Proximity Preservation in an Anonymous Framework

This paper gives a formulation for the condition of preservation of preference proximity which, unlike previous formulations, respects the spirit of anonymity pervading social choice theory. Proximity preservation is however shown to be inconsistent with a very weak condition guaranteeing a minimal non-trivial compensation of pivotal changes.

Impossibility results for infinite-electorate abstract aggregation rules

It is well known that the literature on judgment aggregation inherits the impossibility results from the aggregation of preferences that it generalises. This is due to the fact that the typical judgment aggregation problem induces an ultrafilter on the the set of individuals, as was shown in a model theoretic framework by Herzberg and Eckert (2009), generalising the Kirman-Sondermann correspondence and extending the methodology of Lauwers and Van Liedekerke (1995). In the finite case, dictatorship then immediately follows from the principality of an ultrafilter on a finite set. This is not the case for an infinite set of individuals, where there exist free ultrafilters, as Fishburn already stressed in 1970. The main problem associated with free ultrafilters in the literature on aggregation problems is however, the arbitrariness of their selection combined with the limited anonymity they guarantee (which already led Kirman and Sondermann (1972) to speak about invisible dictators). Following another line of Lauwers and Van Liedekerke's (1995) seminal paper, this note explores another source of impossibility results for free ultrafilters: The domain of an ultraproduct over a free ultrafilter extends the individual factor domains, such that the preservation of the truth value of some sentences by the aggregate model --- if this is as usual to be restricted to the original domain --- may again require the exclusion of free ultrafilters, leading to dictatorship once again.Arrow-type preference aggregation, judgment aggregation, model theory, first-order predicate logic, filter, ultrafilter, reduced product, ultraproduct, existential quantifier

Guilbaud's 1952 theorem on the logical problem of aggregation

In a paper published in 1952, shortly after publication of Arrow's celebrated impossibility result, the French mathematicien Georges-Théodule Guilbaud has obtained a dictatorship result for 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.Aggregation ; judgment aggregation ; logical connectives ; simple game ; ultrafilter

A simple ultrafilter proof for an impossibility theorem in judgment aggregation

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.judgment aggregation

Guilbaud's Theorem : An early contribution to judgment aggregation

In a paper published in 1952, the French mathematician Georges-Théodule 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.Arrow's theorem, aggregation rule, judgment aggregation, logical connexions, simple game, ultrafilter.

Antipodality in committee selection

In this paper we compare a minisum and a minimax procedure as suggested by Brams et al. for selecting committees from a set of candidates. Using a general geometric framework as developed by Don Saari for preference aggregation, we show that antipodality of a unique maximin and a unique minisum winner can occur for any number of candidates larger than two.

General aggregation problems and social structure: A model-theoretic generalisation of the Kirman-Sondermann correspondence

This article proves a very general version of the Kirman-Sondermann [Journal of Economic Theory, 5(2):267-277, 1972] correspondence by extending the methodology of Lauwers and Van Liedekerke [Journal of Mathematical Economics, 24(3):217-237, 1995]. The paper first proposes a unified framework for the analysis of the relation between various aggregation problems and the social structure they induce, based on first-order predicate logic and model theory. Thereafter, aggregators satisfying Arrow-type rationality axioms are shown to be restricted reduced product constructions with respect to the filter of decisive coalitions; an oligarchic impossibility result follows. Under stronger assumptions, aggregators are restricted ultraproduct constructions, whence a generalised Kirman-Sondermann correspondence as well as a dictatorial impossibility result follow.Arrow-type preference aggregation, judgment aggregation, systematicity, model theory, first-order predicate logic, filter, ultrafilter, reduced product, ultraproduct

Guilbaud's Theorem : An early contribution to judgment aggregation

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/CESFramDP2009.htmClassification JEL : D71.Documents de travail du Centre d'Economie de la Sorbonne 2009.47 - ISSN : 1955-611XIn a paper published in 1952, the French mathematician Georges-Théodule 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.Dans un papier publié en 1952, le mathématicien français Georges-Théodule Guilbaud a généralisé le résultat d'impossibilité d'Arrow au cas du "problème logique de l'agrégation", anticipant ainsi la littérature sur la théorie abstraite de l'agrégation et sur l'agrégation des jugements. Nous donnons une reconstruction de la preuve du théorème de Guilbaud, qui a aussi un intérêt technique puisqu'elle peut être vue comme le premier emploi des ultrafiltres en théorie du choix social

Extending DCAM for Metadata Provenance

The Metadata Provenance Task Group aims to define a data model that allows for making assertions about description sets. Creating a shared model of the data elements required to describe an aggregation of metadata statements allows to collectively import, access, use and publish facts about the quality, rights, timeliness, data source type, trust situation, etc. of the described statements. In this paper we outline the preliminary model created by the task group, together with first examples that demonstrate how the model is to be used