Skip to main content
SpringerLink
Log in

Arrovian Social Choice on Economic Domains

  • Chapter
Social Choice Re-examined

Part of the book series: International Economic Association Series ((IEA))

Abstract

Since the pioneering work of Arrow (1951, 1963), social choice theory has developed a long tradition of research on the principles that should guide decision-makers when they have to solve conflicts of interests or judgements among the individuals in a group. In the ordinal non-comparability framework considered by Arrow a social choice issue is described by a profile of preferences and a feasible set. A Social Choice Correspondence selects for each social choice issue a subset of outcomes from the feasible set. Arrow focused on three principles. The first one (weak Pareto) puts some constraints on the set of choices for a given preference profile and a given feasible set. The second one (Arrow’s Choice Axiom) demands invariance of the set of choices when the feasible set shrinks in a specific way but the preference profile is fixed. The third one (Independence of Infeasible Alternatives) demands invariance of the set of choices when the preference profile changes in a specific way but the feasible set is fixed. The domain of the social choice correspondence consists of all the pairs of preference profiles and feasible sets that may arise as possible social choice issues. Arrow proved that if the domain contains all possible preference profiles (Unrestricted Preference Domain) and all finite subsets (Unrestricted Feasible Set Domain) then only the dictatorial social choice correspondences meet the three principles. Hereafter the last part of the statement will be referred to as the Arrow inconsistency.

I would like to thank J. Duggan, M. Fleurbaey, H. Moulin, C. Plott, J. Weymark, and my discussant A. Malishevski for their helpful discussions. This paper has been written while I was visiting the California Institute of Technology. I would like to thank this institution for its hospitality and M. Goodman for her patience in typing this manuscript.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arrow, K. J. (1951) Social Choice and Individual Values (New York: Wiley).

    Google Scholar 

  • Arrow, K. J. (1959) ‘Rational Choice Functions and Orderings’, Economica, vol. 26, pp. 121–7.

    Article  Google Scholar 

  • Arrow, K. J. (1963) Social Choice and Individual Values, 2nd edn (New York: Wiley).

    Google Scholar 

  • Bailey, M. (1979) ‘The Possibility of Rational Social Choice in an Economy’, Journal of Political Economy, vol. 87, pp. 37–56.

    Article  Google Scholar 

  • Blau, J. H. (1957) ‘The Existence of Social Welfare Functions’, Econometrica, vol. 25, pp. 302–13.

    Article  Google Scholar 

  • Border, K. C. (1983) ‘Social Welfare Functions for Economic Environments with and without the Pareto Principle’, Journal of Economic Theory, vol. 29, pp. 205–16.

    Article  Google Scholar 

  • Bordes, G. and Le Breton, M. (1989) ‘Arrovian Theorems with Private Alternatives Domains and Selfish Individuals’, Journal of Economic Theory, vol. 47, pp. 257–81.

    Article  Google Scholar 

  • Bordes, G. and Le Breton, M. (1990a) ‘Arrovian Theorems for Economic Domains: The Case Where There are Simultaneously Private and Public Goods’, Social Choice and Welfare, vol. 7, pp. 1–17.

    Article  Google Scholar 

  • Bordes, G. and Le Breton, M. (1990b) ‘Arrovian Theorems for Economic Domains: Assignments, Matchings and Pairings’, Social Choice and Welfare, vol. 7, pp. 193–208.

    Article  Google Scholar 

  • Bordes, G., Campbell, D. E. and Le Breton, M. (1992) ‘Arrow’s Theorems for Economic Domains and Edgeworth Hyperboxes’, unpublished manuscript, Université d’Aix-Marseille 2.

    Google Scholar 

  • Campbell, D. E. (1992a) ‘Quasitransitive Intergenerational Choice for Economic Environments’, Journal of Mathematical Economics, vol. 21, pp. 229–47.

    Article  Google Scholar 

  • Campbell, D. E. (1992b) Equity, Efficiency, and Social Choice (Oxford: Clarendon Press).

    Google Scholar 

  • Chernoff, H. (1954) ‘Rational Selection of Decision Functions’, Econometrica, vol. 22, pp. 423–43.

    Article  Google Scholar 

  • Chun, Y. and Thomson, W. (1988) ‘Monotonicity of Bargaining Solutions when Applied to Economics’, Mathematical Social Sciences, vol. 15, pp. 11–27.

    Article  Google Scholar 

  • Denicolo, V. (1987) ‘Some Further Results on Nonbinary Social Choice’, Social Choice and Welfare, vol. 4, pp. 277–85.

    Article  Google Scholar 

  • Donaldson, D. and Weymark, J. (1988) ‘Social Choice in Economic Environments’, Journal of Economic Theory, vol. 46, pp. 291–308.

    Article  Google Scholar 

  • Duggan, J. (1994) ‘Arrow’s Theorem in Public Goods Environments with Convex Production Technologies’, mimeo, California Institute of Technology, Pasadena, California, USA.

    Google Scholar 

  • Fishburn, P. C. (1974) ‘On Collective Rationality and a Generalized Impossibility Theorem’, Review of Economic Studies, vol. 41, pp. 445–58.

    Article  Google Scholar 

  • Gibbard, A., Hylland, A. and Weymark, J. (1987) ‘Arrow’s Theorem with a Fixed Feasible Alternative’, Social Choice and Welfare, vol. 4, pp. 105–15.

    Article  Google Scholar 

  • Grether, D. M. and Plott, C. R. (1982) ‘Nonbiliary Social Choice: An Impossibility Theorem’, Review of Economic Studies, vol. 49, pp. 143–9.

    Article  Google Scholar 

  • Hansson, B. (1968) ‘Choice Structures and Preference Relations’, Synthèse, vol. 18, pp. 443–58.

    Article  Google Scholar 

  • Kalai, E., Muller, E. and Satterthwaite, M. A. (1979) ‘Social Welfare Functions when Preferences are Convex, Strictly Monotonic, and Continuous’, Public Choice, vol. 34, pp. 87–97.

    Article  Google Scholar 

  • Lainé, J., Le Breton, M. and Trannoy, A. (1986) ‘Group Decision Making under Uncertainty: A Note on the Aggregation of Ordinal Probabilities’, Theory and Decision, vol. 21, pp. 155–61.

    Article  Google Scholar 

  • Le Breton, M. and Trannoy, A. (1987) ‘Measures of Inequality as an Aggregation of Individual Preferences about Income Distribution: The Arrovian Case’, Journal of Economic Theory, vol. 41, pp. 248–69.

    Article  Google Scholar 

  • Le Breton, M. and Weymark, J. (1990) ‘Social Choice with Analytic Preferences’, mimeo, University of British Columbia.

    Google Scholar 

  • Le Breton, M. and Weymark, J. (1992) ‘An Introduction to Arrovian Social Welfare Functions on Economic and Political Domains’, in Schofield, N. (ed.) (1994), Social Choice and Political Economy (Dordrecht: Kluwer Academic Publishers), Chapter 2.

    Google Scholar 

  • Mas-Colell, A. and Sonnenschein, H. (1972) ‘General Possibility Theorems for Group Decisions’, Review of Economic Studies, vol. 39, pp. 185–92.

    Article  Google Scholar 

  • Maskin, E. S. (1976) ‘Social Welfare Functions for Economics’, unpublished manuscript, Darwin College, Cambridge University and the Department of Economics, Harvard University.

    Google Scholar 

  • Moulin, H. (1987) ‘Egalitarian Equivalent Cost-Sharing of a Public Good’ Econometrica, vol. 55, pp. 963–77.

    Article  Google Scholar 

  • Moulin, H. (1990a) ‘Fair Division under Joint Ownership: Recent Results and Open Problems’, Social Choice and Welfare, vol. 7, pp. 149–70.

    Article  Google Scholar 

  • Moulin, H. (1990b) ‘Joint Ownership of a Convex Technology: Comparison of Three Solutions’, Review of Economic Studies, vol. 57, pp. 439–52.

    Article  Google Scholar 

  • Moulin, H. and Thomson, W. (1988) ‘Can Everyone Benefit from Growth: Two Difficulties’, Journal of Mathematical Economics, vol. 17, pp. 339–45.

    Article  Google Scholar 

  • Nash, J. F. (1950) ‘The Bargaining Problem’, Econometrica, vol. 18, pp. 155–62.

    Article  Google Scholar 

  • Pazner, E. and Schmeidler, D. (1978) ‘Egalitarian Equivalent Allocations: A New Concept of Economic Equity’, Quarterly Journal of Economics, vol. 92, pp. 671–87.

    Article  Google Scholar 

  • Peters, H. and Wakker, P. (1991) ‘Independence of Irrelevant Alternatives and Revealed Group Preferences’, Econometrica, vol. 59, pp. 1787–801.

    Article  Google Scholar 

  • Plott, C. R. (1985) ‘A Relationship between Independence of Irrelevant Alternatives, Game Theory and Implementability’, mimeo, California Institute of Technology, Pasadena, California, USA.

    Google Scholar 

  • Redekop, J. (1991) ‘Social Welfare Functions on Restricted Economic Domains’, Journal of Economic Theory, vol. 53, pp. 396–427.

    Article  Google Scholar 

  • Redekop, J. (1993a) ‘Arrow-Inconsistent Economic Domains’, Social Choice and Welfare, vol. 10, pp. 127–48.

    Google Scholar 

  • Redekop, J. (1993b) ‘Social Welfare Functions on Parametric Domains’, Social Choice and Welfare, vol. 10, pp. 107–26.

    Google Scholar 

  • Redekop, J. (1995) ‘Arrow Theorems in Mixed-Goods, Dynamic, and Stochastic Environments’, forthcoming in Social Choice and Welfare.

    Google Scholar 

  • Roemer, J. (1986) ‘The Mismarriage of Bargaining Theory and Distributive Justice’, Ethics, vol. 97, pp. 88–110.

    Article  Google Scholar 

  • Sen, A. K. (1977) ‘Social Choice Theory: A Re-examination’, Econometrica, vol. 45, pp. 53–89.

    Article  Google Scholar 

  • Weymark, J. (1994) ‘Aggregating of Ordinal Probabilities on Finite Sets’, mimeo, University of British Columbia.

    Google Scholar 

  • Wilson, R. B. (1972) ‘Social Choice without the Pareto Principle’, Journal of Economic Theory, vol. 5, pp. 14–20.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universite D’aix-Marseille, France

    Michel Le Breton

Authors
  1. Michel Le Breton
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Economics, Stanford University, California, USA

    Kenneth J. Arrow

  2. Department of Economics, Harvard University, Cambridge, Massachusetts, USA

    Amartya Sen

  3. Institute of Economic Research, Hitotsubashi University, Tokyo, Japan

    Kotaro Suzumura

Copyright information

© 1997 International Economic Association

About this chapter

Cite this chapter

Le Breton, M. (1997). Arrovian Social Choice on Economic Domains. In: Arrow, K.J., Sen, A., Suzumura, K. (eds) Social Choice Re-examined. International Economic Association Series. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-25849-9_7

Download citation

Publish with us

Policies and ethics

Search

Navigation