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arXiv · 2303.05781

Strategy-proofness with single-peaked and single-dipped preferences

Jorge Alcalde-Unzu·Oihane Gallo·Marc Vorsatz
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Abstract

We analyze the problem of locating a public facility in a domain of single-peaked and single-dipped preferences when the social planner knows the type of preference (single-peaked or single-dipped) of each agent. Our main result characterizes all strategy-proof rules and shows that they can be decomposed into two steps. In the first step, the agents with single-peaked preferences are asked about their peaks and, for each profile of reported peaks, at most two alternatives are preselected. In the second step, the agents with single-dipped preferences are asked to reveal their dips to complete the decision between the preselected alternatives. Our result generalizes the findings of Moulin (1980) and Barber\`a and Jackson (1994) for single-peaked and of Manjunath (2014) for single-dipped preferences. Finally, we show that all strategy-proof rules are also group strategy-proof and analyze the implications of Pareto efficiency.

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Jorge Alcalde-Unzu, Oihane Gallo, Marc Vorsatz. 2023-03-10. Strategy-proofness with single-peaked and single-dipped preferences. https://arxiv.org/abs/2303.05781

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