46 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)
Minimal Stable Sets in Tournaments
We propose a systematic methodology for defining tournament solutions as
extensions of maximality. The central concepts of this methodology are maximal
qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy
of tournament solutions, which encompasses the top cycle, the uncovered set,
the Banks set, the minimal covering set, the tournament equilibrium set, the
Copeland set, and the bipartisan set. Moreover, the hierarchy includes a new
tournament solution, the minimal extending set, which is conjectured to refine
both the minimal covering set and the Banks set.Comment: 29 pages, 4 figures, changed conten
Refinements and Randomised Versions of Some Tournament Solutions
We consider voting rules that are based on the majority graph. Such rules typically output large sets of winners. Our goal is to investigate a general method which leads to refinements of such rules. In particular, we use the idea of parallel universes, where each universe is connected with a permutation over alternatives. The permutation allows us to construct resolute voting rules (i.e. rules that always choose unique winners). Such resolute rules can be constructed in a variety of ways: we consider using binary voting trees to select a single alternative. In turn this permits the construction of neutral rules that output the set the possible winners of every parallel universe. The question of which rules can be constructed in this way has already been partially studied under the heading of agenda implementability. We further propose a randomised version in which the probability of being the winner is the ratio of universes in which the alternative wins. We also investigate (typically novel) rules that elect the alternatives that have maximal winning probability. These rules typically output small sets of winners, thus provide refinements of known tournament solutions
A Strong No Show Paradox is a common flaw in Condorcet Voting Correspondences.
The No Show Paradox (there is a voter who would rather not vote) is known to affect every Condorcet voting function. This paper analyses a strong version of this paradox (there is a voter whose favorite candidate loses the election if she votes honestly, but gets elected if she abstains) in the context of Condorcet voting correspondences. All Condorcet correspondences satisfying some weak domination properties are shown to be affected by this strong form of the paradox. On the other hand, with the exception of the Simpson-Cramer Minmax, all the Condorcet correspondences that (to the best of our knowledge) are proposed in the literature suffer this paradox.
Robust Bounds on Choosing from Large Tournaments
Tournament solutions provide methods for selecting the "best" alternatives
from a tournament and have found applications in a wide range of areas.
Previous work has shown that several well-known tournament solutions almost
never rule out any alternative in large random tournaments. Nevertheless, all
analytical results thus far have assumed a rigid probabilistic model, in which
either a tournament is chosen uniformly at random, or there is a linear order
of alternatives and the orientation of all edges in the tournament is chosen
with the same probabilities according to the linear order. In this work, we
consider a significantly more general model where the orientation of different
edges can be chosen with different probabilities. We show that a number of
common tournament solutions, including the top cycle and the uncovered set, are
still unlikely to rule out any alternative under this model. This corresponds
to natural graph-theoretic conditions such as irreducibility of the tournament.
In addition, we provide tight asymptotic bounds on the boundary of the
probability range for which the tournament solutions select all alternatives
with high probability.Comment: Appears in the 14th Conference on Web and Internet Economics (WINE),
201
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Representative democracy and the implementation of majority-preferred alternatives
In this paper, we contrast direct and representative democracy. In a direct democracy, individuals have the opportunity to vote over the alternatives in every choice problem the population faces. In a representative democracy, the population commits to a candidate ex ante who will then make choices on its behalf. While direct democracy is normatively appealing, representative democracy is the far more common institution because of its practical advantages. The key question, then, is whether representative democracy succeeds in implementing the choices that the group would make under direct democracy. We find that, in general, it does not. We analyze the theoretical setting in which the two methods are most likely to lead to the same choices, minimizing potential sources of distortion. We model a population as a distribution of voters with strict preferences over a finite set of alternatives and a candidate as an ordering of those alternatives that serves as a binding, contingent plan of action. We focus on the case where the direct democracy choices of the population are consistent with an ordering of the alternatives. We show that even in this case, where the normative recommendation of direct democracy is clear, representative democracy may not elect the candidate with this ordering