Social Choice and Welfare

, Volume 24, Issue 1, pp 3–32

The probability of inconsistencies in complex collective decisions

Article

DOI: 10.1007/s00355-003-0253-7

Cite this article as:
List, C. Soc Choice Welfare (2005) 24: 3. doi:10.1007/s00355-003-0253-7

Abstract.

Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the probability of the paradox converges to 1, and when it converges to 0, as the number of individuals increases. Drawing on the Condorcet jury theorem and work by Bovens and Rabinowicz (2001, 2003), I use the model to assess the “truth-tracking” performance of two decision procedures, the premise- and conclusion-based procedures. I compare the present results with existing results on the probability of Condorcet’s paradox. I suggest that the doctrinal paradox is likely to occur under plausible conditions.

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.SPT Program, Research School of Social SciencesAustralian National UniversityCanberraAustralia
  2. 2.Department of GovernmentLondon School of EconomicsLondonU.K