This [The ergodicity problem in economics] seems like it could be important, and might fit in somewhere with the discussions of expected utility. I haven’t really got my head around it though.
Starting with $100, your bankroll increases 50% every time you flip heads. But if the coin lands on tails, you lose 40% of your total. Since you’re just as likely to flip heads as tails, it would appear that you should, on average, come out ahead if you played enough times because your potential payoff each time is greater than your potential loss. In economics jargon, the expected utility is positive, so one might assume that taking the bet is a no-brainer.
Yet in real life, people routinely decline the bet. Paradoxes like these are often used to highlight irrationality or human bias in decision making. But to Peters, it’s simply because people understand it’s a bad deal.
Here’s why. Suppose in the same game, heads came up half the time. Instead of getting fatter, your $100 bankroll would actually be down to $59 after 10 coin flips. It doesn’t matter whether you land on heads the first five times, the last five times or any other combination in between.
This [The ergodicity problem in economics] seems like it could be important, and might fit in somewhere with the discussions of expected utility. I haven’t really got my head around it though.