Article
Judgement aggregation functions and ultraproducts
University Library of Munich, Germany, MPRA Paper 01/2008;
Source: RePEc

Article: Systematic judgment aggregators: An algebraic connection between social and logical structure
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ABSTRACT: We present several results that show that systematic (complete) judgment aggregators can be viewed as both (2valued) Boolean homomorphisms and as syntatic versions of reduced (ultra)products. Thereby, Arrovian judgment aggregators link the Boolean algebraic structures of (i) the set of coalitions (ii) the agenda, and (iii) the set of truth values of collective judgments. Since filters arise naturally in the context of Boolean algebras, these findings provide an explanation for the extraordinary effectiveness of the filter method in abstract aggregation theory.  [Show abstract] [Hide abstract]
ABSTRACT: In a paper published in 1952, the French matematician GeorgesTh�odule Guilbaud has generalized Arrow's impossibility result to the "logical problem of aggregation", thus anticipating the literature on abstract aggregation theory and judgment aggregation. We reconstruct the proof of Guilbaud's theorem, which is also of technical interest, because it can be seen as the first use of ultrafilters in social choice theory.HAL, Universit� Paris1 Panth�onSorbonne (PostPrint and Working Papers). 01/2009;  [Show abstract] [Hide abstract]
ABSTRACT: We show how ultrafilters can be used to prove a central impossibility result in judgement aggregation introduced by Nehring and Puppe (2005), namely that for a logically strongly interconnected agenda, an independent and monotonic judgement aggregation rule which satisfies universal domain, collective rationality and sovereignty is necessarily dictatorial.Economics Bulletin. 01/2009; 29(1):319327.
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