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On the likelihood of Condorcet's profiles

2002
*
Social Choice and Welfare
*

Furthermore, he supplied a famous example where all

doi:10.1007/s355-002-8332-y
fatcat:5j4ydnweqng3tm7tgrtqgz6yzi
*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*. ...##
###
Monotonic incompatibility between electing and ranking

2009
*
Economics Letters
*

Abstract: Borda proposed a method that assigns points to each

doi:10.1016/j.econlet.2009.06.024
fatcat:wfumw4tuond6fjspgvlj5dosri
*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. ...##
###
A trust-augmented voting scheme for collaborative privacy management

2012
*
Journal of Computer Security
*

In spite

doi:10.3233/jcs-2012-0453
fatcat:6rt6k72atrcaxaofzkrpdjc54i
*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). ...##
###
Computing Optimal Bayesian Decisions for Rank Aggregation via MCMC Sampling

2015
*
Conference on Uncertainty in Artificial Intelligence
*

Efficiency

dblp:conf/uai/HughesHX15
fatcat:5ga5maaedbg2zncekvgjjnk2x4
*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. ...##
###
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]

2011
*
Studies in Choice and Welfare
*

Early research

doi:10.1007/978-3-642-20441-8_7
fatcat:ymjpadczwffcfn5fqrubj4tkca
*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. ...##
###
A Trust-Augmented Voting Scheme for Collaborative Privacy Management
[chapter]

2011
*
Lecture Notes in Computer Science
*

Supported by

doi:10.1007/978-3-642-22444-7_9
fatcat:4xhx2a66hfasthuznj54qgbi2u
*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 . ...##
###
Optimal Statistical Hypothesis Testing for Social Choice
[article]

2020
*
arXiv
*
pre-print

By leveraging

arXiv:2006.11362v1
fatcat:uzfm3gre4bacdmhfvsrmozhwpu
*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. ...##
###
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

2009
*
Mathematical Social Sciences
*

A joint probability distribution

doi:10.1016/j.mathsocsci.2008.09.002
fatcat:kr2dxqhxdrc2zjf2b3oocph23m
*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 ...##
###
Rousseau's General Will as a Bound for Strategic Self-Interested Voting

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. ...

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

2011
*
Lecture Notes in Computer Science
*

We find a high consensus among

doi:10.1007/978-3-642-24873-3_13
fatcat:ucvs2rv2hjdelnnjsxagek76by
*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. ...##
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Beyond Condorcet: Optimal Aggregation Rules Using Voting Records

2010
*
Social Science Research Network
*

We observe that any arbitrary evaluation

doi:10.2139/ssrn.1870805
fatcat:etaanmbl4fe7pnlpcmm63d3a3a
*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. ...##
###
The Smoothed Possibility of Social Choice
[article]

2021
*
arXiv
*
pre-print

For Condrocet's paradox, we prove that

arXiv:2006.06875v3
fatcat:x4b4b5q4uvhv5f7vzhvnpbfkay
*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 ...##
###
Bounds on the competence of a homogeneous jury

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. ...

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