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已证明，满足非强加性（即函数的定义域与值域一致）和策略防护性（即选民永远不会因谎报偏好而获益）的唯一单值社会选择函数（SCF）是独裁函数。本文考虑基于Fishburn偏好拓展的集值社会选择对应（SCC），并特别关注顶层循环——这一具有吸引力的SCC通过弱多数关系的传递闭包返回最大元素。我们的主定理表明：在温和条件下，顶层循环是唯一非强加的策略防护性SCC，且其输出仅依赖于备选方案间的量化两两比较。这一结果通过从SCF转向SCC，将Gibbard-Satterthwaite不可能性转化为对顶层循环的完整刻画。该结论作为更一般的策略防护性SCC刻画定理的推论而获得。