Advertisement

Inductive Reasoning in Social Choice Theory

  • Fernando TohméEmail author
  • Federico Fioravanti
  • Marcelo Auday
Article

Abstract

The usual procedure in the theory of social choice consists in postulating some desirable properties which an aggregation procedure should verify and derive from them the features of a corresponding social choice function and the outcomes that arise at each possible profile of preferences. In this paper we invert this line of reasoning and try to infer, up from what we call social situations (each one consisting of a profile and the associated social ordering) the criteria verified in the implicit aggregation procedure. This inference process, which extracts intensional from extensional information can be seen as an exercise in “qualitative statistics”.

Keywords

Induction Aggregation Social situations 

Notes

References

  1. Arrow, K. (1951). Social choice and individual values. New York: Wiley.Google Scholar
  2. Austen-Smith, D., & Banks, J. (1998). Positive political theory I: Collective preference. Ann Arbor, MI: The University of Michigan Press.Google Scholar
  3. Baryshnikov, Y. (1997). Topological and discrete social choice: In a search of a theory. Social Choice and Welfare, 14, 199–209.CrossRefGoogle Scholar
  4. Brown, D. (1974). An approximate solution to Arrow’s problem. Journal of Economic Theory, 9, 375–383.CrossRefGoogle Scholar
  5. Campbell, D., & Kelly, J. (1997). Preference aggregation. Mathematica Japonica, 45, 573–593.Google Scholar
  6. Chichilnisky, G. (1980). Social choice and the topology of spaces of preferences. Advances in Mathematics, 37, 165–176.CrossRefGoogle Scholar
  7. Fishburn, P. (1987). Interprofile conditions and impossibility. Chur: Harwood Academic Publishers‘.Google Scholar
  8. Hansson, B. (1976). The existence of group preferences. Public Choice, 28, 89–98.CrossRefGoogle Scholar
  9. Hurwicz, L. (1960). Optimality and informational efficiency in resource allocation processes. In K. Arrow, S. Karlin, & P. Suppes (Eds.), Mathematical methods in the social sciences. Stanford, CA: Stanford University Press.Google Scholar
  10. Hurwicz, L., & Reiter, S. (2001). Transversals, systems of distinct representatives, mechanism design and matching. Review of Economic Design, 6, 289–304.CrossRefGoogle Scholar
  11. Kirman, A., & Sondermann, D. (1972). Arrow’s theorem, many agents and invisible dictators. Journal of Economic Theory, 5, 267–277.CrossRefGoogle Scholar
  12. Kolany, A. (1993). On the logic of hypergraphs, in computational logic and proof theory. Berlin: Springer.Google Scholar
  13. Lauwers, L. (2000). Topological social choice. Mathematical Social Sciences, 40, 1–39.CrossRefGoogle Scholar
  14. Mount, K., & Reiter, S. (1974). The informational size of message spaces. Journal of Economic Theory, 8, 161–192.CrossRefGoogle Scholar
  15. Reichelstein, S., & Reiter, S. (1988). Game forms with minimal message spaces. Econometrica, 56, 661–692.CrossRefGoogle Scholar
  16. Reiter, S. (1977). Information and performance in the (new)\(^{2}\) welfare economics. American Economic Review, 67, 226–234.Google Scholar
  17. Shoenfield, J. (1967). Mathematical logic. Reading, MA: Addison-Wesley.Google Scholar
  18. Smullyan, R. (1995). First-order logic. New York: Dover.Google Scholar
  19. Stigum, B. (1990). Toward a formal science of economics. Cambridge, MA: MIT Press.Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Universidad Nacional del SurBahía BlancaArgentina
  2. 2.INMABB (CONICET - UNS)Bahía BlancaArgentina

Personalised recommendations