2018/28 | LEM Working Paper Series | ||||||||||||||||
Towards a Unified Aggregation Framework for Preferences and Judgements |
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Luigi Marengo, Simona Settepanella and Yan X. Zhang |
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Abstract | |||||||||||||||||
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 im- possibility
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 ex- pressive” 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.
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