Binary Inversions and Transitive Majorities

  • Wulf Gaertner
Conference paper


A little more than two hundred years ago, in 1785, Marie Jean Antoine Nicolas Caritat, better known as “Marquis de Condorcet”, published his “Essai sur l’application de l’analyse a la probabilité des decisions rendues à la pluralité des voix”. With some justification Condorcet can be considered as one of the founders of social choice theory. In his work Condorcet discussed, among other things, the case of consistent majority voting and — what is perhaps more interesting — the situation where majority voting generates a set of inconsistent propositions. The proposed resolution scheme for the latter case, however, was fairly vague, at least for voting procedures with more than three candidates. Actually, Condorcet never followed the idea of restricting preference profiles.


Simple Majority Extremal Restriction Strict Preference Preference Profile Social Choice Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arrow, K. J. (1951, 1963), Social Choice and Individual Values. New York: Wiley.Google Scholar
  2. Bergson, A. (1938), A Reformulation of Certain Aspects of Welfare Eco-nomics, Quarterly Journal of Economics 52, 310–334.CrossRefGoogle Scholar
  3. Black, D. (1948), On the Rationale of Group Decision-Making, Journal of Political Economy 56, 23–34.CrossRefGoogle Scholar
  4. Black, D. (1958), The Theory of Committees and Elections. Cambridge: Cambridge University Press.Google Scholar
  5. Condorcet, Marquis de (1785), Essai sur l’application de l’analyse la probabilité des decisions rendues a la pluralité des voix, Paris.Google Scholar
  6. Fishburn, P. C. (1973), The Theory of Social Choice. Princeton: Princeton University Press.Google Scholar
  7. Gaertner, W. (1977), Zum Problem der Existenz von Sozialen Wohlfahrts-funktionen im Sinne von Arrow, Zeitschrift für die gesamte Staats-wissenschaft 133, 61–74.Google Scholar
  8. Gaertner, W. and A. Heinecke (1977), On Two Sufficient Conditions for Transitivity of the Social Preference Relation, Zeitschrift für Na-tionalökonomie 37, 61–66.CrossRefGoogle Scholar
  9. Gaertner, W. and A. Heinecke (1978), Cyclically Mixed Preferences: A Necessary and Sufficient Condition for Transitivity of the Social Preference Relation, 169–185, in: Decision Theory and Social Ethics, Issues in Social Choice, ed. by. H. W. Gottinger and W. Leinfellner. Dordrecht: Reidel.Google Scholar
  10. Inada, K. (1964), A Note on the Simple Majority Decision Rule, Econometrica 32, 525–531.CrossRefGoogle Scholar
  11. Inada, K. (1969), The Simple Majority Decision Rule, Econometrica 37, 490–506.CrossRefGoogle Scholar
  12. Saposnik, R. (1975) , On Transitivity of the Social Preference Relation under Simple Majority Rule, J. Econ. Theory 10, 1–7.CrossRefGoogle Scholar
  13. Sen, A. K. (1966), A Possibility Theorem on Majority Decisions, Econometrica 34, 491–499.CrossRefGoogle Scholar
  14. Sen, A. K. (1970), Collective Choice and Social Welfare. San Francisco: Holden-Day, and Edinburgh: Oliver and Boyd.Google Scholar
  15. Sen, A. K. and Pattanaik, P. K. (1969), Necessary and Sufficient Con-ditions for Rational Choice under Majority Decision, J. Econ. Theory 1, 178–202.CrossRefGoogle Scholar
  16. Slutsky, S. (1977), A Characterization of Societies with Consistent Majority Decision, Rev. of Econ. Stud. 44, 211–225.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Wulf Gaertner
    • 1
  1. 1.Department of EconomicsUniversity of OsnabrückOsnabrückGermany

Personalised recommendations