Social Choice and Welfare

, Volume 31, Issue 3, pp 393–413 | Cite as

Sen’s theorem: geometric proof, new interpretations

Original Paper

Abstract

Sen’s classic social choice result supposedly demonstrates a conflict between Pareto and minimal forms of liberalism. By providing the first direct mathematical proof of this seminal result, we underscore a significantly different interpretation: rather than conflicts among rights, Sen’s result occurs because the liberalism assumption negates the requirement that voters have transitive preferences. This explanation enriches interpretations of Sen’s conclusion by introducing radically new kinds of societal conflicts, by suggesting ways to sidestep these difficulties, and by providing insight into other approaches that have been used to avoid the difficulties.

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References

  1. Arrow KJ (1950) A difficulty in the concept of social welfare. J Polit Econ 58(4): 469–484CrossRefGoogle Scholar
  2. Batra RN, Pattanaik PK (1972) On some suggestions for having non-binary social choice functions. Theory Decis 111: 1–11CrossRefGoogle Scholar
  3. Blau JH (1975) Liberal values and independence. Rev Econ Stud 42: 395–401CrossRefGoogle Scholar
  4. Breyer F (1977) The liberal paradox, decisiveness over issues, and domain restrictions. J Econ 37: 45–60Google Scholar
  5. Breyer F, Gigliotti GA (1980) Empathy and respect for the rights of others. J Econ 40: 59–64Google Scholar
  6. Campbell DE, Kelly JS (1997) Sen’s theorem and externalities. Economica 64: 375–386CrossRefGoogle Scholar
  7. Fine B (1975) Individual liberalism in a paretian society. J Polit Econ 83: 1277–1282CrossRefGoogle Scholar
  8. Harel A, Nitzan S (1987) The liberatarian resolutioon of the paretian liberal paradox. J Econ 47: 337–352Google Scholar
  9. Jones B, Radcliff B, Taber C, Timpone R (1995) Condorcet winners and the paradox of voting. Am Polit Sci Rev 89: 137–144CrossRefGoogle Scholar
  10. Riker WH (1982) Liberalism against Populism. W. H. Freeman and Co., San FranciscoGoogle Scholar
  11. Risse M (2001) What to make of the liberal paradox?. Theory Decis 50: 169–196CrossRefGoogle Scholar
  12. Saari DG (1995) Inner consistency or not inner consistency: a reformulation is the answer. In: Barnett W.A., Moulin H., Salles M., Schofield N. (eds) Social choice, welfare, and ethics. Cambridge University Press, Cambridge, pp 187–212Google Scholar
  13. Saari DG (1995) Basic geometry of voting. Springer, New YorkGoogle Scholar
  14. Saari DG (1998) Connecting and resolving Sen’s and Arrow’s theorems. Soc Choice Welf 15: 239–261CrossRefGoogle Scholar
  15. Saari DG (2001) Decisions and elections; explaining the unexpected. Cambridge University Press, New YorkGoogle Scholar
  16. Saari DG (2008) Disposing dictators; demystifying voting paradoxes. Cambridge University Press, New YorkGoogle Scholar
  17. Saari DG, Petron A (2006) Negative externalities and sen’s liberalism theorem. Econ Theory 28: 265–281CrossRefGoogle Scholar
  18. Saari DG, Sieberg K (2001) The sum of the parts can violate the whole. Am Polit Sci Rev 95: 415–433CrossRefGoogle Scholar
  19. Salles M (1997) On modelling individual rights: some conceptual issues: discussion pp 129–133. In: Arrow KJ, Sen AK, Suzumura K (eds) Social choice re-examined, Vol 2; St Martin’s Press, New YorkGoogle Scholar
  20. Salles M (2000) Amartya Sen: droits et choix social. Revue Econ 51: 445–457CrossRefGoogle Scholar
  21. Seidl C (1975) On liberal values. J Econ 35: 257–292Google Scholar
  22. Seidl C (1990) On the impossibility of a generalization of the libertarian resolution of the liberal paradox. J Econ 51: 71–88Google Scholar
  23. Sen AK (1970a) Collective choice and social welfare. Holden-Day, San FranciscoGoogle Scholar
  24. Sen AK (1970b) The impossibility of a Paretian liberal. J Polit Econ 78(1): 152–157CrossRefGoogle Scholar
  25. Sen AK (1976) Liberty, unanimity and rights. Economica 43(171): 217–245CrossRefGoogle Scholar
  26. Sen AK (1983) Liberty and social choice. J Philos 80(1): 5–28CrossRefGoogle Scholar
  27. Sen AK (1992) Minimal liberty. Economica 59(234): 139–160CrossRefGoogle Scholar
  28. Sen AK (1999) The possibility of social choice. Am Econ Rev 89(3): 349–378CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.CoB, EconomicsUniversity of LouisvilleLouisvilleUSA
  2. 2.Institute for Mathematical Behavioral SciencesUniversity of CaliforniaIrvineUSA

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