Thread by @breakingthemark

If everyone is society optimized for arithmetic return, or linear utility, then society would grow wonderfully at first. Society's geometric return would be high. Some people would win big, some would lose big, and the average would be good because many are involved.

Through time though, many people would get unlucky by losing a few times in row and would fall out of contributing because they don’t have much capital/resources/access any longer to help. So now the number of contributors to society’s growth is smaller.

If people keep basing decisions on linear utility, with fewer and fewer winners each round and more and more losers, a funny thing starts to happen. Probability says society stops growing as more people fall out of the game, leaving fewer people capable of creating growth.

After long enough of everyone using “linear utility” society will start to shrink. It will wither away due to a low geo return.

If everyone sizes their bets at the Kelly level though, society grows as a whole at its fastest rate possible (without any transfer payments).

Forever

Now this example is not dissimilar to what would happen on a financial market if every person based their bets on linear utility. At first it would be great. Some unlucky customers would lose a lot, others win more. Soon there’s less people and dollars bidding on the assets

Geometric returns turn negative, and prices fall as only a few people have any capital to play any longer. But if the participants in the market made their bets at Kelly, prices would grow forever, as would most of the investor’s wealth.

Linear utility, aka making decisions on the “expected value” (arithmetic average), is dangerous for an individual and society.

I wish economists would acknowledge it was a huge mistake to have compared rationality to it or evaluated behavior against it in the first place.