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.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
file. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number
2001-W23.