Skip to main content
SpringerLink
Log in

Decisive sets, majority voting and the existence of a group preference function

  • Published:
De Economist Aims and scope Submit manuscript

Summary

The constitutional process in a democratic society is examined by analysing the role ofdecisive sets in determining the preferences of the entire population. Firstly we consider the properties of sets which emerge from a group preference function satisfying the four conditions set by Arrow. Secondly we reverse the analysis and define first a set of desirable properties of the decisive sets. We then prove that under these fairly general conditions a group preference function exists for which all four of Arrow's conditions are simultaneously satisfied.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arrow, K.J.,Social Choice and Individual Values, 2nd edition, New York, 1963.

  2. Bell, J.L. and A.B. Solomon,Models and Ultraproducts: An Introduction, Amsterdam, 1969.

  3. Booth, D., “Ultrafilters on Countable Sets,”Annals of Mathematical Logic, 11 (1970).

  4. Bourbaki, N.,General Topology, Paris, 1966.

  5. Comfort, W.W. and S. Negrepontis,The Theory of Ultrafilters, Berlin-New York, 1974.

  6. Fishburn, P.C., “Arrow's Impossibility Theorem: Concise Proof and Infinite Voters,”Journal of Economic Theory, II (1970), pp. 103–106.

    Google Scholar 

  7. Hansson, B., “The Existence of Group Preference Functions,”Public Choice, XXVIII (1976), pp. 89–97.

    Google Scholar 

  8. Kirman, A.P. and D. Sondermann, “Arrow's Theorem, Many Agents and Invisible Dictators,” Journal of Economic Theory, V (1972), pp. 267–277.

    Google Scholar 

  9. Salles, M., “A General Possibility Theorem for Group Decision Rules with ParetoTransitivity,rd Journal of Economic Theory, XI (1975), pp. 110–118.

    Google Scholar 

  10. Saposnic, R., “On Transitivity of the Social Preference Relation under Simple Majority Rule,” Journal of Economic Theory, X (1975), pp. 1–7.

    Google Scholar 

  11. Sen, A.K.,Collective Choice and Social Welfare, New York, 1970.

  12. Sen, A.K., “Quasi-Transitivity, Rational Choice and Collective Decisions,”Review of Economic Studies, XXXVI (1969).

  13. Wolf, R.P., InDefense of Anarchy, New York, 1970.

Download references

Author information

Authors and Affiliations

  1. Department of Agricultural Economics, he Hebrew University of Jerusalem, Rehovot, Israel

    David Bigman

Authors
  1. David Bigman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

I wish to thank Peter Newman, an anonymous referee and the editor of this Journal for helpful comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bigman, D. Decisive sets, majority voting and the existence of a group preference function. De Economist 129, 241–252 (1981). https://doi.org/10.1007/BF01705810

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01705810

Keywords

Search

Navigation