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I agree that expected value (EV) is not necessarily a good metric for personal financial decisions. In fact, this applies both to EVs greater than and less than
by xenocyon 6y ago
I agree that expected value (EV) is not necessarily a good metric for personal financial decisions. In fact, this applies both to EVs greater than and less than 1.
As you point out, insurance is a good example of a <1 EV; its purpose is to reduce volatility.
Another example: lottery tickets in the occasional case where the EV>1. This is supposed to, for instance, lead a rational economist to buy a lottery ticket (or many lottery tickets!) when the Powerball jackpot hits some particular threshold, say 500 million. However, money isn't linear in terms of value to individuals, and for most people the difference in life impact between winning a billion dollars vs 500 million is not anywhere close to 2x - indeed the two outcomes are more or less effectively identical.
tl;dr: because money is not linear in the value it adds, EV is not a good optimization metric for highly skewed outcomes.
- kqr 6y agoHowever, if you compute EV as the geometric mean of outcomes, instead of the arithmetic mean, it works again. (This is mathematically equivalent to the log utility you allude to.) This is the right way to think of repeated bets (rather than in isolation) and Bernoulli's 1734 paper on it is a very readable intro to thinking in terms of the Kelly criterion.