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Social Choice and Welfare

, Volume 28, Issue 3, pp 491–506 | Cite as

A systematic approach to the construction of non-empty choice sets

  • John Duggan
Original Paper

Abstract

Suppose a strict preference relation fails to possess maximal elements, so that a choice is not clearly defined. I propose to delete particular instances of strict preferences until the resulting relation satisfies one of a number of known regularity properties (transitivity, acyclicity, or negative transitivity), and to unify the choices generated by different orders of deletion. Removal of strict preferences until the subrelation is transitive yields a new solution with close connections to the “uncovered set” from the political science literature and the literature on tournaments. Weakening transitivity to acyclicity yields a new solution nested between the strong and weak top cycle sets. When the original preference relation admits no indifferences, this solution coincides with the familiar top cycle set. The set of alternatives generated by the restriction of negative transitivity is equivalent to the weak top cycle set.

Keywords

Maximal Element Strict Preference Mixed Strategy Equilibrium Political Science Literature Sophisticated Vote 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Austen-Smith D, Banks J (1999) Positive political theory I: collective preference. University of Michigan Press, Ann ArborGoogle Scholar
  2. Banks J (1985) Sophisticated voting outcomes and agenda control. Soc Choice Welfare 1:295–306CrossRefGoogle Scholar
  3. Banks J (1995) Acyclic social choice from finite sets. Soc Choice Welfare 12:293–310CrossRefGoogle Scholar
  4. Banks J, Duggan J, Le Breton M (2002) Bounds for mixed strategy equilibria in the spatial model of elections. J Econ Theory 103:88–105CrossRefGoogle Scholar
  5. Banks J, Duggan J, Le Breton M (2006) Social choice and electoral competition in the general spatial model. J Econ Theory 126:194–234CrossRefGoogle Scholar
  6. Duggan J (1999) A General extension theorem for binary relations. J Econ Theory 86:1–16CrossRefGoogle Scholar
  7. Duggan J (2006) Uncovered sets. MimeoGoogle Scholar
  8. Duggan J, Le Breton M (1997) Dominance-based solutions for strategic form games. MimeoGoogle Scholar
  9. Duggan J, Le Breton M (1999) Mixed refinements of Shapley’s saddles and weak tournaments. CORE discussion paper, no. 9921Google Scholar
  10. Duggan J, Le Breton M (2001) Mixed refinements of Shapley’s saddles and weak tournaments. Soc Choice Welfare 18:65–78CrossRefGoogle Scholar
  11. Fishburn P (1977) Condorcet social choice functions. SIAM J Appl Math 33:469–489CrossRefGoogle Scholar
  12. Mas-Colell A, Sonnenschein H (1972) General possibility theorems for group decisions. Rev Econ Stud 39:185–192CrossRefGoogle Scholar
  13. McKelvey R (1986) Covering, dominance, and institution-free properties of Social Choice. Am J Polit Sci 30:283–314Google Scholar
  14. Miller N (1980) A new solution set for tournaments and majority voting: further graph-theoretical approaches to the theory of voting. Am J Polit Sci 24:68–96Google Scholar
  15. Moulin H (1986) Choosing from a Tournament. Soc Choice Welfare 3: 271–291CrossRefGoogle Scholar
  16. Schwartz T (1986) The logic of collective action. Columbia University Press, New YorkGoogle Scholar
  17. Schwartz T (2001) From arrow to cycles, instability, and chaos by untying alternatives. Soc Choice Welfare 18:1–22CrossRefGoogle Scholar
  18. Sen A (1970) The impossibility of a Paretian liberal. J Polit Econ 78:152–157CrossRefGoogle Scholar
  19. Walker M (1977) On the existence of maximal elements. J Econ Theory 16:470–474CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Political Science and Department of EconomicsUniversity of RochesterRochesterUSA
  2. 2.W. Allen Wallis Institute of Political EconomyUniversity of RochesterRochesterUSA

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