
Generalized Kings and SingleElimination Winners in Random Tournaments
Tournaments can be used to model a variety of practical scenarios includ...
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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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Refining Tournament Solutions via Margin of Victory
Tournament solutions are frequently used to select winners from a set of...
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Robust Optimization for TreeStructured Stochastic Network Design
Stochastic network design is a general framework for optimizing network ...
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Tight High Probability Bounds for Linear Stochastic Approximation with Fixed Stepsize
This paper provides a nonasymptotic analysis of linear stochastic appro...
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Query Complexity of Tournament Solutions
A directed graph where there is exactly one edge between every pair of v...
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Random Utility Theory for Social Choice
Random utility theory models an agent's preferences on alternatives by d...
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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 wellknown 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 graphtheoretic 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.
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