77 research outputs found
Consensus theories: an oriented survey
This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity
Consensus theories: an oriented survey
URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2010.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2010.57 - ISSN : 1955-611XThis article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Cet article présente une vue d'ensemble de sept directions de recherche en théorie du consensus : résultats arrowiens, règles d'agrégation définies au moyen de fédérations, règles définies au moyen de distances, solutions de tournoi, domaines restreints, théories abstraites du consensus, questions de complexité et d'algorithmique. Ce panorama est orienté dans la mesure où il présente principalement – mais non exclusivement – les travaux les plus significatifs obtenus – quelquefois avec d'autres chercheurs – par une équipe de chercheurs français qui sont – ou ont été – membres pléniers ou associés du Centre d'Analyse et de Mathématique Sociale (CAMS)
Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem
This paper provides a general framework to explore the possibility of agenda
manipulation-proof and proper consensus-based preference aggregation rules, so
powerfully called in doubt by a disputable if widely shared understanding of
Arrow's `general possibility theorem'. We consider two alternative versions of
agenda manipulation-proofness for social welfare functions, that are
distinguished by `parallel' vs. `sequential' execution of agenda formation and
preference elicitation, respectively. Under the `parallel' version, it is shown
that a large class of anonymous and idempotent social welfare functions that
satisfy both agenda manipulation-proofness and strategy-proofness on a natural
domain of single-peaked `meta-preferences' induced by arbitrary total
preference preorders are indeed available. It is only under the second,
`sequential' version that agenda manipulation-proofness on the same natural
domain of single-peaked `meta-preferences' is in fact shown to be tightly
related to the classic Arrowian `independence of irrelevant alternatives' (IIA)
for social welfare functions. In particular, it is shown that using IIA to
secure such `sequential' version of agenda manipulation-proofness and combining
it with a very minimal requirement of distributed responsiveness results in a
characterization of the `global stalemate' social welfare function, the
constant function which invariably selects universal social indifference. It is
also argued that, altogether, the foregoing results provide new significant
insights concerning the actual content and the constructive implications of
Arrow's `general possibility theorem' from a mechanism-design perspective
Primary Facets Of Order Polytopes
Mixture models on order relations play a central role in recent
investigations of transitivity in binary choice data. In such a model, the
vectors of choice probabilities are the convex combinations of the
characteristic vectors of all order relations of a chosen type. The five
prominent types of order relations are linear orders, weak orders, semiorders,
interval orders and partial orders. For each of them, the problem of finding a
complete, workable characterization of the vectors of probabilities is
crucial---but it is reputably inaccessible. Under a geometric reformulation,
the problem asks for a linear description of a convex polytope whose vertices
are known. As for any convex polytope, a shortest linear description comprises
one linear inequality per facet. Getting all of the facet-defining inequalities
of any of the five order polytopes seems presently out of reach. Here we search
for the facet-defining inequalities which we call primary because their
coefficients take only the values -1, 0 or 1. We provide a classification of
all primary, facet-defining inequalities of three of the five order polytopes.
Moreover, we elaborate on the intricacy of the primary facet-defining
inequalities of the linear order and the weak order polytopes
A new consensus ranking approach for correlated ordinal information based on Mahalanobis distance
ProducciĂłn CientĂficaWe investigate from a global point of view the existence of cohesiveness among experts’ opinions. We address this general issue from three basic essentials: the management of experts’ opinions when they are expressed by ordinal information; the measurement of the degree of dissensus among such opinions; and the achievement of a group solution that conveys the minimum dissensus to the experts’ group.
Accordingly, we propose and characterize a new procedure to codify ordinal information. We also define a new measurement of the degree of dissensus among individual preferences based on the Mahalanobis distance. It is especially designed for the case of possibly correlated alternatives. Finally, we investigate a procedure to obtain a social consensus solution that also includes the possibility of alternatives that are correlated. In addition, we examine the main traits of the dissensus measurement as well as the social solution proposed. The operational character and intuitive interpretation of our approaches are illustrated by an explanatory example.Ministerio de EconomĂa, Industria y Competitividad (ECO2012–32178
Positional voting rules generated by aggregation functions and the role of duplication
ProducciĂłn CientĂficaIn this paper, we consider a typical voting situation where a group of agents show their preferences over a set of alternatives. Under our approach, such preferences are codied into individual positional values which can be aggregated in several ways through particular functions, yielding positional voting rules and providing a social result in each case. We show that scoring rules belong to such class of positional voting rules. But if we focus our interest on OWA operators as aggregation functions, other well-known voting systems naturally appear. In particular, we determine those ones verifying duplication (i.e., clone irrelevance) and present a proposal of an overall social result provided by them.Ministerio de EconomĂa, Industria y Competitividad (ECO2012-32178)Junta de Castilla y LeĂłn (programa de apoyo a proyectos de investigaciĂłn – Ref. VA066U13
10101 Abstracts Collection -- Computational Foundations of Social Choice
From March 7 to March 12, 2010, the Dagstuhl Seminar 10101
``Computational Foundations of Social Choice \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Marc Barbut au pays des médianes
Mathématique/Théorie des treillis Classification AMS : 06 - Order, lattices, ordered algebraic structures/06B - Lattices 05 - Combinatorics For finite fields/05C - Graph theory for applications of graphs 91 - Game theory, economics, social and behavioral sciences/91B - Mathematical economics for econometrics/91B14 - Social choice URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/document-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2013.39 - ISSN : 1955-611XThe notion of median originally appeared in Statistics was introduced more later in Algebra and Combinatorics. Marc Barbut was the first to develop the link between these two notions of median. I present his precursory works linking the metric medians and the algebraic medians of a distributive lattice and using these links within the framework of the "median procedure" in data analysis. I also give a short survey on the development of the - more general - theory of "median spaces" and I mention some problems about the median procedure.La notion de médiane apparue d'abord en statistique (notamment sous forme métrique) l'a été ensuite en algèbre et combinatoire. Marc Barbut a été le premier à développer le lien entre ces deux aspects. Je présente ses travaux précurseurs reliant les médianes métriques et les médianes latticielles d'un treillis distributif et utilisant leurs liens dans le cadre d'une " procédure médiane " en analyse des données. Je fais aussi un bref survol du développement de la théorie (plus générale) des " espaces à médianes " et des problèmes posés par la procédure médiane
Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement
Spaces with locally varying scale of measurement, like multidimensional
structures with differently scaled dimensions, are pretty common in statistics
and machine learning. Nevertheless, it is still understood as an open question
how to exploit the entire information encoded in them properly. We address this
problem by considering an order based on (sets of) expectations of random
variables mapping into such non-standard spaces. This order contains stochastic
dominance and expectation order as extreme cases when no, or respectively
perfect, cardinal structure is given. We derive a (regularized) statistical
test for our proposed generalized stochastic dominance (GSD) order,
operationalize it by linear optimization, and robustify it by imprecise
probability models. Our findings are illustrated with data from
multidimensional poverty measurement, finance, and medicine.Comment: Accepted for the 39th Conference on Uncertainty in Artificial
Intelligence (UAI 2023
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