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Single-plateaued choice

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  • BOSSERT, Walter
  • PETERS, Hans

Abstract

Single-plateaued preferences generalize single-peaked preferences by allowing for multiple best elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-plateauedness in a choice-theoretic setting. Single-plateaued choice is characterized by means of a collinear interval continuity property in the presence of independence of irrelevant alternatives. Further results establish that our notion of single-plateauedness conforms to the motivation underlying the term and we analyze the consequences of alternative continuity properties. The importance of basic assumptions such as closedness and convexity is discussed.

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File URL: https://papyrus.bib.umontreal.ca/jspui/handle/1866/8640
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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2012-04.

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Length: 14 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:mtl:montde:2012-04

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Keywords: Single-plateauedness; choice correspondences; independence of irrelevant alternatives; continuity;

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  1. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  2. Dolors Berga & Bernardo Moreno, 2007. "Strategic Requirements with Indifference: Single-Peaked versus Single-Plateaued Preferences," Working Papers 325, Barcelona Graduate School of Economics.
  3. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
  4. Bossert, Walter & Peters, Hans, 2006. "Single-peaked choice," Research Memorandum 037, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
  6. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  7. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer, vol. 36(2), pages 305-322, February.
  8. Ehlers, Lars & Storcken, Ton, 2008. "Arrow's Possibility Theorem for one-dimensional single-peaked preferences," Games and Economic Behavior, Elsevier, vol. 64(2), pages 533-547, November.
  9. Lars Ehlers, 2002. "Strategy-proof allocation when preferences are single-plateaued," Review of Economic Design, Springer, vol. 7(1), pages 105-115.
  10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  11. Dutta, Bhaskar & Peters, Hans & Sen, Arunava, 2002. "Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 392-416, October.
  12. Bossert, Walter & Suzumura, Kotaro, 2009. "Consistency, Choice and Rationality," PIE/CIS Discussion Paper 428, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
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