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Economic Theory Bulletin

, Volume 6, Issue 1, pp 1–13 | Cite as

On the ultrafilter representation of coalitionally strategy-proof social choice functions

  • Surekha Rao
  • Achille Basile
  • K. P. S. Bhaskara Rao
Research Article
  • 77 Downloads

Abstract

By means of a simple new characterization of ultrafilters, we elementarily prove, in the case of finitely many alternatives and arbitrarily large societies, that every coalitionally strategy-proof social choice function with at least three alternatives in its range is given by an ultrafilter. This provides an alternate and simple proof of results in Mihara (Soc Choice Welf 17:393–402, 2000). In case there are only two alternatives in the range of a coalitionally strategy-proof social choice function, we describe its structure, supplementing the work of Barberà et al. (Int J Game Theory 41:791–808, 2012).

Keywords

Social choice functions Coalitional strategy proofness Gibbard–Satterthwaite theorem Ultrafilters 

Mathematics Subject Classification

91B14 

JEL Classification

D71 

References

  1. Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis. Springer, Berlin (2006)Google Scholar
  2. Barberà, S., Berga, D., Moreno, B.: Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results. Int. J. Game Theory 41, 791–808 (2012)CrossRefGoogle Scholar
  3. Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41, 587–601 (1973)CrossRefGoogle Scholar
  4. Ishikawa, S., Nakamura, K.: The strategy-proof social choice functions. J. Math. Econ. 6, 283–295 (1979)CrossRefGoogle Scholar
  5. Kirman, A.P., Sondermann, D.: Arrow’s theorem, many agents and invisible dictators. J. Econ. Theory 5, 267–277 (1972)CrossRefGoogle Scholar
  6. Mihara, H.R.: Coalitionally strategy proof functions depend only on the most-preferred alternatives. Soc. Choice Welf. 17, 393–402 (2000)CrossRefGoogle Scholar
  7. Mihara, H.R.: Existence of a coalitionally strategy proof social choice function: a constructive proof. Soc. Choice Welf. 18, 543–553 (2001)CrossRefGoogle Scholar
  8. Pazner, E.A., Wesley, E.: Stability of social choices in infinitely large societies. J. Econ. Theory 14, 252–262 (1977)CrossRefGoogle Scholar
  9. Satterthwaite, M.A.: Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J. Econ. Theory 10, 187–217 (1975)CrossRefGoogle Scholar
  10. Schmeidler, D., Sonnenschein, H.: Two proofs of the Gibbard–Satterthwaite Theorem on the possibility of a strategy-proof social choice function. In: Gottinger, H.W., Leinfellner, W. (eds.) Decision Theory and Social Ethics, pp. 227–234. Reidel Publishing Company, Dordrecht (1978)CrossRefGoogle Scholar

Copyright information

© Society for the Advancement of Economic Theory 2017

Authors and Affiliations

  • Surekha Rao
    • 1
  • Achille Basile
    • 2
  • K. P. S. Bhaskara Rao
    • 3
  1. 1.School of Business and EconomicsIndiana University NorthwestGaryUSA
  2. 2.Dipartimento di Scienze Economiche e StatisticheUniversità Federico IINaplesItaly
  3. 3.Department of Computer Information SystemsIndiana University NorthwestGaryUSA

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