
Robust Bounds on Choosing from Large Tournaments
Tournament solutions provide methods for selecting the "best" alternativ...
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A Quantitative Version of the GibbardSatterthwaite Theorem for Three Alternatives
The GibbardSatterthwaite theorem states that every nondictatorial elec...
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On the Practical use of Variable Elimination in Constraint Optimization Problems: 'Stilllife' as a Case Study
Variable elimination is a general technique for constraint processing. I...
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Testing Preferential Domains Using Sampling
A preferential domain is a collection of sets of preferences which are l...
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On random primitive sets, directable NDFAs and the generation of slowly synchronizing DFAs
We tackle the problem of the randomized generation of slowly synchronizi...
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The threshold for SDPrefutation of random regular NAE3SAT
Unlike its cousin 3SAT, the NAE3SAT (notallequal3SAT) problem has th...
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The efficacy of tournament designs
Tournaments are a widely used mechanism to rank alternatives in a noisy ...
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Generalized Kings and SingleElimination Winners in Random Tournaments
Tournaments can be used to model a variety of practical scenarios including sports competitions and elections. A natural notion of strength of alternatives in a tournament is a generalized king: an alternative is said to be a kking if it can reach every other alternative in the tournament via a directed path of length at most k. In this paper, we provide an almost complete characterization of the probability threshold such that all, a large number, or a small number of alternatives are kkings with high probability in two random models. We show that, perhaps surprisingly, all changes in the threshold occur in the range of constant k, with the biggest change being between k=2 and k=3. In addition, we establish an asymptotically tight bound on the probability threshold for which all alternatives are likely able to win a singleelimination tournament under some bracket.
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