On the Indecisiveness of Kelly-Strategyproof Social Choice Functions

Social choice functions (SCFs) map the preferences of a group agents over some set alternatives to non-empty subset alternatives. The Gibbard-Satterthwaite theorem has shown that only extremely restrictive SCFs are strategyproof when there more than two For set-valued SCFs, or so-called social correspondences, situation is less clear. There miscellaneous -- mostly negative results using variety strategyproofness notions and additional requirements. simple intuitive notion Kelly-strategyproofness turned out be particularly compelling because it weak enough still allow for positive results. example, Pareto rule even weak, number attractive (such as top cycle, uncovered set, essential set) strict preferences. In this paper, we show that, preferences, indecisive can satisfy strategyproofness. particular, (i) every rank-based SCF violates Pareto-optimality, (ii) support-based (which generalize Fishburn's C2 SCFs) satisfies Pareto-optimality returns at least one most preferred alternative voter, (iii) non-imposing Condorcet loser in profile. We also discuss consequences these randomized choice.