Aggregating sets of judgments : two impossibility results compared

List, Christian ORCID: 0000-0003-1627-800X and Pettit, Philip (2004) Aggregating sets of judgments : two impossibility results compared. Synthese, 140 (1-2). 207 -235. ISSN 1573-0964

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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.

Item Type:	Article
Official URL:	http://springerlink.metapress.com/openurl.asp?genr...
Additional Information:	Published 2004 © Springer. The original publication is available at www.springerlink.com. LSE has developed LSE Research Online so that users may access research output of the School. Copyright and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (<http://eprints.lse.ac.uk>) of the LSE Research Online website.
Divisions:	Government Philosophy, Logic and Scientific Method CPNSS
Subjects:	J Political Science > JA Political science (General)
Date Deposited:	10 Mar 2006
Last Modified:	11 Dec 2024 22:50
URI:	http://eprints.lse.ac.uk/id/eprint/665

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