We consider situations of multiple referendum: finitely many yes-or-no issues have to be socially assessed from a set of approval ballots, where voters approve as many issues as they want. Each approval ballot is extended to a complete preorder over the set of outcomes by means of a preference extension. We characterize, under a mild richness condition, the largest domain of top-consistent and separable preference extensions for which issue-wise majority voting is Pareto efficient, i.e., always yields out a Pareto-optimal outcome. (...) Top-consistency means that voters’ ballots are their unique most preferred outcome. It appears that the size of this domain becomes negligible relative to the size of the full domain as the number of issues increases. (shrink)

An electoral evaluation of a set of expert opinions proceeds by treating the experts as voters. Although this method allows us to formalise our naive views about how to take expert advice, the formalisations are plagued by paradoxes which parallel those found in literature on social aggregation devices. This parallel suggests that our naive views about taking expert advice are in as much need of revision as our naive views about deriving group preferences from individual preferences. * I am indebted (...) to Joseph Hanna for a number of criticisms and corrections to a previous draft. (shrink)

Suppose n Bayesian agents need to make a decision as a group. The groupas a whole is also supposed to be a Bayesian agent whose probabilities andutilities are derived or aggregated in reasonable ways from the probabilitiesand utilities of the group members. The aggregation could beex ante, i.e., interms of expected utilities, or it could be ex post, i.e., in terms of utilitiesonly, or in terms of utilities and probabilities separately. This study exploresthe ex post approach. Using the Bolker/Jeffrey framework, (...) we show thatex post aggregation is subject to an instability phenomenon. That is, it mayhappen that the group preference between actions ``flips back and forth'''' dependingon the level of detail in which the decision problem is described. Structurally verysimilar phenomena also occur elsewhere in social choice theory, in statistics (Simpson''sParadox), and in voting theory (Ostrogorski''s Paradox). (shrink)

The ``doctrinal paradox'' or ``discursive dilemma'' shows that propositionwise majority voting over the judgments held by multiple individuals on some interconnected propositions can lead to inconsistent collective judgments on these propositions. List and Pettit (2002) have proved that this paradox illustrates a more general impossibility theorem showing that there exists no aggregation procedure that generally produces consistent collective judgments and satisfies certain minimal conditions. Although the paradox and the theorem concern the aggregation of judgments rather than preferences, they invite comparison (...) with two established results on the aggregation of preferences: the Condorcet paradox and Arrow's impossibility theorem. We may ask whether the new impossibility theorem is a special case of Arrow's theorem, or whether there are interesting disanalogies between the two results. In this paper, we compare the two theorems, and show that they are not straightforward corollaries of each other. We further suggest that, while the framework of preference aggregation can be mapped into the framework of judgment aggregation, there exists no obvious reverse mapping. Finally, we address one particular minimal condition that is used in both theorems – an independence condition – and suggest that this condition points towards a unifying property underlying both impossibility results. (shrink)

The budget-voting paradox states that, when social alternatives are proper subsets of a finite set of decisions, choosing decision-wise according to the majority rule may select an alternative that is covered in the majority tournament among alternatives. Individual preferences are defined on single decisions, and are extended to preferences over the alternative set by means of a preference extension rule. We prove the existence of the paradox for any rank-based, monotone, and independent extension rule.

In JAP 9 (1992) Gordon Graham argued that liberals cannot be counted on to support democratic institutions since there are no conceptual or strongly contingent links between democracy and liberal ideals. This paper responds to Graham's challenge by claiming that his model of liberal aristocracy is not liberal in several respects. In particular, the liberal should recognise a right to democratic participation which individuals may plausibly claim as an element in a respectable conception of how to live well. The right (...) to democratic participation is shown to stand alongside other important liberal ideals which may be justified in this fashion, e.g. freedom of religious worship and freedom of association. Furthermore, I argue against those who claim that political participation enacts delusory aspirations that the rights which are promoted and protected within a democratic constitution are necessary for both individual and collective autonomy — and so the liberal should defend them. (shrink)

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 , 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. (shrink)

Os mais importantes paradoxos de decisáo social, ou seja, de votaçáo sáo apresentados. A apresentaçáo indica tanto a origem dos paradoxos discutidos quanto uma breve discussáo das mais importantes tentativas de os resolver. Sáo considerados paradoxos em que a regra de votaçáo preve ruma igualdade de peso entre os eleitores, bem como paradoxos com regras altemativas de votaçáo. A democracia tem se firmado entre a grande maioria dos povos como a maneira mais justa de organizaçáo social e , especialmente em (...) se tratando da esco lha das autoridades de uma democracia representativa, em quase axiomático 0 uso da regra da igualdade de peso de cada eleitor, embora outras regras tambem sejam usadas em clubes, instituições finançeiras e outros bastante conhecido, porem que tanto o proprio conceito de democracia quanto a referida a regra de escolh sáo isentas de problemas e, em especial, geram certos paradoxos. Assim passa-se em revista aqui alguns dos mais importantesparadoxos eleitorais, sem a pretensáo de resoIve-los", mas com o intuito de ampliar a discussao critica e portanto, fortalecer praticas politicas desejaveis. (shrink)