Three essays on social choice theory

Abstract

This thesis consists of three essays on social choice theory. In the first essay, we study implementation via two-stage rights structures, introduced by Yildiz (2013) as a multi-stage version of the rights structure framework of Koray and Yildiz (2018). While Yildiz established the implementability of the Nash bargaining solution, we consider the two-stage rights structure in the standard environment with a finite set of alternatives and linear order profiles. We identify necessary conditions for implementable social choice rules and provide a sufficient condition, contributing to a characterization of implementation via two-stage rights structures. In the second essay, we revisit the notion of selection-closedness introduced by Koray and Senocak (2024) within the tops-only domain of social choice functions. We show that a subset of neutral functions on this domain is selection-closed if and only if all its members are self-selective. We propose two weakenings of selection-closedness: one corrects Senocak’s (2009) results on scoring correspondences, while the other yields a partial characterization of correspondences whose singleton-valued refinements form a weakly selection-closed family. In the third essay, we study ordinal interdependent preferences and the problem of implementing a social choice correspondence in dominant-strategy equilibrium. We identify a monotonicity condition that is necessary and, in rich domains, sufficient for implementation. We characterize interdependence structures under which a counterpart of the Gibbard–Satterthwaite theorem holds. When interdependence is “weak,” we show that dictatorship is the only dominant-strategy incentive compatible rule; when it is not, even dictatorship fails to be implementable. These results complement the robust mechanism design literature, which focuses on ex-post incentive compatibility, by highlighting the restrictiveness of dominant-strategy incentive compatibility.