One seminal question in social choice theory was: is it possible to find a social choice function such that each agent is always better off when telling the truth concerning his preferences no matter what the others report? In other words, can we find a strategy-proof voting rule? With at least three alternatives and two voters, the answer is clearly no under a very general framework, as was proved independently by Allan Gibbard and Mark Satterthwaite. Since then, the Gibbard-Satterthwaite theorem is at the core of social choice theory, game theory, and mechanism design.
Since K. Arrow’s 1951 analysis, which marks the revival of the theory of social choice, economists investigate from an axiomatic point of view the aggregation of individual preferences in order to obtain a social welfare function (i.e., a complete and transitive ranking based on the individual preferences) or a social choice function (i.e., one alternative from the individual preferences). Such...
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