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Vaniver comments on Risk aversion vs. concave utility function - Less Wrong
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Comments (33)
Then you have a contradiction in terms, because you shouldn't have a strict preference for outcomes with the same number of utilons.
The sqrt(paperclips) agent should be indifferent between 16 paperclips and {.5: 9; .5: 25} paperclips. It has a strict preference for 16.5 paperclips to either 16 paperclips or {.5: 9; .5: 25} paperclips.
Savage's 4th axiom- the strict preference- says that in order for you to strictly prefer 16.5 paperclips to 16 paperclips, there has to be a difference in the utilon values. There is- 16.5 paperclips represents 4.06 utilons vs. only 4 for 16 paperclips.
By the 4th axiom, we can construct other bets: say, {.5: 9.4; .5; 25.4}. The agent strictly prefers 16.5 paperclips to that deal (which has 4.05 utilons).
Upvoted. In my opinion, the literature on risk-averse agents is logically consistent, and being risk-averse does not imply irrationality. I agree with Vaniver's comments. Also, humans are, on average*, risk averse.
*For example, with respect to markets, 'market clearing' average in a Walrasian auction sense.