Abstract
This article establishes versions of Moulin’s (Public Choice 35:437–455, 1980) characterizations of various classes of strategy-proof social choice functions when the domain consists of all profiles of single-peaked preferences on an arbitrary subset of the real line. Two results are established that show that the median of 2n + 1 numbers can be expressed using a combination of minimization and maximization operations applied to subsets of these numbers when either these subsets or the numbers themselves are restricted in a particular way. These results are used to show how Moulin’s characterizations of generalized median social choice functions can be obtained as corollaries of his characterization of min–max social choice functions.
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Acknowledgments
This article has been written to honour Salvador Barberà on the occasion of his 65th birthday. I am grateful to Bernardo Moreno and an anonymous referee for their comments.
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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Weymark, J.A. A unified approach to strategy-proofness for single-peaked preferences. SERIEs 2, 529–550 (2011). https://doi.org/10.1007/s13209-011-0064-5
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DOI: https://doi.org/10.1007/s13209-011-0064-5
Keywords
- Generalized median social choice functions
- Moulin min–max rules
- Single-peaked preferences
- Strategy-proofness