Aggregating sets of judgments: Two impossibility results compared

Synthese 140 (1-2):207 - 235 (2004)
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Abstract

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.

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Author Profiles

Christian List
Ludwig Maximilians Universität, München
Philip Pettit
Australian National University

Citations of this work

Dynamic logic for belief revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.
Arrow's theorem in judgment aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.

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References found in this work

Social Choice and Individual Values.Irving M. Copi - 1952 - Science and Society 16 (2):181-181.
Social Choice and Individual Values.Kenneth Joseph Arrow - 1951 - New York, NY, USA: Wiley: New York.
Social Choice Theory and Deliberative Democracy: A Reconciliation.Christian List & John Dryzek - 2003 - British Journal of Political Science 33 (1):1-28.
A model of path-dependence in decisions over multiple propositions.Christian List - 2004 - American Political Science Review 98 (3):495-513.

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