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Some results on approximating the minimax solution in approval voting

Rob LeGrand, Evangelos Markakis, Aranyak Mehta
2007 Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems - AAMAS '07  
Here, we study a voting protocol for multi-winner elections, called approval voting, and we investigate the complexity of computing the minimax solution, concentrating on elections for committees of fixed  ...  Our heuristics have low running times (provably polynomial) and our experimental results show that they perform very well on average, computing solutions that are very close to the optimal minimax solutions  ...  In fact for some heuristics the average error in the approximation can be as low as 0.05%. Finally, in Section 5, we focus on the question of manipulating the minimax solution.  ... 
doi:10.1145/1329125.1329365 dblp:conf/atal/LeGrandMM07 fatcat:dfdk4xczkva7xklusp3bnxezya

Approximation and Parameterized Complexity of Minimax Approval Voting

Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, Krzysztof Sornat
2018 The Journal of Artificial Intelligence Research  
We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance d from the solution to the votes.  ...  We show Minimax Approval Voting admits no algorithm running in time O*(2o(d log d)), unless the Exponential Time Hypothesis (ETH) fails.  ...  Acknowledgments A preliminary version of this work appeared in the proceedings of AAAI-17 (Cygan, Kowalik, Soca la, & Sornat, 2017)  ... 
doi:10.1613/jair.1.11253 fatcat:2vuo4kjwsfdgbf434qvfa3d35e

Approximation and Parameterized Complexity of Minimax Approval Voting [article]

Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, Krzysztof Sornat
2016 arXiv   pre-print
We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance d from the solution to the votes.  ...  Finally, we get a new polynomial-time randomized approximation scheme for Minimax Approval Voting, which runs in time n^O(1/ϵ^2 ·(1/ϵ))·poly(m), almost matching the running time of the fastest known PTAS  ...  Previous results on Minimax Approval Voting First approximation result was a simple 3-approximation algorithm due to LeGrand, Markakis and Mehta [18] , obtained by choosing an arbitrary vote and taking  ... 
arXiv:1607.07906v1 fatcat:zq63yrsslnewlc4cuvfwspmemm

PTAS for Minimax Approval Voting [chapter]

Jarosław Byrka, Krzysztof Sornat
2014 Lecture Notes in Computer Science  
We consider Approval Voting systems where each voter decides on a subset to candidates he/she approves.  ...  In this paper we give a PTAS for this problem and hence resolve the open question raised by Carragianis et al. [AAAI'10]. The result is obtained by adapting the techniques developed by Li et al.  ...  more difficult to approximate than Minimax in the context of Approval Voting systems.  ... 
doi:10.1007/978-3-319-13129-0_15 fatcat:f7ffjhe3fnen3gkirv5fy2irja

A Generalization of the Minisum and Minimax Voting Methods

Shankar Sivarajan
2018 SIAM Undergraduate Research Online  
In this paper, we propose a family of approval voting-schemes for electing committees based on the preferences of voters.  ...  Supported by examples, we suggest that using a small value of p, such as 2 or 3, provides a good compromise between the minisum and minimax voting methods with regard to the weightage given to approvals  ...  Narahari for giving me the opportunity to work on this summer project, and Palash Dey for his guidance.  ... 
doi:10.1137/16s014870 fatcat:u63b62shvbbvhilnxbyfvbtpry

Strategic voting and nomination

James Green-Armytage
2013 Social Choice and Welfare  
Using computer simulations based on three separate data generating processes, I estimate the fraction of elections in which sincere voting will be a core equilibrium given each of eight single-winner voting  ...  I find that Hare is least vulnerable to strategic voting in general, whereas Borda, Coombs, approval, and range are most vulnerable.  ...  when all of the voters who prefer to vote to approve and no one else. 4.1.1.  ... 
doi:10.1007/s00355-013-0725-3 fatcat:npzduuzvszeqdlx2f3r5tfs6bi

Computational Aspects of Approval Voting [chapter]

Dorothea Baumeister, Gábor Erdélyi, Edith Hemaspaandra, Lane A. Hemaspaandra, Jörg Rothe
2010 Studies in Choice and Welfare  
This paper is concerned with the computational aspects of approval voting and some of its variants, with a particular focus on the complexity of problems that model various ways of tampering with the outcome  ...  Finally, we study local search heuristics for minimax approval voting, a variant of approval voting proposed by Brams, Kilgour, and Sanver [BKS04] (see also [BKS07a, BKS07b]) for the purpose of electing  ...  In particular, we will present an approximation algorithm and some local search heuristics for "minimax approval voting," an interesting variant of approval voting that was proposed by Brams, Kilgour,  ... 
doi:10.1007/978-3-642-02839-7_10 fatcat:arteomngqfdannmzaubhzhkbwa

On Choosing Committees Based on Approval Votes in the Presence of Outliers [article]

Palash Dey, Neeldhara Misra, Y. Narahari
2015 arXiv   pre-print
For the approval voting rule, we resolve the parameterized complexity of this problem for all subsets of parameters except one. We also study approximation algorithms for this problem.  ...  We study the computational complexity of committee selection problem for several approval-based voting rules in the presence of outliers.  ...  Hardness of Approximation In the previous section, we demonstrated some approaches for approximating the target score in the context of minisum voting rule.  ... 
arXiv:1511.04190v1 fatcat:eeeemn6gvvd4nevevtjr5tbhsu

On the Computation of Fully Proportional Representation

Nadja Betzler, Arkadii Slinko, Johannes Uhlmann
2011 Social Science Research Network  
In the general case these "minimax" versions of classical rules appeared to be still NP-hard.  ...  Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners  ...  Moreover, we like to thank Steven Brams for his interest in this work and valuable discussions and Rolf Niedermeier for his useful comments and support.  ... 
doi:10.2139/ssrn.1952497 fatcat:zkxr26fmwbbkvglnfosiwjcwum

Minimax is the best electoral system after all [article]

Richard B. Darlington
2016 arXiv   pre-print
In computer simulations, minimax and minimax-T nearly always pick the same winners as CMO.  ...  Minimax-T adds a new tie-breaker. It surpasses competing systems on a combination of simplicity, transparency, voter privacy, input flexibility, resistance to strategic voting, and rarity of ties.  ...  become the Condorcet winner with the least change to the voting results in some reasonable sense.  ... 
arXiv:1606.04371v2 fatcat:ivcozoz5znbrtj6ov6phvsnjue

On the Computation of Fully Proportional Representation

N. Betzler, A. Slinko, J. Uhlmann
2013 The Journal of Artificial Intelligence Research  
In the general case these "minimax" versions of classical rules appeared to be still NP-hard.  ...  Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners  ...  Finally, observe that for the minimax versions in a similar style hardness results given for the approval misrepresentation function directly transfer to misrepresentation functions in which a voter is  ... 
doi:10.1613/jair.3896 fatcat:jq4dcme5sfh3bnkk3nf56b6fmy

Computational Aspects of Conditional Minisum Approval Voting in Elections with Interdependent Issues

Evangelos Markakis, Georgios Papasotiropoulos
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
Approval voting provides a simple, practical framework for multi-issue elections, and the most representative example among such election rules is the classic Minisum approval voting rule.  ...  Overall, our work provides a better understanding on the complexity implications introduced by conditional voting.  ...  Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  ... 
doi:10.24963/ijcai.2020/43 dblp:conf/ijcai/MarkakisP20 fatcat:nje2374nybgzjddw5nd6aa6cky

Mathematical Programming formulations for the efficient solution of the k-sum approval voting problem [article]

Diego Ponce, Justo Puerto, Federica Ricca, Andrea Scozzari
2017 arXiv   pre-print
The problem is widely studied in voting theory; for a variety of voting rules the problem was shown to be computationally difficult and approximation algorithms and heuristic techniques were proposed in  ...  In this paper we follow an Ordered Weighted Averaging approach and study the k-sum approval voting (optimization) problem in the general case 1 ≤ k <n.  ...  This paper has been written during a sabbatical leave of the second author in La Sapienza, Universitá di Roma whose support is also acknowledged.  ... 
arXiv:1707.09225v1 fatcat:cfrna3wgtndbtinyiyxgkunrby

Strategic sequential voting in multi-issue domains and multiple-election paradoxes

Lirong Xia, Vincent Conitzer, Jérôme Lang
2011 Proceedings of the 12th ACM conference on Electronic commerce - EC '11  
In each step, the voters simultaneously vote on one issue, and the order of the issues is determined before the process. We call this model strategic sequential voting.  ...  In many settings, a group of agents must come to a joint decision on multiple issues. In practice, this is often done by voting on the issues in sequence.  ...  For the sake of benchmarking our results, we also study the minimax satisfaction index for some common voting rules (under truthful voting). The results are summarized in Table 1 .  ... 
doi:10.1145/1993574.1993602 dblp:conf/sigecom/XiaCL11 fatcat:jkk5n5qlyrg5dc2rbkji3qz5iy

Voting: Beyond Simple Majorities and Single-Winner Elections (Dagstuhl Seminar 17261)

Dorothea Baumeister, Piotr Faliszewski, Annick Laruelle, Toby Walsh, Marc Herbstritt
2017 Dagstuhl Reports  
one to present their results).  ...  The seminar was mostly focused on multiwinner elections (from discussions of their algorithmic properties to political-science considerations), but the topics of real-life voting experiments and strategic  ...  Also I will show our last results on approximating the minimization version of Proportional Approval Voting (PAV) [2] .  ... 
doi:10.4230/dagrep.7.6.109 dblp:journals/dagstuhl-reports/BaumeisterFLW17 fatcat:l7w33zdcivheras6b2m2lctb7a
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