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On the likelihood of Condorcet's profiles

Vincent Merlin, Monica Tataru, Fabrice Valognes
2002 Social Choice and Welfare  
Furthermore, he supplied a famous example where all the positional rules select simultaneously the same winner while the majority rule picks another one.  ...  is then the alternative that receives the highest number of points.  ...  The value of P 1 (s) is unknown for any other value of s. For s = 1, we shall obtain the probability P , i.e., the likelihood of Condorcet's profiles.  ... 
doi:10.1007/s355-002-8332-y fatcat:5j4ydnweqng3tm7tgrtqgz6yzi

Monotonic incompatibility between electing and ranking

Michel Balinski, Andrew Jennings, Rida Laraki
2009 Economics Letters  
Abstract: Borda proposed a method that assigns points to each of the m candidates. Condorcet proposed a method that assigns points to each of the m! rankings of candidates.  ...  Abstract Borda proposed a method that assigns points to each of the m candidates. Condorcet proposed a method that assigns points to each of the m! rankings of candidates.  ...  This profile is now used to show that Condorcet's method fails choicemonotonicity. First, create profile P 1 from P 0 by having one of the voters who ranked C immediately above A swap them.  ... 
doi:10.1016/j.econlet.2009.06.024 fatcat:wfumw4tuond6fjspgvlj5dosri

A trust-augmented voting scheme for collaborative privacy management

Yanjie Sun, Chenyi Zhang, Jun Pang, Baptiste Alcalde, Sjouke Mauw, Gilles Barthe, Jorge Cuellar, Javier Lopez, Alexander Pretschner
2012 Journal of Computer Security  
In spite of the fact that these sites provide users with a variety of attractive features, much to users' dismay, however, they are prone to expose users' private information.  ...  Our algorithms are compared and justified by experimental results, which support the usability of our trust-augmented voting scheme.  ...  The authors thank the anonymous referees for their helpful comments. Chenyi Zhang is supported by the Australian Research Council (ARC) Linkage Project (LP0989643).  ... 
doi:10.3233/jcs-2012-0453 fatcat:6rt6k72atrcaxaofzkrpdjc54i

Computing Optimal Bayesian Decisions for Rank Aggregation via MCMC Sampling

David Hughes, Kevin Hwang, Lirong Xia
2015 Conference on Uncertainty in Artificial Intelligence  
Efficiency of our algorithms are illustrated by experiments on real-world datasets.  ...  We show that the mixing time of our Markov chain for Mallows' model is polynomial in ϕ −kmax , d max , and the input size, where ϕ is the dispersion of the model, k max measures agents' largest total bias  ...  ACKNOWLEDGMENTS We thank Zhibing Zhao and anonymous reviewers of UAI-15 for helpful comments. This work is supported in part by NSF CAREER under award number IIS-1453542.  ... 
dblp:conf/uai/HughesHX15 fatcat:5ga5maaedbg2zncekvgjjnk2x4

Page 5660 of Mathematical Reviews Vol. , Issue 2003g [page]

2003 Mathematical Reviews  
Overall, it turns out that the likelihood of Condorcet’s paradox is greater when the num- ber of voters is smaller.  ...  Condorcet’s paradox and the likelihood of its occurrence: different perspectives on balanced preferences. (English summary) Theory and Decision 52 (2002), no. 2, 171-199.  ... 

The Value of Research Based on Simple Assumptions about Voters' Preferences [chapter]

William V. Gehrlein, Dominique Lepelley
2011 Studies in Choice and Welfare  
Early research on the general topic of the probability that various paradoxical election outcomes might be observed was typically based on very simple models to describe the likelihood that voters might  ...  The objective of this study is to clarify the intent and value of the basic research that is based on these simple assumptions.  ...  the likelihood with which Condorcet's Paradox can be expected to be observed.  ... 
doi:10.1007/978-3-642-20441-8_7 fatcat:ymjpadczwffcfn5fqrubj4tkca

A Trust-Augmented Voting Scheme for Collaborative Privacy Management [chapter]

Yanjie Sun, Chenyi Zhang, Jun Pang, Baptiste Alcade, Sjouke Mauw
2011 Lecture Notes in Computer Science  
Supported by the grant TR-PDR BFR08-038 from the Fonds National de la Recherche, Luxembourg. 1 2 < p < 1. Taking Example 1, the likelihood of the total order P 1 P 2 P 3 P 4 to be  ...  An inference technique is introduced to infer a best privacy policy for a user based on his voting history.  ...  A (preferential) voting form is made for Alice, Bob and Clare in which they fill in their preferential list on the available policies, as shown in the voting profile on the left of Fig. 1 .  ... 
doi:10.1007/978-3-642-22444-7_9 fatcat:4xhx2a66hfasthuznj54qgbi2u

Optimal Statistical Hypothesis Testing for Social Choice [article]

Lirong Xia
2020 arXiv   pre-print
By leveraging the theory of uniformly least favorable distributions in the Neyman-Pearson framework to finite models and randomized tests, we characterize uniformly most powerful (UMP) tests, which is  ...  a well-accepted statistical optimality w.r.t. robustness, for testing whether a given alternative is the winner under Mallows' model and under Condorcet's model, respectively.  ...  Let P n denote the collection of n agents' votes, called an (n-)profile. For any profile P and any pair of alternatives a, b, we let P (a b) denote the number of votes in P where a is preferred to b.  ... 
arXiv:2006.11362v1 fatcat:uzfm3gre4bacdmhfvsrmozhwpu

Page 811 of Mathematical Reviews Vol. , Issue 85b [page]

1985 Mathematical Reviews  
This paper is an extensive survey of what is known about the likelihood of the paradox by one of the most important contribu- tors to this question.  ...  Gehrlein, William V. (1-DE) Condorcet’s paradox. Theory and Decision 15 (1983), no. 2, 161-197. Suppose that pairwise comparisons of alternatives are made on the basis of simple majority voting.  ... 

An invariance result for homogeneous juries with correlated votes

Serguei Kaniovski
2009 Mathematical Social Sciences  
A joint probability distribution on the set of voting profiles is called second-order invariant if the probability of a jury collectively making the correct decision under simple majority rule (Condorcet's  ...  This paper establishes the existence of such distributions for homogeneous juries of an arbitrary size.  ...  uniquely define a joint probability distribution on the set of voting profiles, and there exist distributions for which Condorcet's probability is invariant to the second-order correlation coefficient  ... 
doi:10.1016/j.mathsocsci.2008.09.002 fatcat:kr2dxqhxdrc2zjf2b3oocph23m

Rousseau's General Will as a Bound for Strategic Self-Interested Voting

Gustavo Bodanza, Sebastián Linares Lejarraga
2022 Revista latinoamericana de filosofía  
Condorcet's voting method, as its extension known as the Kemeny-Young rule, is often seen as the incarnation of Rousseau's general will.  ...  On the other hand, the uncovered set, the set of all the alternatives that are not covered, puts limits to insincere votes of sophisticated voters under certain conditions.  ...  profile of individual preferences.  ... 
doi:10.36446/rlf2022263 fatcat:n2vy53lcmjel5dau6s4ypny33m

Empirical Evaluation of Voting Rules with Strictly Ordered Preference Data [chapter]

Nicholas Mattei
2011 Lecture Notes in Computer Science  
We find a high consensus among the different voting rules; almost no instances of Condorcet's Paradox; almost no support for restricted preference profiles, and very little support for many of the statistical  ...  We examine the Condorcet Efficiency of each of the rules and the probability of occurrence of Condorcet's Paradox.  ...  Judy Goldsmith and Elizabeth Mattei for their helpful discussion and comments on preliminary drafts of this paper. We gratefully acknowledge the support of NSF EAGER grant CCF-1049360.  ... 
doi:10.1007/978-3-642-24873-3_13 fatcat:ucvs2rv2hjdelnnjsxagek76by

Beyond Condorcet: Optimal Aggregation Rules Using Voting Records

Eyal Baharad, Jacob Goldberger, Moshe Koppel, Shmuel Nitzan
2010 Social Science Research Network  
We observe that any arbitrary evaluation of the decision-maker's capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills  ...  We show that such equilibrium exists and offer a procedure for finding one.  ...  Hence, a column j a in the matrix a is the judgments profile on issue j ; similarly, a row a i is the judgment profile of voter i.  ... 
doi:10.2139/ssrn.1870805 fatcat:etaanmbl4fe7pnlpcmm63d3a3a

The Smoothed Possibility of Social Choice [article]

Lirong Xia
2021 arXiv   pre-print
For Condrocet's paradox, we prove that the smoothed likelihood of the paradox either vanishes at an exponential rate as the number of agents increases, or does not vanish at all.  ...  For the ANR impossibility on the non-existence of voting rules that simultaneously satisfy anonymity, neutrality, and resolvability, we characterize the rate for the impossibility to vanish, to be either  ...  Smoothed Likelihood of Condorcet's Paradox and Smoothed Folklore (Im)possibility Theorem We first apply the main technical lemma (Lemma 1) to characterize the smoothed likelihood of Condorcet's paradox  ... 
arXiv:2006.06875v3 fatcat:x4b4b5q4uvhv5f7vzhvnpbfkay

Bounds on the competence of a homogeneous jury

Alexander Zaigraev, Serguei Kaniovski
2010 Theory and Decision  
The maximum is less than one, while the minimum of zero can be attained for infinitely many combinations of distribution moments.  ...  We also derive the bounds on the voting power of an individual juror as the minimum and maximum probability of her/his casting a decisive vote.  ...  The probabilities of voting profiles and Condorcet's probability are linear in the correlation coefficients.  ... 
doi:10.1007/s11238-010-9216-5 fatcat:lshimp6dgjdmtkahnamoerk7ii
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