Gibbard and Satterthwaite have shown that the only single-valued social choice functions (SCFs) that satisfy non-imposition (i.e., the function's range coincides with its codomain) and strategyproofness (i.e., voters are never better off by misrepresenting their preferences) are dictatorships. In this paper, we consider set-valued social choice correspondences (SCCs) that are strategyproof according to Fishburn's preference extension and, in particular, the top cycle, an attractive SCC that returns the maximal elements of the transitive closure of the weak majority relation. Our main theorem implies that, under mild conditions, the top cycle is the only non-imposing strategyproof SCC whose outcome only depends on the quantified pairwise comparisons between alternatives. This result effectively turns the Gibbard-Satterthwaite impossibility into a complete characterization of the top cycle by moving from SCFs to SCCs. It is obtained as a corollary of a more general characterization of strategyproof SCCs.
翻译:Gibbard 和 Satterthwaite 已经表明,唯一一个符合不刺激的单一价值社会选择功能(即该功能的范围与其共同域相吻合)和战略防护性(即选民通过歪曲其偏好而永远得不到更好的选择)是专制的。在本文中,我们认为,根据Fishburn的优惠扩展,特别是顶级周期,具有战略防护性的定值社会选择通信(SCC)具有战略防护性,具有吸引力的SCC,它返回了弱多数关系过渡性关闭的最大要素。我们的主要理论是,在温和的条件下,顶级周期是唯一一个非强制性战略防护SCC,其结果仅取决于替代品之间量化的对等比较。结果有效地将Gibbard-Setthwaite不可能性转化为从SFC转移到SCC对顶级周期的完整定性。它是对战略防护性SC的更一般性定性的必然结果。