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badger comments on Open thread, Mar. 9 - Mar. 15, 2015 - Less Wrong Discussion
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Comments (109)
From the Even Odds thread:
Assume there are n people. Let S_i be person i's score for the event that occurs according to your favorite proper scoring rule. Then let the total payment to person i be
(i.e. the person's score minus the average score of everyone else). If there are two people, this is just the difference in scores. The person makes a profit if T_i is positive and a payment if T_i is negative.
This scheme is always strategyproof and budget-balanced. If the Bregman divergence associated with the scoring rule is symmetric (like it is with the quadratic scoring rule), then each person expects the same profit before the question is resolved.