Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

Busetto, F.; Codognato, G.; Tonin, S.

doi:10.1007/978-3-662-46439-7_10

Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

Busetto, F.; Codognato, G.; Tonin, S.

Authors

F. Busetto

G. Codognato

S. Tonin

Contributors

C. Binder
Editor

G. Codognato
Editor

M. Teschl
Editor

Y. Xu
Editor

Abstract

In the line opened by Kalai and Muller (J Econ Theory 16:457–469, 1977), we explore new conditions on preference domains which make it possible to avoid Arrow’s impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictatorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman et al. (Math Oper Res 28:309–326, 2003; J Econ Theory 128:232–254, 2006). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.’s work and specify integer programs in which variables are allowed to assume values in the set {0,12,1}: indeed, we show that there exists a one-to-one correspondence between the solutions of an integer program defined on this set and the set of all Arrovian social welfare functions—without restrictions on the range.

Citation

Busetto, F., Codognato, G., & Tonin, S. (2015). Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach. In C. Binder, G. Codognato, M. Teschl, & Y. Xu (Eds.), Individual and collective choice and social welfare : essays in honor of Nick Baigent (149-169). Springer Verlag. https://doi.org/10.1007/978-3-662-46439-7_10

Publication Date	May 1, 2015
Deposit Date	Sep 28, 2015
Publisher	Springer Verlag
Pages	149-169
Series Title	Studies in choice and welfare
Book Title	Individual and collective choice and social welfare : essays in honor of Nick Baigent.
Chapter Number	10
DOI	https://doi.org/10.1007/978-3-662-46439-7_10
Keywords	Arrovian social welfare function, Integer programming, Nondictatorial domain.
Public URL	https://durham-repository.worktribe.com/output/1644779