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Preference aggregation theory without acyclicity: The core without majority dissatisfaction

  • Kumabe, Masahiro
  • Mihara, H. Reiju

Acyclicity of individual preferences is a minimal assumption in social choice theory. We replace that assumption by the direct assumption that preferences have maximal elements on a fixed agenda. We show that the core of a simple game is nonempty for all profiles of such preferences if and only if the number of alternatives in the agenda is less than the Nakamura number of the game. The same is true if we replace the core by the core without majority dissatisfaction, obtained by deleting from the agenda all the alternatives that are non-maximal for all players in a winning coalition. Unlike the core, the core without majority dissatisfaction depends only onthe players' sets of maximal elements and is included in the union of such sets. A result for an extended framework gives another sense in which the core without majority dissatisfaction behaves better than the core.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11728.

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Date of creation: 24 Nov 2008
Date of revision:
Handle: RePEc:pra:mprapa:11728
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  1. Truchon, M., 1993. "Voting Games and Acyclic Collective Choice Rules," Papers 9315, Laval - Recherche en Politique Economique.
  2. Mathieu Martin & Vincent Merlin, 2006. "On the Chacteristic Numbers of Voting Games," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200609, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
  3. H. Reiju Mihara, 1996. "Coalitionally strategyproof functions depend only on the most-preferred alternatives," Public Economics 9604003, EconWPA, revised 24 Apr 1996.
  4. Elizabeth Penn, 2006. "The Banks Set in Infinite Spaces," Social Choice and Welfare, Springer, vol. 27(3), pages 531-543, December.
  5. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, Econometric Society, vol. 70(6), pages 2481-2488, November.
  6. Andjiga, Nicolas Gabriel & Moyouwou, Issofa, 2006. "A note on the non-emptiness of the stability set when individual preferences are weak orders," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 67-76, July.
  7. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
  8. E. Ray Canterbery, 1984. "Introduction," Journal of Post Keynesian Economics, M.E. Sharpe, Inc., vol. 7(1), pages 4-6, October.
  9. Mihara, H.R., 1994. "Arrow's Theorem and Turing Computability," Papers 276, Minnesota - Center for Economic Research.
  10. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany.
  11. Attila Ambrus & Kareen Rozen, 2008. "Revealed Conflicting Preferences," Levine's Working Paper Archive 122247000000002161, David K. Levine.
  12. Andjiga, N G & Moulen, J, 1989. "Necessary and Sufficient Conditions for l-Stability of Games in Constitutional Form," International Journal of Game Theory, Springer, vol. 18(1), pages 91-110.
  13. Masahiro Kumabe & H. Reiju Mihara, 2008. "The Nakamura numbers for computable simple games," Social Choice and Welfare, Springer, vol. 31(4), pages 621-640, December.
  14. Banks, Jeffrey S., 1984. "Sophisticated Voting Outcomes and Agenda Control," Working Papers 524, California Institute of Technology, Division of the Humanities and Social Sciences.
  15. Attila Ambrus & Kareen Rozen, 2012. "Rationalizing Choice with Multi-Self Models," Levine's Working Paper Archive 786969000000000512, David K. Levine.
  16. Andjiga, Nicolas Gabriel & Mbih, Boniface, 2000. "A note on the core of voting games," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 367-372, April.
  17. H. Reiju Mihara, 1997. "Arrow's Theorem, countably many agents, and more visible invisible dictators," Public Economics 9705001, EconWPA, revised 07 May 1997.
  18. John Duggan, 2007. "A systematic approach to the construction of non-empty choice sets," Social Choice and Welfare, Springer, vol. 28(3), pages 491-506, April.
  19. Le Breton, M & Salles, M, 1990. "The Stability Set of Voting Games: Classification and Genericity Results," International Journal of Game Theory, Springer, vol. 19(2), pages 111-27.
  20. Lipman, Barton L, 1991. "How to Decide How to Decide How to. . . : Modeling Limited Rationality," Econometrica, Econometric Society, vol. 59(4), pages 1105-25, July.
  21. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, 09.
  22. Rubinstein, Ariel, 1980. "Stability of decision systems under majority rule," Journal of Economic Theory, Elsevier, vol. 23(2), pages 150-159, October.
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