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.
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