16 research outputs found
Fuzzy Arrovian Theorems when preferences are complete
In this paper we study the aggregation of fuzzy preferences on
non-necessarily finite societies. We characterize in terms of possibility and
impossibility a family of models of complete preferences in which the
transitivity is defined for any t-norm. For that purpose, we have described
each model by means of some crisp binary relations and we have applied the
results obtained by Kirman and Sondermann
An abstract result on projective aggregation functions
A general characterization result of projective aggregation functions is shown, the proof of which makes use of the celebrated Arrow''s theorem, thus providing a link between aggregation functions theory and social choice theory. The result can be viewed as a generalization of a theorem obtained by Kim (1990) for real-valued aggregation functions defined on the n-dimensional Euclidean space in the context of measurement theory. In addition, two applications of the core theorem of the article are shown. The first is a simple extension of the main result to the context of multi-valued aggregation functions. The second offers a new characterization of projective bijection aggregators, thus connecting aggregation operators theory with social choice
Oligarchy and soft incompleteness
The assumption that the social preference relation is complete is demanding. We distinguish between “hard” and “soft” incompleteness, and explore
the social choice implications of the latter. Under soft incompleteness, social preferences can take values in the unit interval. We motivate interest in
soft incompleteness by presenting a version of the strong Pareto rule that
is suited to the context of a [0, 1]-valued social preference relation. Using a
novel approach to the quasi-transitivity of this relation we prove a general
oligarchy theorem. Our framework allows us to make a distinction between
a “strong” and a “weak” oligarchy, and our theorem identifies when the oligarchy must be strong and when it can be weak. Weak oligarchy need not be
undesirable
Universal algebra for general aggregation theory: Many-valued propositional-attitude aggregators as MV-homomorphisms
Herzberg F. Universal algebra for general aggregation theory: Many-valued propositional-attitude aggregators as MV-homomorphisms. Journal of Logic and Computation. 2015;25(3):965-977
Oligarchy and soft incompleteness
The assumption that the social preference relation is complete is demanding. We distinguish between “hard” and “soft” incompleteness, and explore
the social choice implications of the latter. Under soft incompleteness, social preferences can take values in the unit interval. We motivate interest in
soft incompleteness by presenting a version of the strong Pareto rule that
is suited to the context of a [0, 1]-valued social preference relation. Using a
novel approach to the quasi-transitivity of this relation we prove a general
oligarchy theorem. Our framework allows us to make a distinction between
a “strong” and a “weak” oligarchy, and our theorem identifies when the oligarchy must be strong and when it can be weak. Weak oligarchy need not be
undesirable
Assigning Numerical Scores to Linguistic Expressions
ProducciĂłn CientĂficaIn this paper, we study different methods of scoring linguistic expressions defined on a
finite set, in the search for a linear order that ranks all those possible expressions. Among them,
particular attention is paid to the canonical extension, and its representability through distances in a graph plus some suitable penalization of imprecision. The relationship between this setting and the classical problems of numerical representability of orderings, as well as extension of orderings from a set to a superset is also explored. Finally, aggregation procedures of qualitative rankings and scorings are also analyzed.Ministerio de EconomĂa, Industria y Competitividad (Projects ECO2015-65031-R, MTM2015-63608-P, ECO2016-77900-P and TIN2016-77356-P)European Regional Development Fund (ERDF)Research Services of the Universidad PĂşblica de Navarra (Spain
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