Strategy-Proof Social Choice Correspondences and Single Peaked

  1. Carmelo Rodríguez-Álvarez 1
  1. 1 Instituto Complutense de Análisis Económico Universidad Complutense de Madrid
Revista:
Documentos de Trabajo (ICAE)

ISSN: 2341-2356

Año de publicación: 2024

Número: 2

Páginas: 1-19

Tipo: Documento de Trabajo

DIALNET GOOGLE SCHOLAR lock_openDocta Complutense editor

Otras publicaciones en: Documentos de Trabajo (ICAE)

Resumen

We examine social choice correspondences (SCCs) -mappings from preference profiles to sets of alternatives- that satisfy strategy-proofness and unanimity when individuals are endowed with single-peaked preferences over alternatives, preferences over sets are consistent with Expected Utility Theory, uniform prior probabilities, and Bayesian Updating. Leveraging the relation between SCCs and probabilistic decision schemes -mappings from preference profiles to lotteries over alternatives- we extend the results by Ingalagavi and Sadhukhan (2023, Journal of Mathematical Economics 109, 102912). In one-dimensional spaces of alternatives, only the union of two single-valued strategy-proof SCCs satisfy strategy-proofness and unanimity. In multi-dimensional convex spaces of alternatives, only unions of up to two dictatorships satisfy both properties.

Referencias bibliográficas

  • Barbera`, S. (2011) “Strategy-proof social choice”, in by K.J. Arrow, A.K. Sen, K. Suzu- mura (eds) “Handbook of Social Choice and Welfare. Volume 2”. Elsevier. North– Holland, Amsterdam.
  • Barbera`, S., Dutta, B., Sen, A. (2001) Strategy–proof social choice correspondences. Jour- nal of Economic Theory 101: 374–394.
  • Barbera`, S., Gul, F., Stacchetti, E. (1993) Generalized median voter schemes. Journal of Economic Theory 61: 262–289.
  • Bhattacharya, M., O. Khare (2024) Strategy-proof interval-social choice correspondences over extended single-peaked domains. International Journal of Game Theory, forthcoming.
  • Dutta, B., Peters, H., Sen, A. (2002) Strategy-proof probabilistic mechanisms in economies with pure public goods. Journal of Economic Theory 106: 392–416 .
  • Ehlers, L., Peters, H., Storcken, T. (2002) Probabilistic collective decision schemes for one dimensional single peaked preferences. Journal of Economic Theory 105, 408–434.
  • Feldman, A. (1980) Strongly non manipulable multi–valued collective choice rules. Public Choice 35: 503–509.
  • Gibbard, A. (1973) Manipulation of voting schemes: A general result. Econometrica 41: 587–601.
  • Gibbard, A. (1977) Manipulation of voting schemes that mix voting with chance. Econo- metrica 45: 665-681.
  • Heo, E.J. (2013) Strategy-proof rules for two public goods: Double median rules. Social Choice and Welfare 41: 895–922.
  • Ingalagavi, C., Sadhukhan, T. (2023) On a class of strategy-proof social choice correspondences with single-peaked utility functions. Journal of Mathematical Economics, 109, Art. 102912.
  • Klaus, B., Protopapas, P. (2020) On strategy-proofness and single- peakedness: median- voting over intervals. International Journal of Game Theory 49, 1059–1080.
  • Klaus. B., Storcken, T. (2002) Choice correspondences for public goods. Social Choice and Welfare 19: 127–154.
  • Miyagawa, E. (1998) Mechanisms for providing a menu of public goods’.Thesis Disserta- tion, University of Rochester. Rochester, NY.
  • Miyagawa, E. (2001) Locating libraries on a street. Social Choice and Welfare 18, 527– 541.
  • Moulin, H. (1980) On strategy-proofness and single-peakedness. Public Choice 35: 437– 455.
  • Peters, H., Roy, S. , Sen, A., Storcken, T. (2014) Probabilistic strategy- proof rules over single-peaked domains, Journal of Mathematical Economics 52, 123–127.
  • Rodríguez-Álvarez, C. (2017) On single-peakedness and strategy- proofness: Ties between adjacent alternatives. Economics Bulletin 37, 1966–1974.
  • Rodríguez-Álvarez, C. (2024) Strategy-proof interval selection. Working Paper ICAE- Universidad Complutense de Madrid.
  • Satterthwaite, M.A. (1975) Strategy-proofness and Arrow’s conditions: Existence and correspondence theorems for voting procedure and social welfare functions. Journal of Economic Theory 10:187-217
  • Zhou, L. (1991) Impossibility of strategy-proof mechanisms in economies with pure public goods, Review of Economics Studies 58: 107–119
Fuente de los datos: Dialnet