Synthese

, 171:257 | Cite as

Preference-based choice functions: a generalized approach

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Abstract

Although choice and preference are distinct categories, it may in some contexts be a useful idealization to treat choices as fully determined by preferences. In order to construct a general model of such preference-based choice, a method to derive choices from preferences is needed that yields reasonable outcomes for all preference relations, even those that are incomplete and contain cycles. A generalized choice function is introduced for this purpose. It is axiomatically characterized and is shown to compare favourably with alternative constructions.

Keywords

Choice Choice function Preference Preference relation Preference cycles Cyclic preferences Incomplete preferences 

References

  1. Arrow K. (1977) Extended sympathy and the possibility of social choice. The American Economic Review 67: 219–225Google Scholar
  2. Duggan J. (2007) A systematic approach to the construction of non-empty choice sets. Social Choice and Welfare 28: 491–506CrossRefGoogle Scholar
  3. Duggan J., Le Breton M. (2001) Mixed refinements of Shapley’s saddles and weak tournaments. Social Choice and Welfare 18: 65–78CrossRefGoogle Scholar
  4. Dutta B. (1988) Covering sets and a new condorcet choice correspondence. Journal of Economic Theory 44: 63–80CrossRefGoogle Scholar
  5. Fishburn P. C. (1977) Condorcet social choice functions. SIAM Journal on Applied Mathematics 33: 469–489CrossRefGoogle Scholar
  6. Hansson S. O. (1990) Defining ‘good’ and ‘bad’ in terms of ‘better’. Notre Dame Journal of Formal Logic 31: 136–149CrossRefGoogle Scholar
  7. Hansson S. O. (1991) Norms and values. Crítica 23: 3–13Google Scholar
  8. Hansson S. O. (1992) A procedural model of voting. Theory and Decision 32: 269–301CrossRefGoogle Scholar
  9. Hansson S. O. (2001) The structure of values and norms. Cambridge University Press, CambridgeGoogle Scholar
  10. Herzberger H. V. (1973) Ordinal preference and rational choice. Econometrica 412: 187–237CrossRefGoogle Scholar
  11. Kalai E., Schmeidler D. (1977) An admissible set occurring in various bargaining situations. Journal of Economic Theory 14: 402–411CrossRefGoogle Scholar
  12. Miller N. (1977) Graph-theoretical approaches to voting. American Journal of Political Science 21: 769–803CrossRefGoogle Scholar
  13. Miller N. (1980) A new solution set for tournaments and majority voting: Further graph-theoretical approaches to the theory of voting. American Journal of Political Science 24: 68–96CrossRefGoogle Scholar
  14. Reynolds J. F., Paris D. C. (1979) The concept of ‘choice’ and arrow’s theorem. Ethics 89: 354–371CrossRefGoogle Scholar
  15. Samuelson P. (1938a) A note on the pure theory of consumer behaviour. Economica 5(17): 61–71CrossRefGoogle Scholar
  16. Samuelson P. (1938b) A note on pure theory of consumer behaviour: An addendum. Economica 5(19): 353–354CrossRefGoogle Scholar
  17. Sánchez M. C., Llinares J.-V., Subiza B. (2003) A KKM-result and an application for binary and non-binary choice functions. Economic Theory 21: 185–193CrossRefGoogle Scholar
  18. Schwartz T. (1972) Rationality and the myth of the maximum. Nous 6: 97–117Google Scholar
  19. Schwartz T. (1986) The logic of collective action. Columbia University Press, New YorkGoogle Scholar
  20. Sen A. (1973) Behaviour and the concept of preference. Economica 40: 241–259CrossRefGoogle Scholar
  21. Subiza B., Peris J. E. (2000) Choice functions: Rationality re-examined. Theory and Decision 48: 287–304CrossRefGoogle Scholar
  22. Ullmann-Margalit E., Morgenbesser S. (1977) Picking and choosing. Social Research 44: 757–785Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Royal Institute of TechnologyStockholmSweden

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