Towards a Unified Aggregation Framework for Preferences and Judgements

The "doctrinal paradox", also called "discursive dilemma", shows that the aggregation of judgements held by different individuals is problematic and can lead to group-level inconsistencies, although each individual is consistent. This aggregation problem has intuitive similarities with the Condorcet paradox in the aggregation of preferences. Indeed, List and Pettit (2002) proved an impossibility theorem in the framework of judgement aggregation, analogous to Arrow's Theorem from the framework of preference aggregation. However, List and Pettit (2004) claim that the judgement aggregation framework is "more expressive" than the classical social choice framework, in the sense that while the framework of preference aggregation can be mapped into the framework of judgement aggregation, there exists no obvious reverse mapping. In this paper we show instead that the social choice framework has enough power to express the judgement aggregation framework. To do so, we present a graph-theoretic version of the social choice framework and show that it is sufficient to embed the judgement aggregation framework. As an application of this framework, we show that the doctrinal paradox and Condorcet's paradox (both under the majority aggregation rule) arise for essentially the same reason.