book titled "Extraordinary Popular Delusions and the Madness of Crowds and Confusion of Confusiones". The book is still being published, which attests to its insight. Even a casual reading should convince you that the current stock market will go down in history as one of the great bubbles. In case MacKay's treatise is not enough to convince you, here's more to think about.
The stock market has more than tripled in recent years. Sales and profits are up, but by nowhere near as much. Financial valuation ratios, such as price/book and price/earnings ratios have skyrocketed. For example, the S&P500 index's price/book and price/earnings ratios are about 5 and 30, respectively. Can this divergence from historical levels be justified?
According to the stock valuation theory taught in graduate business schools, a stock's value stems from its ability to throw off cash. In particular, a high price/book or price/earnings ratio is justified only to the extent that the company will be able to earn unusually high profits on its investments (abnormal profits).
Assume that the S&P500's risk is such that investors require a 10% expected return on their investment (If you want to use a higher number, the implications will be worse.). Suppose the index's return on equity is 10% and its growth rate is 0% annually. Then the theory says that the index should sell at a price/book ratio of 1.0 and a price/earnings ratio of 10.0. These two numbers are not far off the S&P500's long-term historical averages. They imply that the market should be selling for well under half its current price.
Leave the index's return on equity assumption at 10%. Posit a growth rate of 20% annually for the first ten years and then let its growth rate decline one percentage point per year until it reaches 5% in year 25. Thereafter, let the growth rate be 5% annually. Make no mistake, this is a wildly optimistic growth rate forecast. The index's fair price/book and price/earnings ratios still are only 1.0 and 10.0, respectively. Growth alone does not bestow value. Betcha that was a surprise.
Now, keep the optimistic growth forecast, but increase the forecast return on equity to 20% for the first ten years with a decline of one percentage point per year until it reaches 10% in year 20. Thereafter, let return on equity be 10%. Make no mistake, this is a wildly optimistic profitability forecast. Now, the index's fair price/book and price/earnings ratios are about 3.6 and 17.8, respectively. This illustrates that abnormal profitability is required to justify high valuation ratios. However, even this wildly optimistic forecast of growth and profitability implies a fair price for the S&P500 about 30% below its current level.
Let's apply this theory to the internet retail stocks, like Amazon.com.
Relatively cheap talent is available to set up and run web sites, and to handle operations, i.e., ordering and delivering merchandise, and inventory management. Thus, this industry has essentially no barrier to entry.
A low barrier to entry fosters competition. This has happened in the Internet store industry. Barnes and Noble was able to compete with Amazon.com in the Internet book business as soon as it made economic sense. Neither Internet store has been competitive in books for some time. Other, smaller, Internet book stores undercut them regularly.
The availability of shopping "bots" that locate the Internet stores selling the merchandise you want at the lowest price has created, for the first time, the economist's dream of the perfectly competitive market. A fundamental characteristic of a perfectly competitive market is the absence of abnormal profitability. Thus, it is unrealistic to think that the Amazon.coms of the world will ever be unusually profitable. If so, Internet retailers' current valuation ratios never will be justified.
Even if my analysis is right, it does not imply a market crash. Valuation ratios can decline because prices come down, earnings and book values rise, or a combination of the two. Personally, I'm hoping for a really big crash, because it's so exciting.
The stock market has more than tripled in recent years. Sales and profits are up, but by nowhere near as much. Financial valuation ratios, such as price/book and price/earnings ratios have skyrocketed. For example, the S&P500 index's price/book and price/earnings ratios are about 5 and 30, respectively. Can this divergence from historical levels be justified?
According to the stock valuation theory taught in graduate business schools, a stock's value stems from its ability to throw off cash. In particular, a high price/book or price/earnings ratio is justified only to the extent that the company will be able to earn unusually high profits on its investments (abnormal profits).
Assume that the S&P500's risk is such that investors require a 10% expected return on their investment (If you want to use a higher number, the implications will be worse.). Suppose the index's return on equity is 10% and its growth rate is 0% annually. Then the theory says that the index should sell at a price/book ratio of 1.0 and a price/earnings ratio of 10.0. These two numbers are not far off the S&P500's long-term historical averages. They imply that the market should be selling for well under half its current price.
Leave the index's return on equity assumption at 10%. Posit a growth rate of 20% annually for the first ten years and then let its growth rate decline one percentage point per year until it reaches 5% in year 25. Thereafter, let the growth rate be 5% annually. Make no mistake, this is a wildly optimistic growth rate forecast. The index's fair price/book and price/earnings ratios still are only 1.0 and 10.0, respectively. Growth alone does not bestow value. Betcha that was a surprise.
Now, keep the optimistic growth forecast, but increase the forecast return on equity to 20% for the first ten years with a decline of one percentage point per year until it reaches 10% in year 20. Thereafter, let return on equity be 10%. Make no mistake, this is a wildly optimistic profitability forecast. Now, the index's fair price/book and price/earnings ratios are about 3.6 and 17.8, respectively. This illustrates that abnormal profitability is required to justify high valuation ratios. However, even this wildly optimistic forecast of growth and profitability implies a fair price for the S&P500 about 30% below its current level.
Let's apply this theory to the internet retail stocks, like Amazon.com.
Relatively cheap talent is available to set up and run web sites, and to handle operations, i.e., ordering and delivering merchandise, and inventory management. Thus, this industry has essentially no barrier to entry.
A low barrier to entry fosters competition. This has happened in the Internet store industry. Barnes and Noble was able to compete with Amazon.com in the Internet book business as soon as it made economic sense. Neither Internet store has been competitive in books for some time. Other, smaller, Internet book stores undercut them regularly.
The availability of shopping "bots" that locate the Internet stores selling the merchandise you want at the lowest price has created, for the first time, the economist's dream of the perfectly competitive market. A fundamental characteristic of a perfectly competitive market is the absence of abnormal profitability. Thus, it is unrealistic to think that the Amazon.coms of the world will ever be unusually profitable. If so, Internet retailers' current valuation ratios never will be justified.
Even if my analysis is right, it does not imply a market crash. Valuation ratios can decline because prices come down, earnings and book values rise, or a combination of the two. Personally, I'm hoping for a really big crash, because it's so exciting.
Thursday, June 08, 2006
Delusions of Grandeur (written a while back)
Roughly speaking the stock market is ten times higher than it was not much more than ten years ago. It would seem that we are all a lot wealthier. In a sense we are. Each one of us can sell our stock and buy many things we could not afford before. However, we can't all do this. If a significant fraction of us tried to, our attempts to sell would drive the stock market down to where it started. Evidently, the recent stock market rise has not made us wealthier, as a group. We are simply suffering from delusions of grandeur.
Paper wealth is wealth only to the extent we can use it to buy things we like. But we can only buy things that exist. The stock market's rise has not been matched by a significant increase in the number of things that exist. There is not much more production equipment and plant. Neither is there much more of anything else that we like to have, such as cars and houses. Thus, the per capita number of things we like to have has not increased significantly. Indeed, things per capita can't change much over the short term, because it takes a lot of time to make a lot of things.
If things per capita can't increase significantly over the short term, it is plainly impossible to buy or hold significantly more things per capita over the short term. In other words, society as a whole is not wealthier just because the stock market goes up a lot over the short term, no matter how far it goes up.
If you need more convincing, consider the implications if the stock market were to rise so high that all of us were worth ten million dollars, on paper. This is enough for all of us to retire, if you believe that stock market wealth is real wealth. Suppose everybody did retire. Nobody would be working, so production would cease. Consequently, there would be nothing to consume, and consumption would cease. We would all be poor, no matter what we were worth on paper.
If a big stock market rise doesn't make us significantly wealthier, as a group, then a big stock market decline doesn't make us much poorer. So, when the crash comes, just don't read the paper, listen to the radio, or watch TV, and you'll be all right if you've avoided undue borrowing. This, of course, presumes that Government, various regulators and experts, and business leaders act sensibly. Hmm, maybe you should be a little concerned, after all. You never know what will go through these peoples' heads.
Is the stock market likely to crash, or at least have very disappointing performance? All it takes is the reverse of what made it go up so high. What was that? Simply investors' desire, on average, to have a little more of their portfolios allocated to stocks.
Consider an example. Suppose the financial market consists of $50 of cash and $50 of stock. Then total wealth is $100 and the average investor's equity allocation is 50%. Suppose the average investor decides that he wants an equity allocation of 60%. Then stocks must go up until they represent 60% of the total market. This means that stocks must rise from $50 to $75. The stock market rises 50%. This may make investors so optimistic about the stock market that they decide stocks should be 75% of their portfolios. This requires a stock market worth $150. Stocks are now up another 100%, for a total of 200% (You did catch that 50% plus 100% equals 200%, didn't you?).
At some point, investors' are satisfied with their stock allocation, and the stock market stops rising. Then, the average investor may decide the action is over. He may try to enjoy his newfound wealth, say by selling some of his stock to buy a bigger house. Put more precisely, the average investor may decide to reduce his equity allocation proportion to 60% from 75%. The stock market then drops, instantly, from $150 to $75, a decline of 50%. This happens before the average investor can sell his stock. He doesn't even get to buy his house.
Paper wealth is wealth only to the extent we can use it to buy things we like. But we can only buy things that exist. The stock market's rise has not been matched by a significant increase in the number of things that exist. There is not much more production equipment and plant. Neither is there much more of anything else that we like to have, such as cars and houses. Thus, the per capita number of things we like to have has not increased significantly. Indeed, things per capita can't change much over the short term, because it takes a lot of time to make a lot of things.
If things per capita can't increase significantly over the short term, it is plainly impossible to buy or hold significantly more things per capita over the short term. In other words, society as a whole is not wealthier just because the stock market goes up a lot over the short term, no matter how far it goes up.
If you need more convincing, consider the implications if the stock market were to rise so high that all of us were worth ten million dollars, on paper. This is enough for all of us to retire, if you believe that stock market wealth is real wealth. Suppose everybody did retire. Nobody would be working, so production would cease. Consequently, there would be nothing to consume, and consumption would cease. We would all be poor, no matter what we were worth on paper.
If a big stock market rise doesn't make us significantly wealthier, as a group, then a big stock market decline doesn't make us much poorer. So, when the crash comes, just don't read the paper, listen to the radio, or watch TV, and you'll be all right if you've avoided undue borrowing. This, of course, presumes that Government, various regulators and experts, and business leaders act sensibly. Hmm, maybe you should be a little concerned, after all. You never know what will go through these peoples' heads.
Is the stock market likely to crash, or at least have very disappointing performance? All it takes is the reverse of what made it go up so high. What was that? Simply investors' desire, on average, to have a little more of their portfolios allocated to stocks.
Consider an example. Suppose the financial market consists of $50 of cash and $50 of stock. Then total wealth is $100 and the average investor's equity allocation is 50%. Suppose the average investor decides that he wants an equity allocation of 60%. Then stocks must go up until they represent 60% of the total market. This means that stocks must rise from $50 to $75. The stock market rises 50%. This may make investors so optimistic about the stock market that they decide stocks should be 75% of their portfolios. This requires a stock market worth $150. Stocks are now up another 100%, for a total of 200% (You did catch that 50% plus 100% equals 200%, didn't you?).
At some point, investors' are satisfied with their stock allocation, and the stock market stops rising. Then, the average investor may decide the action is over. He may try to enjoy his newfound wealth, say by selling some of his stock to buy a bigger house. Put more precisely, the average investor may decide to reduce his equity allocation proportion to 60% from 75%. The stock market then drops, instantly, from $150 to $75, a decline of 50%. This happens before the average investor can sell his stock. He doesn't even get to buy his house.
Counting Ballots
One often hears that the one-person-one-vote principle must prevail. Presumably, the reason is that it is supposed to assure a final tally consistent with voters' choices.
The assumption implicit in the one-person-one-vote principle is that including more ballots in the count increases the accuracy of the final proportion of votes assigned to each candidate. This is true for one unbiased counting process. However, actual counting processes usually are biased even if they are impartial. Combining the results of two impartial counting processes having significantly different error rates can reduce accuracy relative to using only the results from the process with the lowest error rate. For example, reasonable assumptions imply that adding the results of a hand count of machine rejected ballots to the results of a machine count reduces accuracy.
In all likelihood, applying the one-person-one-vote rule rigidly will work against what it was designed to achieve.
What could the one-person-one-vote principle have been intended to achieve? Probably, a result that is consistent with voter's choices. If so, then the appropriate goal should be to count ballots only if doing so increases the accuracy of the final proportion of votes assigned to each candidate. Counting all ballots is not usually consistent with this goal.
Here is an example (albeit extreme) that proves the point. Suppose an election is held to choose one of two candidates and:
¨ 6,000,000 people vote.
¨ Machines count 5,999,000 of the ballots.
¨ People count 1,000 of the ballots.
¨ The proportion of the votes for each candidate is the same for the machine and people counted ballots.
¨ Machines make errors at the rate of one per trillion ballots.
¨ People make errors at the rate of one per two ballots.
For all practical purposes, the machine count will be completely accurate. The error in the counted proportion of the votes for each candidate is far less for the machine count taken alone than for a combined machine-people count. The people count just adds noise. It is best not to include the people count in the results.
The previous example overstates the accuracy of machines relative to people. The next example probably understates it. If so, the truth is more discouraging than portrayed.
¨ 450,000 people vote.
¨ Machines count 405,000 of the ballots.
¨ People count 45,000 of the ballots.
¨ The proportion of the votes for each candidate is the same for the machine and people counted ballots.
¨ Machines make errors at the rate of one in a thousand.
¨ People make errors at the rate of one in a hundred.
¨ The true vote is 65/35 for candidate A over candidate B.
The machine determined proportion of votes for each candidate has a typical error (root mean square error, for the techies) of 0.000608. The corresponding figure for the people count is 0.00607 (898% greater than for the machine count). The figure for the combined count is 0.00115 (89% greater than for the machine count alone).
An unbiased counting process is one where votes assigned in error are assigned to each candidate with a probability equal to his true proportion of the vote. For example, suppose Candidates A and B received 65% and 35% of the votes, respectively. Then when an unbiased counting process makes an error, the probabilities of Candidates A and B being assigned the vote are 65% and 35%, respectively.
Unbiased counting processes are desirable. However, for all practical purposes, they do not exist. For example, as shown below, an honest count generally is biased.
An impartial ballot counting process is one that is blind to the candidates. Counting errors occur at the same rate for each candidate and each candidate has an equal chance that the vote will be assigned to him.
According to this definition, a typical machine or honest person can be considered an impartial counter.
Impartial counting processes are feasible, at least approximately. However, as shown below, they are virtually always biased.
Any counting process assigns a proportion of the ballots to each candidate. Counting errors cause the assigned proportion to differ from the true proportions (the will of the voters). A counting process is unbiased if the expected error in the assigned proportions is zero. It is biased if the expected error in the assigned proportions is not zero. Bias is defined as the expected error in the assigned proportions.
Consider an impartial machine that is so poorly functioning that it errs on every ballot. Then it assigns about 50% of the ballots to candidate A and the other 50% to candidate B. There are four possible outcomes.
¨ A ballot marked for candidate A is assigned to candidate A.
¨ A ballot marked for candidate B is assigned to candidate B.
¨ A ballot marked for candidate A is assigned to candidate B.
¨ A ballot marked for candidate B is assigned to candidate A.
If each candidate truly has 50% of the votes, then these outcomes are equally likely. Consequently, the expected number of net votes received by candidate A due to machine error is 0, and the counting process is unbiased. Nevertheless, the likelihood that the true vote in any election will be perfectly equally divided among the candidates is essentially zero.
If candidate A truly has 100% of the votes, then these outcomes are not equally likely. The second and fourth outcomes are impossible. The first and third outcomes each occur about 50% of the time. Each candidate will be assigned about 50% of the votes. Candidate A, who received 100% of the true votes will tally about 50% of them. Candidate B, who received 0% of the true votes also will tally about 50% of them. The bias is 50% in favor of candidate B.
The second example illustrates a fundamental fact. To the extent an impartial machine makes mistakes, the expected result is bias in favor of the underdog. A person can be thought of as an unusually error prone machine. Thus, impartial hand counts are particularly biased when the true vote favors one candidate.
Other things equal, an impartial counting process's bias is large to the extent one candidate is favored over another. Thus, a recount of ballots already counted should, on average, show a net gain for the underdog if the recounting process has a higher error rate than the original counting process and both counting processes are impartial. Arguably, hand recounts of ballots already counted by machine that increase the winner's margin are evidence against impartiality.
To the extent that voters truly favor one candidate over another, it is likely that this kind of bias will overwhelm other sources of impartial counting error. In the second example, the bias in the machine count proportion is 0.000600 in favor of candidate B and that in the people count proportion is 0.00600 in favor of candidate B. The bias in the machine-person count is 0.001140, about 90% greater than for the machine count alone. All three bias figures are almost 100% of the corresponding total typical errors.
Impartial counting process errors tend to cluster around the bias. The error standard deviation is a measure of the typical difference between the proportionate error and the proportionate bias. In the second example, the error standard deviations for the machine count, person count, and machine-person count are 0.0000993, 0.000938, and 0.000130, respectively. The machine-person count figure is about 31% greater than for the machine count.
The total typical error due to both the bias and the clustering of errors around the bias is measured by the root-mean-square error, or RMS for short. This is the measure of counting process error used in the second example.
All impartial recounts simply replace one error series with another. This makes it possible to convert a loss to a win. Thus, the underdog benefits from any impartial recount, complete or partial. Impartial counting of representative ballots not previously counted also helps the underdog, for the same reason.
The higher the recounting process's error rate, the more the underdog is helped. Suppose the recounting process's error rate is higher than that for the original counting process. Then the bias in favor of the underdog is increased. The typical cumulative error also is increased. A recounting process with the highest feasible error rate maximizes the probability of a net gain for the underdog large enough to win. Replacing a machine count with a hand count is an example of this.
Think of the proportion of the ballots assigned to the underdog after a count as a stock price. Then the underdog's situation is akin to holding an out of the money call option that has just expired. This call option is worthless. An impartial recount will result in a new proportion for the underdog, either higher or lower. This change is like a stock price change. Allowing the recount is like extending the call option's life. It adds value. Allowing recounts is equivalent to forcing the candidate who is ahead to give a free call option to the underdog.
The proportion of all uncounted ballots representing votes for the underdog should be about the same as for the counted ballots. However, it is easy to find localities where uncounted ballots particularly favor the underdog. Counting only or predominantly these ballots introduces unusually large bias; hence is particularly likely to convert a loss to a win. This practice is equivalent to an error process that is not blind to the candidates, hence does not satisfy the criteria for impartiality.
The assumption implicit in the one-person-one-vote principle is that including more ballots in the count increases the accuracy of the final proportion of votes assigned to each candidate. This is true for one unbiased counting process. However, actual counting processes usually are biased even if they are impartial. Combining the results of two impartial counting processes having significantly different error rates can reduce accuracy relative to using only the results from the process with the lowest error rate. For example, reasonable assumptions imply that adding the results of a hand count of machine rejected ballots to the results of a machine count reduces accuracy.
In all likelihood, applying the one-person-one-vote rule rigidly will work against what it was designed to achieve.
What could the one-person-one-vote principle have been intended to achieve? Probably, a result that is consistent with voter's choices. If so, then the appropriate goal should be to count ballots only if doing so increases the accuracy of the final proportion of votes assigned to each candidate. Counting all ballots is not usually consistent with this goal.
Here is an example (albeit extreme) that proves the point. Suppose an election is held to choose one of two candidates and:
¨ 6,000,000 people vote.
¨ Machines count 5,999,000 of the ballots.
¨ People count 1,000 of the ballots.
¨ The proportion of the votes for each candidate is the same for the machine and people counted ballots.
¨ Machines make errors at the rate of one per trillion ballots.
¨ People make errors at the rate of one per two ballots.
For all practical purposes, the machine count will be completely accurate. The error in the counted proportion of the votes for each candidate is far less for the machine count taken alone than for a combined machine-people count. The people count just adds noise. It is best not to include the people count in the results.
The previous example overstates the accuracy of machines relative to people. The next example probably understates it. If so, the truth is more discouraging than portrayed.
¨ 450,000 people vote.
¨ Machines count 405,000 of the ballots.
¨ People count 45,000 of the ballots.
¨ The proportion of the votes for each candidate is the same for the machine and people counted ballots.
¨ Machines make errors at the rate of one in a thousand.
¨ People make errors at the rate of one in a hundred.
¨ The true vote is 65/35 for candidate A over candidate B.
The machine determined proportion of votes for each candidate has a typical error (root mean square error, for the techies) of 0.000608. The corresponding figure for the people count is 0.00607 (898% greater than for the machine count). The figure for the combined count is 0.00115 (89% greater than for the machine count alone).
An unbiased counting process is one where votes assigned in error are assigned to each candidate with a probability equal to his true proportion of the vote. For example, suppose Candidates A and B received 65% and 35% of the votes, respectively. Then when an unbiased counting process makes an error, the probabilities of Candidates A and B being assigned the vote are 65% and 35%, respectively.
Unbiased counting processes are desirable. However, for all practical purposes, they do not exist. For example, as shown below, an honest count generally is biased.
An impartial ballot counting process is one that is blind to the candidates. Counting errors occur at the same rate for each candidate and each candidate has an equal chance that the vote will be assigned to him.
According to this definition, a typical machine or honest person can be considered an impartial counter.
Impartial counting processes are feasible, at least approximately. However, as shown below, they are virtually always biased.
Any counting process assigns a proportion of the ballots to each candidate. Counting errors cause the assigned proportion to differ from the true proportions (the will of the voters). A counting process is unbiased if the expected error in the assigned proportions is zero. It is biased if the expected error in the assigned proportions is not zero. Bias is defined as the expected error in the assigned proportions.
Consider an impartial machine that is so poorly functioning that it errs on every ballot. Then it assigns about 50% of the ballots to candidate A and the other 50% to candidate B. There are four possible outcomes.
¨ A ballot marked for candidate A is assigned to candidate A.
¨ A ballot marked for candidate B is assigned to candidate B.
¨ A ballot marked for candidate A is assigned to candidate B.
¨ A ballot marked for candidate B is assigned to candidate A.
If each candidate truly has 50% of the votes, then these outcomes are equally likely. Consequently, the expected number of net votes received by candidate A due to machine error is 0, and the counting process is unbiased. Nevertheless, the likelihood that the true vote in any election will be perfectly equally divided among the candidates is essentially zero.
If candidate A truly has 100% of the votes, then these outcomes are not equally likely. The second and fourth outcomes are impossible. The first and third outcomes each occur about 50% of the time. Each candidate will be assigned about 50% of the votes. Candidate A, who received 100% of the true votes will tally about 50% of them. Candidate B, who received 0% of the true votes also will tally about 50% of them. The bias is 50% in favor of candidate B.
The second example illustrates a fundamental fact. To the extent an impartial machine makes mistakes, the expected result is bias in favor of the underdog. A person can be thought of as an unusually error prone machine. Thus, impartial hand counts are particularly biased when the true vote favors one candidate.
Other things equal, an impartial counting process's bias is large to the extent one candidate is favored over another. Thus, a recount of ballots already counted should, on average, show a net gain for the underdog if the recounting process has a higher error rate than the original counting process and both counting processes are impartial. Arguably, hand recounts of ballots already counted by machine that increase the winner's margin are evidence against impartiality.
To the extent that voters truly favor one candidate over another, it is likely that this kind of bias will overwhelm other sources of impartial counting error. In the second example, the bias in the machine count proportion is 0.000600 in favor of candidate B and that in the people count proportion is 0.00600 in favor of candidate B. The bias in the machine-person count is 0.001140, about 90% greater than for the machine count alone. All three bias figures are almost 100% of the corresponding total typical errors.
Impartial counting process errors tend to cluster around the bias. The error standard deviation is a measure of the typical difference between the proportionate error and the proportionate bias. In the second example, the error standard deviations for the machine count, person count, and machine-person count are 0.0000993, 0.000938, and 0.000130, respectively. The machine-person count figure is about 31% greater than for the machine count.
The total typical error due to both the bias and the clustering of errors around the bias is measured by the root-mean-square error, or RMS for short. This is the measure of counting process error used in the second example.
All impartial recounts simply replace one error series with another. This makes it possible to convert a loss to a win. Thus, the underdog benefits from any impartial recount, complete or partial. Impartial counting of representative ballots not previously counted also helps the underdog, for the same reason.
The higher the recounting process's error rate, the more the underdog is helped. Suppose the recounting process's error rate is higher than that for the original counting process. Then the bias in favor of the underdog is increased. The typical cumulative error also is increased. A recounting process with the highest feasible error rate maximizes the probability of a net gain for the underdog large enough to win. Replacing a machine count with a hand count is an example of this.
Think of the proportion of the ballots assigned to the underdog after a count as a stock price. Then the underdog's situation is akin to holding an out of the money call option that has just expired. This call option is worthless. An impartial recount will result in a new proportion for the underdog, either higher or lower. This change is like a stock price change. Allowing the recount is like extending the call option's life. It adds value. Allowing recounts is equivalent to forcing the candidate who is ahead to give a free call option to the underdog.
The proportion of all uncounted ballots representing votes for the underdog should be about the same as for the counted ballots. However, it is easy to find localities where uncounted ballots particularly favor the underdog. Counting only or predominantly these ballots introduces unusually large bias; hence is particularly likely to convert a loss to a win. This practice is equivalent to an error process that is not blind to the candidates, hence does not satisfy the criteria for impartiality.
Just Wondering
Is a big US trade deficit really bad? Are foreign workers willing to work for low wages really unfairly stealing away US jobs?
Doesn’t a US trade deficit imply that we are buying more foreign goods than foreigners are buying US goods? Why is it a bad thing when foreigners are sending us more valuable stuff than we are sending them? It sounds like a good deal for us.
Wouldn't it be even better if we didn't have to send foreigners anything in return for their goods? That would mean that we were getting their goods for free. It would also make our trade deficit bigger.
If foreigners decide to exchange their dollars for US goods, doesn’t that reduce our trade deficit by making us work for them?
Are foreign workers who receive low wages being taken advantage of? Is it immoral to buy goods made with cheap foreign labor? What if foreign workers are better off with these jobs than without them?
It must be that foreign workers are better off with jobs exported from the US. Otherwise, they wouldn’t take them. Does fairness to foreign workers require not providing them with jobs that they want and that make them better off?
Is such outsourcing really unfair, even if some displaced US workers end up with lower paying jobs? Suppose these US workers, perhaps through political pressure, have been preventing firms from using cheaper foreign labor. Isn’t the fair value of their labor what foreign workers charge? In this case, aren’t domestic workers forcing US consumers to pay more than fair value for their labor and for the goods produced with it? Isn’t this coercion and theft? Isn’t it disingenuous to argue that fairness requires that coercion and theft be allowed to continue? Doesn’t fairness require that those who steal return to their victims what was stolen and that those who would steal be prevented from doing so?
Doesn’t a US trade deficit imply that we are buying more foreign goods than foreigners are buying US goods? Why is it a bad thing when foreigners are sending us more valuable stuff than we are sending them? It sounds like a good deal for us.
Wouldn't it be even better if we didn't have to send foreigners anything in return for their goods? That would mean that we were getting their goods for free. It would also make our trade deficit bigger.
If foreigners decide to exchange their dollars for US goods, doesn’t that reduce our trade deficit by making us work for them?
Are foreign workers who receive low wages being taken advantage of? Is it immoral to buy goods made with cheap foreign labor? What if foreign workers are better off with these jobs than without them?
It must be that foreign workers are better off with jobs exported from the US. Otherwise, they wouldn’t take them. Does fairness to foreign workers require not providing them with jobs that they want and that make them better off?
Is such outsourcing really unfair, even if some displaced US workers end up with lower paying jobs? Suppose these US workers, perhaps through political pressure, have been preventing firms from using cheaper foreign labor. Isn’t the fair value of their labor what foreign workers charge? In this case, aren’t domestic workers forcing US consumers to pay more than fair value for their labor and for the goods produced with it? Isn’t this coercion and theft? Isn’t it disingenuous to argue that fairness requires that coercion and theft be allowed to continue? Doesn’t fairness require that those who steal return to their victims what was stolen and that those who would steal be prevented from doing so?
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