Dictatorial domains in preference aggregation

Ugur Ozdemir*, M. Remzi Sanver

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We call a domain of preference orderings "dictatorial" if there exists no Arrovian (Pareto optimal, IIA and non-dictatorial) social welfare function defined over that domain. In a finite world of alternatives where indifferences are ruled out, we identify a condition which implies the dictatoriality of a domain. This condition, to which we refer as "being essentially saturated", is fairly weak. In fact, independent of the number of alternatives, there exists an essentially saturated (hence dictatorial) domain which consists of precisely six orderings. Moreover, this domain exhibits the superdictatoriality property, i.e., every superdomain of it is also dictatorial. Thus, given m alternatives, the ratio of the size of a superdictatorial domain to the size of the full domain may be as small as 6/m!, converging to zero as m increases.

Original languageEnglish
Pages (from-to)61-76
Number of pages16
JournalSocial Choice and Welfare
Volume28
Issue number1
Early online date12 Aug 2006
DOIs
Publication statusPublished - Jan 2007

Keywords

  • social choice
  • social welfare function
  • preference aggregation
  • social choice function
  • full domain

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