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Social Choice and Welfare

, Volume 47, Issue 2, pp 295–314 | Cite as

Weak independence and the Pareto principle

  • Susumu CatoEmail author
Original Paper

Abstract

In this paper, the independence of irrelevant alternatives and the Pareto principle are simultaneously weakened in the Arrovian framework of social choice. Moreover, we also relax transitivity of social preferences. We show that impossibility remains under weaker versions of Arrow’s original conditions. Our results complement the recent work by Coban and Sanver (Soc Choice Welf 43(4):953–961, 2014).

JEL Classification

D63 D71 

Notes

Acknowledgments

I thank an anonymous referee of this journal and Marc Fleurbaey for their valuable comments. This paper was financially supported by JSPS KAKENHI Grant Number 26870477. I also supported by Postdoctoral Fellowships for Research Abroad of JSPS.

References

  1. Arrow KJ (1963) Social choice and individual values, 2nd edn. Wiley, New YorkGoogle Scholar
  2. Baigent N (1987) Twitching weak dictators. J Econ 47(4):407–411CrossRefGoogle Scholar
  3. Banks JS (1995) Acyclic social choice from finite sets. Soc Choice Welf 12(3):293–310CrossRefGoogle Scholar
  4. Blair DH, Pollak RA (1979) Collective rationality and dictatorship: the scope of the Arrow theorem. J Econ Theory 21(1):186–194CrossRefGoogle Scholar
  5. Blair DH, Bordes G, Kelly JS, Suzumura K (1976) Impossibility theorems without collective rationality. J Econ Theory 13(3):361–379CrossRefGoogle Scholar
  6. Blau JH (1979) Semiorders and collective choice. J Econ Theory 21(1):195–206CrossRefGoogle Scholar
  7. Border KC (1983) Social welfare functions for economic environments with and without the Pareto principle. J Econ Theory 29(2):205–216CrossRefGoogle Scholar
  8. Bordes G (1976) Consistency, rationality and collective choice. Rev Econ Stud 43(3):451–457CrossRefGoogle Scholar
  9. Bossert W, Suzumura K (2010) Consistency, choice and rationality. Harvard University Press, CambridgeGoogle Scholar
  10. Brown DJ (1975) Aggregation of preferences. Q J Econ, 89(3):456–469Google Scholar
  11. Campbell DE (1976) Democratic preference functions. J Econ Theory 12(2):259–272CrossRefGoogle Scholar
  12. Campbell DE (1990) Intergenerational social choice without the Pareto principle. J Econ Theory 50(2):414–423CrossRefGoogle Scholar
  13. Campbell DE, Kelly JS (1993) \(t\) or \(1-t\). That is the trade-off. Econometrica: J Econom Soc 61(6):1355–1365Google Scholar
  14. Campbell DE, Kelly JS (2000a) Weak independence and veto power. Econ Lett 66(2):183–189CrossRefGoogle Scholar
  15. Campbell DE, Kelly JS (2000b) Information and preference aggregation. Soc Choice Welf 17(1):3–24CrossRefGoogle Scholar
  16. Cato S (2012) Social choice without the Pareto principle: a comprehensive analysis. Soc Choice Welf 39(4):869–889CrossRefGoogle Scholar
  17. Cato S (2013) Remarks on Suzumura consistent collective choice rules. Math Soc Sci 65(1):40–47CrossRefGoogle Scholar
  18. Cato S (2014) Weak independence and social semi-orders. Jpn Econ Rev 66(3):311–321. doi: 10.1111/jere.12051
  19. Cato S (2015) Weak independent decisiveness and the existence of a unique vetoer. Econ Lett 131:59–61CrossRefGoogle Scholar
  20. Cato S, Hirata D (2010) Collective choice rules and collective rationality: a unified method of characterizations. Soc Choice Welf 34(4):611–630CrossRefGoogle Scholar
  21. Cato S, Sekiguchi Y (2012) A generalization of Campbell and Kelly’s trade-off theorem. Soc Choice Welf 38(2):237–246CrossRefGoogle Scholar
  22. Coban C, Sanver MR (2014) Social choice without the Pareto principle under weak independence. Soc Choice Welf 43(4):953–961CrossRefGoogle Scholar
  23. Fleurbaey M, Suzumura K, Tadenuma K (2005) Arrovian aggregation in economic environments: how much should we know about indifference surfaces? J Econ Theory 124(1):22–44CrossRefGoogle Scholar
  24. Fountain J, Suzumura K (1982) Collective choice rules without the Pareto principle. Int Econ Rev 23(2):299–308CrossRefGoogle Scholar
  25. Gaertner W (2001) Domain conditions in social choice theory. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  26. Kalai E, Muller E, Satterthwaite MA (1979) Social welfare functions when preferences are convex, strictly monotonic, and continuous. Public Choice 34(1):87–97CrossRefGoogle Scholar
  27. Kelly JS (1994) The free triple assumption. Soc Choice Welf 11(2):97–101CrossRefGoogle Scholar
  28. Le Breton M, Weymark JA (2011) Arrovian social choice theory on economic domains. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 2. North Holland, Amsterdam, pp 191–299CrossRefGoogle Scholar
  29. Malawski M, Zhou L (1994) A note on social choice theory without the Pareto principle. Soc Choice Welf 11(2):103–107CrossRefGoogle Scholar
  30. Mas-Colell A, Sonnenschein HF (1972) General possibility theorems for group decisions. Rev Econ Stud 39(2):185–192CrossRefGoogle Scholar
  31. Miller MK (2009) Social choice theory without Pareto: the pivotal voter approach. Math Soc Sci 58(2):251–255CrossRefGoogle Scholar
  32. Murakami Y (1968) Logic and social choice. Routledge, LondonGoogle Scholar
  33. Suzumura K (1983) Rational choice, collective decisions, and social welfare. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  34. Wilson R (1972) Social choice theory without the Pareto principle. J Econ Theory 5(3):478–486CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Social ScienceThe University of TokyoTokyoJapan

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