On the complexity of bribery and manipulation in tournaments with uncertain information

Mattei, Nicholas; Goldsmith, Judy; Klapper, Andrew; Mundhenk, Martin

doi:10.1016/j.jal.2015.03.004

Cited by 26 publications

(12 citation statements)

References 31 publications

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“…A long line of work has investigated various forms of bribery and manipulation in tournaments. This includes manipulating the tournament bracket to help a certain candidate win the tournament (Vu, Altman, and Shoham 2009;Vassilevska Williams 2010;Kim, Suksompong, and Vassilevska Williams 2017;Aziz et al 2018) and bribing players to intentionally lose matches (Russell and Walsh 2009;Kim and Vassilevska Williams 2015;Mattei et al 2015;Konicki and Vassilevska Williams 2019). In particular, Russell and Walsh (2009) considered a model where only a given subset of edges can be reversed, while other edges are assumed to be fixed.…”

Section: Related Workmentioning

confidence: 99%

Refining Tournament Solutions via Margin of Victory

Brill

Schmidt-Kraepelin

Suksompong

2020

AAAI

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Tournament solutions are frequently used to select winners from a set of alternatives based on pairwise comparisons between alternatives. Prior work has shown that several common tournament solutions tend to select large winner sets and therefore have low discriminative power. In this paper, we propose a general framework for refining tournament solutions. In order to distinguish between winning alternatives, and also between non-winning ones, we introduce the notion of margin of victory (MoV) for tournament solutions. MoV is a robustness measure for individual alternatives: For winners, the MoV captures the distance from dropping out of the winner set, and for non-winners, the distance from entering the set. In each case, distance is measured in terms of which pairwise comparisons would have to be reversed in order to achieve the desired outcome. For common tournament solutions, including the top cycle, the uncovered set, and the Banks set, we determine the complexity of computing the MoV and provide worst-case bounds on the MoV for both winners and non-winners. Our results can also be viewed from the perspective of bribery and manipulation.

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Section: Related Workmentioning

confidence: 99%

Refining Tournament Solutions via Margin of Victory

Brill

Schmidt-Kraepelin

Suksompong

2020

AAAI

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“…To test the modeling power of CR, we generated pairwise probabilities with 0.0 < Pr(b) ≤ 0.5. We then computed, for each of the real world datasets and all values of Pr(b) in steps of 0.01, the probabilities that teams would win a knockout tournament using a simple sampling procedure which converged to the actual probability quickly; uniformly sampling over all possible seedings and updating the probability estimates for each team for a particular seeding, the probability that every team wins the tournament can be computed efficiently [29,46,45].…”

Section: Verifying Real World Tournament Modelsmentioning

confidence: 99%

Empirical Evaluation of Real World Tournaments

Mattei,

Walsh

2016

Preprint

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Computational Social Choice (ComSoc) is a rapidly developing field at the intersection of computer science, economics, social choice, and political science. The study of tournaments is fundamental to ComSoc and many results have been published about tournament solution sets and reasoning in tournaments [4]. Theoretical results in Com-Soc tend to be worst case and tell us little about performance in practice. To this end we detail some experiments on tournaments [24] using real wold data from soccer and tennis. We make three main contributions to the understanding of tournaments using real world data from English Premier League, the German Bundesliga, and the ATP World Tour: (1) we find that the NP-hard question of finding a seeding for which a given team can win a tournament is easily solvable in real world instances, (2) using detailed and principled methodology from statistical physics we show that our real world data obeys a log-normal distribution; and (3) leveraging our log-normal distribution result and using robust statistical methods, we show that the popular Condorcet Random (CR) tournament model does not generate realistic tournament data.

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“…Many algorithmic ideas of Faliszewski et al [20] are useful in our setting as well. Bribery was later studied by various researchers [8,22,24,39,49], sometimes in settings other than those regarding elections [3,40,45] (these references are meant as examples only, see the survey of Faliszewski, Hemaspaandra, and Hemaspaandra [21] for some more discussion). In particular, Faliszewski [19] and Elkind et al [15,16] introduced the idea of voter prices that depend on the extent to which a given vote is affected.…”

Section: Related Workmentioning

confidence: 99%

The complexity of priced control in elections

Miasko

Faliszewski

2015

Ann Math Artif Intell

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We study the complexity of priced control in elections. Naturally, if a given control type is NP-hard for a given voting system E then its priced variant is NP-hard for this rule as well. It is, however, interesting what effect introducing prices has on the complexity of those control problems that without prices are tractable. We show that for four prominent voting rules (plurality, approval, Condorcet, and Copeland) introducing prices does not increase the complexity of control by adding/deleting candidates/voters. However, we do show an example of a scoring rule for which such an effect takes place.

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On the complexity of bribery and manipulation in tournaments with uncertain information

Cited by 26 publications

References 31 publications

Refining Tournament Solutions via Margin of Victory

Refining Tournament Solutions via Margin of Victory

Empirical Evaluation of Real World Tournaments

The complexity of priced control in elections

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