• Satish Kumar JainEmail author


The chapter introduces the subject matter of the monograph, namely, the derivation of Inada-type conditions for transitivity and quasi-transitivity under various rules and classes of rules, and spells out the plan of the book. The notions of sufficient conditions for transitivity (quasi-transitivity), Inada-type necessary conditions for transitivity (quasi-transitivity), and Inada-type necessary and sufficient conditions for transitivity (quasi-transitivity) are rigourously defined.


  1. Arrow, Kenneth J. 1951. Social choice and individual values, 2nd ed., 1963. New York: Wiley.Google Scholar
  2. Batra, Raveendra, and Prasanta K. Pattanaik. 1971. Transitivity of social decisions under some more general group decision rules than the method of majority voting. Review of Economic Studies 38: 295–306.CrossRefGoogle Scholar
  3. Batra, Raveendra, and Prasanta K. Pattanaik. 1972. Transitive multi-stage majority decisions with quasi-transitive individual preferences. Econometrica 40: 1121–1135.MathSciNetCrossRefGoogle Scholar
  4. Black, D. 1948. On the rationale of group decision making. The Journal of Political Economy 56: 23–34.CrossRefGoogle Scholar
  5. Black, Duncan. 1958. The theory of committees and elections. London: Cambridge University Press.zbMATHGoogle Scholar
  6. Condorcet, Marquis de. 1785. Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. Paris.Google Scholar
  7. Dummett, Michael, and Robin Farquharson. 1961. Stability in voting. Econometrica 29: 33–43.MathSciNetCrossRefGoogle Scholar
  8. Fine, Kit. 1973. Conditions for the existence of cycles under majority and non-minority rules. Econometrica 41: 888–899.MathSciNetCrossRefGoogle Scholar
  9. Fishburn, Peter C. 1970b. Conditions for simple majority decision with intransitive individual indifference. Journal of Economic Theory 2: 354–367.Google Scholar
  10. Fishburn, Peter C. 1972. Conditions on preferences that guarantee a simple majority winner. The Journal of Mathematical Sociology 2: 105–112.CrossRefGoogle Scholar
  11. Fishburn, Peter C. 1973. The theory of social choice. Princeton: Princeton University Press.zbMATHGoogle Scholar
  12. Gaertner, Wulf. 1988. Binary inversions and transitive majorities. In Measurement in economics, ed. Wolfgang Eichhorn, 253–267. Berlin: Springer.CrossRefGoogle Scholar
  13. Gaertner, Wulf. 2001. Domain conditions in social choice theory. London: Cambridge University Press.CrossRefGoogle Scholar
  14. Gaertner, Wulf, and Achim Heinecke. 1977. On two sufficient conditions for transitivity of the social preference relation. Zeitschrift für Nationalökonomie 37: 61–66.CrossRefGoogle Scholar
  15. Gaertner, Wulf, and Achim Heinecke. 1978. Cyclically mixed preferences - A necessary and sufficient condition for transitivity of the social preference relation. In Decision theory and social ethics, ed. Hans W. Gottinger, and Werner Leinfellner, 169–186. Dordrecht: D. Reidel.CrossRefGoogle Scholar
  16. Inada, Ken-ichi. 1964. A note on the simple majority decision rule. Econometrica 32: 525–531.MathSciNetCrossRefGoogle Scholar
  17. Inada, Ken-ichi. 1969. The simple majority decision rule. Econometrica 37: 490–506.CrossRefGoogle Scholar
  18. Inada, Ken-ichi. 1970. Majority rule and rationality. Journal of Economic Theory 2: 27–40.MathSciNetCrossRefGoogle Scholar
  19. Jain, Satish K. 1983. Necessary and sufficient conditions for quasi-transitivity and transitivity of special majority rules. Keio Economic Studies 20: 55–63.Google Scholar
  20. Jain, Satish K. 1984. Non-minority rules: Characterization of configurations with rational social preferences. Keio Economic Studies 21: 45–54.Google Scholar
  21. Jain, Satish K. 1985. A direct proof of Inada-Sen-Pattanaik theorem on majority rule. The Economic Studies Quarterly 36: 209–215.Google Scholar
  22. Jain, Satish K. 1986a. Special majority rules: Necessary and sufficient condition for quasi-transitivity with quasi-transitive individual preferences. Social Choice and Welfare 3: 99–106.Google Scholar
  23. Jain, Satish K. 1986b. Semi-strict majority rules: Necessary and sufficient conditions for quasi-transitivity and transitivity. Unpublished manuscript. Centre for Economic Studies and Planning, Jawaharlal Nehru University.Google Scholar
  24. Jain, Satish K. 1987. Maximal conditions for transitivity under neutral and monotonic binary social decision rules. The Economic Studies Quarterly 38: 124–130.Google Scholar
  25. Jain, Satish K. 1989. Characterization theorems for social decision rules which are simple games. Paper presented at the IX World Congress of the International Economic Association, Economics Research Center, Athens School of Economics & Business, Athens, Greece, held on Aug 28 - Sep 1, 1989.Google Scholar
  26. Jain, Satish K. 1991. Non-minority rules: Necessary and sufficient condition for quasi-transitivity with quasi-transitive individual preferences. Keio Economic Studies 28: 21–27.Google Scholar
  27. Jain, Satish K. 2009. The method of majority decision and rationality conditions. In Ethics, welfare, and measurement, Volume 1 of Arguments for a better world: Essays in honor of Amartya Sen, ed. Kaushik Basu, and Ravi Kanbur, 167–192. New York: Oxford University Press.Google Scholar
  28. Kelly, J.S. 1974. Necessity conditions in voting theory. Journal of Economic Theory 8: 149–160.MathSciNetCrossRefGoogle Scholar
  29. Murakami, Yasusuke. 1968. Logic and social choice. London: Routledge & Kegan Paul.Google Scholar
  30. Nicholson, Michael B. 1965. Conditions for the ‘voting paradox’ in committee decisions. Metroeconomica 7: 29–44.CrossRefGoogle Scholar
  31. Pattanaik, Prasanta K. 1970. On social choice with quasitransitive individual preferences. Journal of Economic Theory 2: 267–275.MathSciNetCrossRefGoogle Scholar
  32. Pattanaik, Prasanta K. 1971. Voting and collective choice. Cambridge: Cambridge University Press.Google Scholar
  33. Pattanaik, Prasanta K., and Manimay Sengupta. 1974. Conditions for transitive and quasi-transitive majority decisions. Economica 41: 414–423.CrossRefGoogle Scholar
  34. Saposnik, Rubin. 1975. On the transitivity of the social preference relation under simple majority rule. Journal of Economic Theory 10: 1–7.MathSciNetCrossRefGoogle Scholar
  35. Sen, Amartya K. 1966. A possibility theorem on majority decisions. Econometrica 34: 491–499.CrossRefGoogle Scholar
  36. Sen, Amartya K. 1970. Collective choice and social welfare. San Francisco: Holden-Day.zbMATHGoogle Scholar
  37. Sen, Amartya K., and Prasanta K. Pattanaik. 1969. Necessary and sufficient conditions for rational choice under majority decision. Journal of Economic Theory 1: 178–202.MathSciNetCrossRefGoogle Scholar
  38. Slutsky, Steven M. 1977. A characterisation of societies with consistent majority decision. Review of Economic Studies 44: 211–225.CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Formerly ProfessorJawaharlal Nehru UniversityNew DelhiIndia

Personalised recommendations