Bracketology

In general, I dislike the idea of making predictions about the future. After all, the future is uncertain, and if you are ever asked to make any kind of prediction you should always just pick the most likely outcome. Usually, making predictions in this sense is not a very interesting process, since people often agree on what the most likely outcome is. Who is most likely to win the World Series next year? Anyone who is knowledgable about baseball would say the Yankees. However, people like to make predictions that other teams will win the World Series- some people might pick, say, the Mets. Why? Usually not because they actually believe the Mets are more likely to win than the Yankees, but because they want to make the statement that they think other people are underrating the Mets. What they really mean by picking the Mets is something like, "most people think the Mets have a 2% chance of winning the World Series, but I think it's more like 10%." Which is a substantive and potentially interesting thing to say, so why not just say that? Because even if the Mets do win the World Series, it's not like it was inevitable, so it really doesn't even validate their opinion.

Which brings me to the topic of filling out NCAA tournament brackets. Is filling out your bracket in the office pool a similarly meaningless exercise in which you should just pick all the higher seeds to win? Actually, no- not in the same way. The reason is, that you're not trying to maximize your chance of picking the correct bracket, you're trying to maximize your chances of beating everyone else in your pool. And that can lead to very different reasoning.

For the sake of argument, say you're in a pool with 1,000,000 other people, and everyone agrees that Kansas is the favorite and has a 15% chance of winning, while Kentucky is the second favorite and has a 14% chance of winning. What if the other 999,999 people in the pool pick Kansas to go all the way? Even if you agree that Kansas is the favorite, it's not going to make sense to pick Kansas and then hope that you'll beat everyone else and be one in a million on the strength of your other picks. Rather, you should pick Kentucky, and if they make good on that 14% chance you'll be in good shape to win your pool.

What I'm curious about is, I can't think of any other area in life where this kind of reasoning applies. When else is it the case that maximizing the expected value of the decisionmaker's outcome would lead to one decision, but maximizing the probability that the value of the decisionmaker's outcome exceeds some finite group of competitors leads to a different decision, and the latter is in fact what really is the decisionmaker's goal?