Suppose a committee has to take a stand on a complex issue, where the decision presupposes answering a number of sub-questions. There is an agreement within the committee which sub-questions should be posed. All questions are of the ”yes or no?”-type and the main question is to be given the yes-answer if and only if each sub-question is answered with “yes”. Two different voting procedures can be used. On one procedure, the committee members vote on each sub-question and the voting (...) results then determine the committee’s conclusion on the main issue. This premise-based procedure (or pbp, for short) can be contrasted with the conclusion-based procedure (cbp), on which the members directly vote on the conclusion, with the vote of each member being guided by her views on the relevant sub-questions. The problem we want to examine concerns the relative advantages and disadvantages of the two procedures from the epistemic point of view. In some cases one can assume that the question before the committee has a right answer, which the committee is trying to reach. Is one of the two procedures better when it comes to tracking the truth? As it turns out, the answer to this query is not univocal: On the basis of Condorcet’s jury theorem we shall show that the premise-based procedure is clearly superior if we want to reach truth for the right reasons, i.e. without making any mistakes on the road to the conclusion. However, if the goal instead is to reach truth for whatever reasons, right or wrong, there will be special cases in which using the conclusion-based procedure turns out to be more reliable. But for the most part, the premise-based procedure will still retain its superiority. In this respect, our results disconfirm the tentative conjectures that have been put forward in Pettit and Rabinowicz (2001). (shrink)

Many studies have considered the probability that a pairwise majority rule (PMR) winner exists for three candidate elections. The absence of a PMR winner indicates an occurrence of Condorcet's Paradox for three candidate elections. This paper summarizes work that has been done in this area with the assumptions of: Impartial Culture, Impartial Anonymous Culture, Maximal Culture, Dual Culture and Uniform Culture. Results are included for the likelihood that there is a strong winner by PMR, a weak winner by PMR, and (...) the probability that a specific candidate is among the winners by PMR. Closed form representations are developed for some of these probabilities for Impartial Anonymous Culture and for Maximal Culture. Consistent results are obtained for all cultures. In particular, very different behaviors are observed for odd and even numbers of voters. The limiting probabilities as the number of voters increases are reached very quickly for odd numbers of voters, and quite slowly for even numbers of voters. The greatest likelihood of observing Condorcet's Paradox typically occurs for small numbers of voters. Results suggest that while examples of Condorcet's Paradox are observed, one should not expect to observe them with great frequency in three candidate elections. (shrink)

The two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote (...) these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect. (shrink)

Economics and Philosophy 23(3) (in press).

Journal of Theoretical Politics 19(4) (in press).

in P. Anand, C. Puppe and P. Pattaniak (eds.), Oxford Handbook of Rational and Social Choice, Oxford (Oxford University Press) (forthcoming).