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AlexMennen comments on Harsanyi's Social Aggregation Theorem and what it means for CEV - Less Wrong Discussion

21 Post author: AlexMennen 05 January 2013 09:38PM

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Comment author: AlexMennen 07 January 2013 11:23:47PM *  3 points [-]

Lets say there are 3 possible outcomes: A, B, and C, and 2 agents: x and y. The utility functions are x(A)=0, x(B)=1, x(C)=4, y(A)=4, y(B)=1, y(C)=0.

One possible prior probability distribution over pairs of gambles is that there is a 50% chance that the aggregation will be asked to choose between A and B, and a 50% chance that the aggregation will be asked to choose between B and C (in this simplified case, all the anticipated "gambles" are actually certain outcomes). Your maximin aggregation would choose B in each case, so both agents anticipate an expected utility of 1. But the aggregation that maximizes the sum of each utility function would choose A in the first case and C in the second, and each agent would anticipate an expected utility of 2. Since both agents could agree that this aggregation is better than maximin, maximin is not Pareto optimal with respect to that probability distribution.

Upvoted for suggesting a good example. I had suspected my explanation might be confusing, and I should have thought to include an example.

Comment author: Kindly 08 January 2013 12:07:34AM 0 points [-]

Thank you, I understand it now.