Complex Collective Decisions and the Probability of Collective Inconsistencies
Many 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.
When requesting a correction, please mention this item's handle: RePEc:nuf:econwp:0123. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Maxine Collett)
If references are entirely missing, you can add them using this form.