Public Choice

, Volume 130, Issue 3–4, pp 395–400 | Cite as

1 dictator = 2 voters

Original Article


For the case of strict preferences, a measure of a voter’s average power in a dictatorial social welfare function is defined making the dictator never have more average power than three voters and, as the number of voters grows, making the dictator average power converge to the average power of two voters. This result suggests, as those in Tangian (2004), that dictatorial social welfare functions might not be as undesirable aggregation rules as traditionally held.


Arrow’s theorem Social welfare function Strict preference Voters’ power 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arrow, K. (1963). Social choice and individual values (2nd edn). New York: Wiley.Google Scholar
  2. Brualdi, R.A. (1999). Introductory combinatorics (3rd edn). Upper Saddle River, New Jersey: Prentice Hall.Google Scholar
  3. Tangian, A. (2003). Combinatorial and probabilistic investigation of Arrow’s paradox, Diskussionsbeitrag Nr. 336 des Fachbereichs Wirtschaftswissenschaft der FernUniversität Hagen, Hagen. Retrieved from
  4. Tangian, A. (2004). How dictatorial are Arrow’s dictators? (Paper presented at the 7th International Meeting of the Society for Social Choice and Welfare, Osaka).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Departament d’EconomiaUniversitat Rovira i VirgiliReusSpain

Personalised recommendations