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Arrovian Social Choice Theory on Economic Domains

  • Le Breton, Michel
  • Weymark, John

This article surveys the literature that investigates the consistency of Arrow's social choice axioms when his unrestricted domain assumptions are replaced by domain conditions that incorporate the restrictions on agendas and preferences encountered in economic environments. Both social welfare functions and social choice correspondences are considered.

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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 143.

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Date of creation: 2002
Date of revision: Sep 2003
Publication status: Published in in Handbook of Social Choice and Welfare, Kenneth J. Arrow, Armatya Sen and Kotaro Suzumura (eds.), vol. 2, chapter 8, Elsevier Science, 2010.
Handle: RePEc:ide:wpaper:586
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  1. Redekop, James, 1993. "The questionnaire topology on some spaces of economic preferences," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 479-494.
  2. Michel Le Breton & John A. Weymark, 2000. "Social Choice with Analytic Preferences," Vanderbilt University Department of Economics Working Papers 0023, Vanderbilt University Department of Economics, revised Mar 2001.
  3. Le Breton, Michel & Trannoy, Alain, 1987. "Measures of inequality as an aggregation of individual preferences about income distribution: The arrowian case," Journal of Economic Theory, Elsevier, vol. 41(2), pages 248-269, April.
  4. Campbell, Donald E., 1990. "Intergenerational social choice without the Pareto principle," Journal of Economic Theory, Elsevier, vol. 50(2), pages 414-423, April.
  5. Donaldson, David & Weymark, John A., 1988. "Social choice in economic environments," Journal of Economic Theory, Elsevier, vol. 46(2), pages 291-308, December.
  6. Yanovskaya, Elena B., 1994. "Correspondence between social choice functions and solutions of cooperative games," Mathematical Social Sciences, Elsevier, vol. 27(2), pages 217-234, April.
  7. Gaertner,Wulf, 2001. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521791021, June.
  8. Bailey, Martin J, 1979. "The Possibility of Rational Social Choice in an Economy," Journal of Political Economy, University of Chicago Press, vol. 87(1), pages 37-56, February.
  9. Campbell, Donald E, 1992. "Transitive Social Choice in Economic Environments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 341-52, May.
  10. Georges Bordes & Peter J. Hammond & Michel Le Breton, 1997. "Social Welfare Functionals on Restricted Domains and in Economic Environments," Working Papers 97023, Stanford University, Department of Economics.
  11. Kannai, Yakar, 1974. "Approximation of convex preferences," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 101-106, August.
  12. James Redekop, 1996. "Arrow theorems in mixed goods, stochastic, and dynamic economic environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 95-112, January.
  13. Ehud Kalai & Eitan Muller & Mark Satterthwaite, 1979. "Social welfare functions when preferences are convex, strictly monotonic, and continuous," Public Choice, Springer, vol. 34(1), pages 87-97, March.
  14. Saari, Donald G., 1991. "Calculus and extensions of Arrow's theorem," Journal of Mathematical Economics, Elsevier, vol. 20(3), pages 271-306.
  15. Redekop, James, 1991. "Social welfare functions on restricted economic domains," Journal of Economic Theory, Elsevier, vol. 53(2), pages 396-427, April.
  16. Campbell, Donald E., 1992. "Quasitransitive intergenerational choice for economic environments," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 229-247.
  17. Kim Border, 1984. "An impossibility theorem for spatial models," Public Choice, Springer, vol. 43(3), pages 293-305, January.
  18. Bordes, Georges & Campbell, Donald E & Le Breton, Michel, 1995. "Arrow's Theorem for Economic Domains and Edgeworth Hyperboxes," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(2), pages 441-54, May.
  19. Ehlers,Lars & Storcken,Ton, 2001. "Arrow's Theorem in Spatial Environments," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  20. Jeffrey Richelson, 1984. "Social choice and the status quo," Public Choice, Springer, vol. 42(3), pages 225-234, January.
  21. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
  22. Ehud Kalai & Zvi Ritz, 1978. "Characterization of the Private Alternative Domains Admitting Arrow Social Welfare Functions," Discussion Papers 341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  23. Campbell, Donald E, 1992. "Implementation of Social Welfare Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 525-33, August.
  24. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
  25. Nitzan, Shmuel, 1976. "On Linear and Lexicographic Orders, Majority Rule and Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 213-19, February.
  26. Campbell, Donald E., 1992. "The arrow and plott independence conditions," Economics Letters, Elsevier, vol. 39(2), pages 143-146, June.
  27. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
  28. Lars Ehlers & John A. Weymark, 2003. "Candidate stability and nonbinary social choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(2), pages 233-243, 09.
  29. Bordes, Georges & Breton, Michel Le, 1989. "Arrovian theorems with private alternatives domains and selfish individuals," Journal of Economic Theory, Elsevier, vol. 47(2), pages 257-281, April.
  30. Ehlers, Lars, 2001. "Independence axioms for the provision of multiple public goods as options," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 239-250, March.
  31. Weymark, John A., 1998. "Welfarism on economic domains1," Mathematical Social Sciences, Elsevier, vol. 36(3), pages 251-268, December.
  32. Campbell, Donald E., 1990. "Can equity be purchased at the expense of efficiency? An axiomatic inquiry," Journal of Economic Theory, Elsevier, vol. 51(1), pages 32-47, June.
  33. John Bone, 2003. "Simple Arrow-type propositions in the Edgeworth domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(1), pages 41-48.
  34. Inada, Ken-ichi, 1971. "Social Welfare Function and Social Indifference Surfaces," Econometrica, Econometric Society, vol. 39(3), pages 599-624, May.
  35. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-37, July.
  36. Border, Kim C., 1983. "Social welfare functions for economic environments with and without the pareto principle," Journal of Economic Theory, Elsevier, vol. 29(2), pages 205-216, April.
  37. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  38. David M. Grether & Charles R. Plott, 1982. "Nonbinary Social Choice: An Impossibility Theorem," Review of Economic Studies, Oxford University Press, vol. 49(1), pages 143-149.
  39. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 153-170.
  40. Campbell, Donald E., 1993. "Euclidean individual preference and continuous social preference," European Journal of Political Economy, Elsevier, vol. 9(4), pages 541-550, November.
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