On strategy-proofness and single-peakedness: median-voting over intervals
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On strategy-proofness and single-peakedness: median-voting over intervals Bettina Klaus1
· Panos Protopapas1
Accepted: 20 July 2020 / Published online: 17 November 2020 © The Author(s) 2020
Abstract We study correspondences that choose an interval of alternatives when agents have single-peaked preferences over locations and ordinally extend their preferences over intervals. We extend the main results of Moulin (Public Choice 35:437–455, 1980) to our setting and show that the results of Ching (Soc Choice Welf 26:473–490, 1997) cannot always be similarly extended. First, strategy-proofness and peaks-onliness characterize the class of generalized median correspondences (Theorem 1). Second, this result neither holds on the domain of symmetric and single-peaked preferences, nor can in this result min/max continuity substitute peaks-onliness (see counterExample 3). Third, strategy-proofness and voter-sovereignty characterize the class of efficient generalized median correspondences (Theorem 2). Keywords Correspondences · Generalized median correspondences · Single-peaked preferences · Strategy-proofness JEL Classification C71 · D63 · D78 · H41
We gratefully acknowledge financial support from the Swiss National Science Foundation (SNFS) for project 100018_156201. This work has also been partly supported by COST Action IC1205 on Computational Social Choice. We would like to thank Sidartha Gordon, Flip Klijn, Jordi Massó, William Thomson, and two anonymous referees and an associate editor for their very valuable feedback.
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Bettina Klaus [email protected] Panos Protopapas [email protected]
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Faculty of Business and Economics, University of Lausanne, Internef, 1015 Lausanne, Switzerland
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B. Klaus, P. Protopapas
1 Introduction We study the problem where an interval of alternatives is chosen from the interval [0, 1] based on the preferences of a finite number of agents. This interval can be considered as the political spectrum, while the chosen interval can in turn be considered as the legislative constitution or the governmental coalition (in the sense that some “extreme” views are not accounted for by the constitution or are not represented by any member(s) of the governmental coalition). We assume that agents have single-peaked preferences defined over all alternatives on [0, 1]; that is, an agent’s welfare is strictly increasing up to his “peak” (his favorite alternative), and is strictly decreasing thereafter. Other examples for the type of social choice problems we are interested in would be the planning of public parking zones where an agent knows that he will (eventually) find a parking spot in the designated parking zone but he does not know where this will be, or the drafting of an “if-needed” list of candidate locations to build a public facility, e.g., a hospital. The motivation behind our model also resembles that of two-stage voting procedures such as, for example, Black’s procedure (e.g. Fishburn 1977) or the “rule of k names” (e.g. Barberà and Coelho 2000), or situations where
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