Strategyproof social choice when preferences and outcomes may contain ties

• 成果类型: Article
• 署名作者: Brandt, Felix; Saile, Christian; Stricker, Christian
• 署名单位: Technical University of Munich
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2022.105447
• 发表日期: 2022
• 关键词: Gibbard-Satterthwaite theorem; Social choice theory; strategyproofness; Pareto optimality

摘要

The Gibbard-Satterthwaite theorem implies that all anonymous, Pareto-optimal, and single-valued social choice functions can be strategically manipulated. In this paper, we investigate whether there exist social choice correspondences (SCCs), that satisfy these conditions under various assumptions about how single alternatives are eventually selected from the choice set. These assumptions include even-chance lotteries as well as resolute choice functions and linear tie-breaking orderings unknown to the agents. We show that (i) all anonymous Pareto-optimal SCCs where ties are broken according to some linear tie-breaking ordering or by means of even-chance lotteries are manipulable, and that (ii) all pairwise Pareto-optimal SCCs are manipulable for any deterministic tie-breaking rule. These results are proved by reducing the statements to finite-yet very large-formulas in propositional logic, which are then shown to be unsatisfiable by a computer. (c) 2022 Elsevier Inc. All rights reserved.