Synthese

, Volume 163, Issue 2, pp 227–243 | Cite as

On the role of language in social choice theory

Article

Abstract

Axiomatic characterization results in social choice theory are usually compared either regarding the normative plausibility or regarding the logical strength of the axioms involved. Here, instead, we propose to compare axiomatizations according to the language used for expressing the axioms. In order to carry out such a comparison, we suggest a formalist approach to axiomatization results which uses a restricted formal logical language to express axioms. Axiomatic characterization results in social choice theory then turn into definability results of formal logic. The advantages of this approach include the possibility of non-axiomatizability results, a distinction between absolute and relative axiomatizations, and the possibility to ask how rich a language needs to be to express certain axioms. We argue for formal minimalism, i.e., for favoring axiomatizations in the weakest language possible.

Keywords

Social choice theory Logic Judgment aggregation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arrow K. (1951). Social choice and individual values. Yale University Press.Google Scholar
  2. Campbell D., Kelly J. (2000). A simple characterization of majority rule. Economic Theory 15, 689–700CrossRefGoogle Scholar
  3. Enderton, H. (1972). A mathematical introduction to logic. Academic Press.Google Scholar
  4. Gibbard A. (1973). Manipulation of voting schemes: A general result. Econometrica, 41, 587–601CrossRefGoogle Scholar
  5. Hintikka, J. (1996). The principles of mathematics revisited. Cambridge University Press.Google Scholar
  6. List, C. http://personal.lse.ac.uk/LIST/doctrinalparadox.htm.Google Scholar
  7. List C., Pettit P. (2002). Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18, 89–110Google Scholar
  8. Maskin, E. (1995). Majority rule, social welfare functions, and game forms. In K. Basu, P. Pattanaik, & K. Suzumura (Eds.), Choice, welfare, and development (pp. 100–109). Oxford University Press.Google Scholar
  9. May K.O. (1952). A set of independent necessary and sufficient conditions for simple majority decision. Econometrica 20, 680–684CrossRefGoogle Scholar
  10. Pauly, M. (2007) Axiomatizing collective judgment sets in a minimal logical language. Synthese, 158(2), 233-250.Google Scholar
  11. Roberts K. (1980). Social choice theory: The single-profile and multi-profile approaches. Review of Economic Studies 47, 441–450CrossRefGoogle Scholar
  12. Rubinstein A. (1984). The single profile analogues to multi profile theorems: Mathematical logic’s approach. International Economic Review 25, 719–730CrossRefGoogle Scholar
  13. Satterthwaite M. (1975). Strategy-proofness and arrow’s conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10, 187–217CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of PhilosophyStanford UniversityStanfordUSA

Personalised recommendations