We analyze the relation between strategy-proofness and preference reversal in the case that agents may declare indifference. Interestingly, Berga and Moreno (2020), have recently derived preference reversal from group strategy-proofness of social choice functions on strict preferences domains if the range has no more than three elements. We extend this result and at the same time simplify it. Our analysis points out the role of individual strategy-proofness in deriving the preference reversal property, giving back to the latter its original individual nature (cfr. Eliaz, 2004).
Moreover, we show that the difficulties Berga and Moreno highlighted relaxing the assumption on the cardinality of the range, disappear under a proper assumption on the domain. We introduce the concept of complete sets of preferences and show that individual strategy-proofness is sufficient to obtain the preference reversal property when the agents' feasible set of orderings is complete. This covers interesting cases like single peaked preferences, rich domains admitting regular social choice functions, and universal domains. The fact that we use individual rather than group strategy-proofness, allows to get immediately some of the known, and some new, equivalences between individual and group strategy-proofness. Finally, we show that group strategy-proofness is only really needed to obtain preference reversal if there are infinitely many voters.
On voting rules satisfying false-name-proofness and participation
Université Jean Monnet Saint-Étienne, CNRS, Université Lyon 2, emlyon business school, GATE（圣艾蒂安让·莫内大学、法国国家科学研究中心、里昂第二大学、emlyon商学院、GATE）；Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis and CONICET（圣路易斯应用数学研究所、圣路易斯国立大学和阿根廷国家科学研究委员会）
A characterization of strategy-proof probabilistic assignment rules
Indian Institute of Technology Kanpur（印度坎普尔理工学院）；Indian Statistical Institute, Kolkata（印度统计学院，加尔各答）；Indian Institute of Technology Hyderabad（印度海得拉巴理工学院）
Non-obvious Manipulability with Groups in Shapley-Scarf Housing Markets
CREST, Ecole Polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院）；University of Barcelona（巴塞罗那大学）；Université Jean Monnet, Saint-Étienne, GATE-LSE（让·莫内大学）；University of Padova（帕多瓦大学）；Kyushu University（九州大学）
