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Manfred comments on Strategyproof Mechanisms: Possibilities - LessWrong
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Poor Cato.
Cato swapping with Brutus produces the same absolute gains as Antonius swapping with Brutus - is there a strategyproof mechanism that goes that way instead?
How about "a soldier can signal that they don't have the job they want. Then, the people who want to change jobs are ordered into a random loop, and jobs are rotated one place."
Hm, but if Antonius doesn't want his job either, we could end up with a bad outcome. Is Cato really hosed?
It turns out the only Pareto efficient, individually rational (ie everyone never gets something worse than their initial job), and strategyproof mechanism is Top Trading Cycles. In order to make Cato better off, we'd have to violate one of those in some way.