The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Arrow’s Theorem

  • Kenneth J. Arrow
Reference work entry


Any satisfactory method of making a social choice should be in some measure representative of the individual criteria which enter into it, should use the range of possible actions, and should observe consistency conditions among the choices made for different data sets. Arrow’s Theorem, or the Impossibility Theorem, states that there is no social choice mechanism which satisfies such reasonable conditions and which will be applicable to any arbitrary set of individual criteria. This article sets out the proof of the theorem.


Arrow’s th Bentham J. Compensation principle Condorcet Marquis de Constitutions Edgeworth F. Hicks J. Impossibility th Independence of irrelevant alternatives Intransitivity Kaldor N. Pareto principle Preference orderings Rawls J. Scitovsky T. Sidgwick H. Single-peaked preferences Social choice Social welfare function Voting 

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  1. Arrow, K.J. 1950. A difficulty in the concept of social welfare. Journal of Political Economy 58: 328–346.CrossRefGoogle Scholar
  2. Arrow, K.J. 1951. Social choice and individual values. New York: Wiley. (2nd edn, New Haven: Yale University Press, 1963, identical except for an additional chapter.)Google Scholar
  3. Arrow, K.J. 1973. Formal theories of social welfare. In Dictionary of the history of ideas, ed. P.P. Wiener, vol. 4, 276–284. New York: Scribner’s.Google Scholar
  4. Bergson (Burk), A. 1938. A reformulation of certain aspects of welfare economics. Quarterly Journal of Economics 52: 310–334.CrossRefGoogle Scholar
  5. Black, D. 1948. On the rationale of group decision-making. Journal of Political Economy 56: 23–34.CrossRefGoogle Scholar
  6. Black, D. 1958. Theory of committees and elections. Cambridge: Cambridge University Press.Google Scholar
  7. Blau, J. 1957. The existence of social welfare functions. Econometrica 25: 302–313.CrossRefGoogle Scholar
  8. Bowen, H.R. 1943. The interpretation of voting in the allocation of economic resources. Quarterly Journal of Economics 58: 27–48.CrossRefGoogle Scholar
  9. Condorcet, M. de Caritat, Marquis de. 1785. Essai sur l’application de l’analyse à la probabilité des decisions rendues à la pluralité des voix. Paris: Imprimerie Royale.Google Scholar
  10. Edgeworth, F.Y. 1897. The pure theory of taxation. In Papers relating to political economy, ed. F.Y. Edgeworth, vol. II, 63–125. London: Macmillan, 1925.Google Scholar
  11. Hicks, J.R. 1939. The foundations of welfare economics. Economic Journal 49 (696–700): 711–712.Google Scholar
  12. Kaldor, N. 1939. Welfare propositions of economics and interpersonal comparisons of utility. Economic Journal 49: 549–552.CrossRefGoogle Scholar
  13. Kelly, J.S. 1978. Arrow impossibility theorems. New York: Academic Press.Google Scholar
  14. Murakami, Y. 1961. A note on the general possibility theorem of social welfare function. Econometrica 29: 244–246.CrossRefGoogle Scholar
  15. Rawls, J. 1971. A theory of justice. Cambridge, MA: Harvard University Press.Google Scholar
  16. Scitovsky, T. 1941. A reconsideration of the theory of tariffs. Review of Economic Studies 9: 92–95.Google Scholar
  17. Sen, A.K. 1986. Social choice theory. In handbook of mathematical economics, ed. K.J. Arrow and M. Intriligator, vol. III, 1073–81. Amsterdam, North-Holland.Google Scholar
  18. Sidgwick, H. 1901. Principles of political economy. 3rd ed. London: Macmillan.Google Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Kenneth J. Arrow
    • 1
  1. 1.