Complex Collective Decisions and the Probability of Collective Inconsistencies
AbstractMany groups are required to make collective decisions over multiple interconnected propositions. The "doctrinal paradox" or "discursive dilemma" shows that propostionwise majority voting can lead to inconsistent collective outcomes, even when the judgments of individual group members are consistent. How likely is the occurence of this paradox? This paper develops a simple model for determining the probability of the paradox's occurrence, given various assumptions about the probability of different individual judgments. Several convergence results will be proved, identifying conditions under which the probability of the paradox's occurrence converges to certainty as the number of individuals increases, and conditions under which that probability vanishes. The present model will also be used for assessing the "truth-tracking" performance of two escape-routes from the paradox, the premise- and conclusion-based procedures. Finally, the results on the probability of the doctrinal paradox will be compared with existing results on the probability of Condorcet's paradox of cyclical preferences. It will be suggested that the doctrinal paradox is more likely to occur than Condorcet's paradox.
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Bibliographic InfoPaper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2001-W23.
Length: 32 pages
Date of creation: 13 Nov 2001
Date of revision:
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Web page: http://www.nuff.ox.ac.uk/economics/
Find related papers by JEL classification:
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-12-14 (All new papers)
- NEP-CDM-2001-12-14 (Collective Decision-Making)
- NEP-HPE-2001-12-14 (History & Philosophy of Economics)
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