Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T16:48:15.540Z Has data issue: false hasContentIssue false
  • English
  • Français

A Welfarist Proof of Arrow’s Theorem

Published online by Cambridge University Press:  17 August 2016

Charles Blackorby ,
David Donaldson  and
John A. Weymark
Charles Blackorby
Affiliation:
University of British Columbia, Vancouver
David Donaldson
Affiliation:
University of British Columbia, Vancouver
John A. Weymark
Affiliation:
University of British Columbia, Vancouver
Get access

Summary

This article presents a proof of Arrow’s Theorem which highlights the theorem’s relationship to welfarism and which emphasizes its underlying geometric structure. In addition, this method of proof is adapted to provide a proof of a single-preference-profile version of Arrow’s Theorem. The relationship between Arrovian social choice theory and Bergson-Samuelson welfare economics is also considered.

Résumé

Résumé

Cet article présente une preuve du théorème d’Arrow, mettant en lumière, d’une part, sa relation au welfarisme et d’autre part, sa structure géométrique. En outre, nous donnons une preuve de la version “profil de préférences unique” du théorème d’Arrow basée sur cette méthode. La relation entre la théorie du choix social d’Arrow et les conceptions du bien-être de Bergson-Samuelson est aussi discutée.

Keywords

024025024025
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 56 , Issue 3-4: A Special Issue in Honor of Professor A. Sen : Alternatives to Welfarism , 1990 , pp. 259 - 286
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

During the preparation of this article, Blackorby was a visitor at GREQE. We thank the Social Sciences and Humanities Research Council of Canada for research support. This article was prepared to honour Amartya Sen on the occassion of his receiving an honorary degree from the Université Catholique de Louvain. Readers familiar with our research will be aware of the immense intellectual debt we owe to Amartya. We are also deeply indebted to him for the encouragement and help he has given us over the years. We offer this article as a small token of our appreciation.

References

Arrow, K.J. (1951), Social Choice and Individual Values, New York, John Wiley.Google Scholar
Arrow, K.J. (1963), Social Choice and Individual Values, Second Edition, New York, John Wiley.Google Scholar
Bergson, A. (1938), A reformulation of certain aspects of welfare economics, Quarterly Journal of Economics, 52, pp. 310–334.Google Scholar
Blackorby, C, Donaldson, D., and Weymark, J.A. (1984), Social choice with interpersonal utility comparisons : A diagrammatic introduction, International Economic Review, 25, pp. 327–356.Google Scholar
Blair, D.H. and Pollak, R.A. (1983), Rational collective choice, Scientific American, 249, pp. 88–95.Google Scholar
Blau, J.H. (1976), Neutrality, monotonicity, and the right of veto: A comment, Econometrica, 44, p. 603.Google Scholar
Boadway, R.W. and Bruce, N. (1984), Welfare Economics, Oxford, Basil Blackwell.Google Scholar
d’Aspremont, C. (1985), Axioms for social welfare orderings, in: Hurwicz, L., Schmeidler, D., and Sonnenschein, H. (eds.), Social Goals and Social Organization, Cambridge, Cambridge University Press, pp. 19–76.Google Scholar
d’Aspremont, C. and Gevers, L. (1977), Equity and the informational basis of social choice, Review of Economic Studies, 44, pp. 199–209.Google Scholar
Dixit, A.K. (1980), Interpersonal comparisons and social welfare functions, mimeographed lecture notes, University of Warwick.Google Scholar
Gevers, L. (1979), On interpersonal comparability and social welfare orderings, Econometrica, 47, pp. 75–90.Google Scholar
Guha, A.S. (1972), Neutrality, monotonicity, and the right of veto, Econometrica, 40, pp. 821–826.Google Scholar
Hammond, P.J. (1979), Equity in two person situations: Some consequences, Econometrica, 47, pp. 1127–1136.Google Scholar
Kemp, M.C. and Ng, Y.-K. (1976), On the existence of social welfare functions, social orderings, and social decision functions, Economica, 43, pp. 59–66.Google Scholar
Parks, R.P. (1976), An impossibility theorem for fixed preferences: A dictatorial Bergson-Samuelson social welfare function, Review of Economic Studies, 43, pp. 447–450.Google Scholar
Pollak, R.A. (1979), Bergson-Samuelson social welfare functions and the theory of social choice, Quarterly Journal of Economics, 93, pp. 73–90.Google Scholar
Roberts, K.W.S. (1980a), Interpersonal comparability and social choice theory, Review of Economic Studies, 47, pp. 421–439.Google Scholar
Roberts, K.W.S. (1980b), Social choice theory: The single-profile and multi-profile approaches, Review of Economic Studies, 47, pp. 441–450.Google Scholar
Samuelson, P.A. (1947), Foundations of Economic Analysis, Cambridge, Mass., Harvard University Press.Google Scholar
Samuelson, P.A. (1977), Reaffirming the existence of “reasonable” Bergson-Samuelson social welfare functions, Economica, 44, pp. 81–88.Google Scholar
Sen, A.K. (1970), Collective Choice and Social Welfare, San Francisco, Holden-Day.Google Scholar
Sen, A.K. (1974), Informational bases of alternative welfare approaches: Aggregation and income distribution, Journal of Public Economics, 3, pp. 387–403.Google Scholar
Sen, A.K. (1977), On weights and measures: Informational constraints in social welfare analysis, Econometrica, 45, pp. 1539–1572.Google Scholar
Sen, A.K. (1979), Personal utilities and public judgements : Or what’s wrong with welfare economics?, Economic Journal, 89, pp. 537–538.Google Scholar
Sen, A.K. (1984), Social choice theory, in: Arrow, K.J. and Intriligator, M.D. (eds.), Handbook of Mathematical Economics, Volume III, Amsterdam, North-Holland, pp. 1073–1181.Google Scholar
Wilson, R.B. (1972), Social choice theory without the Pareto principle, Journal of Economic Theory, 5, pp. 478–486.Google Scholar