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Single-Plateaued Choice

  • Walter Bossert
  • Hans Peters

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 singleplateauedness 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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Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 05-2012.

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Length: 18 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:mtl:montec:05-2012
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  1. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
  2. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer, vol. 41(2), pages 213-230, November.
  3. Dolors Berga & Bernardo Moreno, 2008. "Strategic Requirements with Indifference: Single-Peaked versus Single-Plateaued Preferences," Working Papers 2008-7, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
  4. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
  5. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer, vol. 36(2), pages 305-322, February.
  6. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994.
  7. 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.
  8. Lars Ehlers, 2002. "Strategy-proof allocation when preferences are single-plateaued," Review of Economic Design, Springer, vol. 7(1), pages 105-115.
  9. 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.
  10. 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.
  11. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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