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Tight Approximation for Proportional Approval Voting

Szymon Dudycz, Pasin Manurangsi, Jan Marcinkowski, Krzysztof Sornat
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
We provide a tight polynomial time approximation algorithm for a natural class of geometrically dominant weights that includes such voting rules as Proportional Approval Voting or p-Geometric.  ...  In approval-based multiwinner elections, we are given a set of voters, a set of candidates, and, for each voter, a set of candidates approved by the voter.  ...  We would like to thank Mateusz Lewandowski for initial discussion and the anonymous reviewers for their helpful comments.  ... 
doi:10.24963/ijcai.2020/39 dblp:conf/ijcai/DudyczMMS20 fatcat:n6jtrnynbjd2pkxd4vq6zvgbt4

Online Approval Committee Elections [article]

Virginie Do, Matthieu Hervouin, Jérôme Lang, Piotr Skowron
2022 arXiv   pre-print
Assume the voters use approval ballots, i.e., for each candidate they only specify whether they consider it acceptable or not. This setting can be seen as a voting variant of choosing k secretaries.  ...  Each time one appears, it must be immediately selected or rejected – a decision that is made by a group of individuals through voting.  ...  We also thank the IJCAI-22 anonymous reviewers for useful comments and suggestions.  ... 
arXiv:2202.06830v4 fatcat:qhziys46abhvpdybntjls4vq7y

Proportional Representation in Vote Streams [article]

Palash Dey, Nimrod Talmon, Otniel van Handel
2017 arXiv   pre-print
proportional representation voting rules; specifically, we consider the Approval-based and the Borda-based variants of both the Chamberlin-- ourant rule and the Monroe rule.  ...  vote streams with huge number of voters.  ...  DISCUSSION AND OUTLOOK We have described streaming algorithms which find approximate winners for several well-known proportional representation multiwinner voting rules.  ... 
arXiv:1702.08862v1 fatcat:wf43qe7fyrg2pcj7qu2yr4cwze

The Core of the Participatory Budgeting Problem [article]

Brandon Fain, Ashish Goel, Kamesh Munagala
2016 arXiv   pre-print
well-known concept of proportional fairness.  ...  We use our theoretical insights to perform experiments on real participatory budgeting voting data.  ...  We thank Anilesh Krishnaswamy for useful discussions, and the Stanford Crowdsourced Democracy Team for the use of their data.  ... 
arXiv:1610.03474v2 fatcat:6piychd6erbabnl5pdmanzqs2i

Approximation and Parameterized Complexity of Minimax Approval Voting

Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, Krzysztof Sornat
2018 The Journal of Artificial Intelligence Research  
Finally, we get a new polynomial-time randomized approximation scheme for Minimax Approval Voting, which runs in time nO(1/ε2⋅log(1/ε))⋅poly(m), where n is a number of voters and m is a number of alternatives  ...  Motivated by this, we then show a parameterized approximation scheme, running in time O*((3/ε)2d), which is essentially tight assuming ETH.  ...  to Proportional Approval Voting.  ... 
doi:10.1613/jair.1.11253 fatcat:2vuo4kjwsfdgbf434qvfa3d35e

Approximation and Parameterized Complexity of Minimax Approval Voting

Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, Krzysztof Sornat
2017 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Finally, we get a new polynomial-time randomized approximation scheme for MINIMAX APPROVAL VOTING, which runs in time nO(1/ε2·log(1/ε))· poly(m), almost matching the running time of the fastest known PTAS  ...  Motivated by this, we then show a parameterized approximation scheme, running in time O⋆((3/ε)2d), which is essentially tight assuming ETH.  ...  Marek Cygan would like to thank Daniel Lokshtanov for helpful conversations about existing algorithms for the Closest (Sub)String problem.  ... 
doi:10.1609/aaai.v31i1.10575 fatcat:dnrxkfhylraitlrf7n5khvavtq

Truthful and Near-Optimal Mechanisms for Welfare Maximization in Multi-Winner Elections

Umang Bhaskar, Varsha Dani, Abheek Ghosh
2018 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We show that for a particular input format called threshold approval voting, where each agent is presented with an independently chosen threshold, there is a mechanism with nearly optimal distortion when  ...  We further tighten these lower bounds and show that for truthful mechanisms our first upper bound is tight.  ...  We thank Swaprava Nath, Tom Hayes, Ariel Procaccia, and Nisarg Shah for discussing the problem, as well as anonymous referees for helping improve the presentation.  ... 
doi:10.1609/aaai.v32i1.11480 fatcat:pcunspwe4re37ky43qkgxxsz6q

Multi-Winner Voting with Approval Preferences [article]

Martin Lackner, Piotr Skowron
2022 arXiv   pre-print
The corresponding multi-winner voting rules are called approval-based committee (ABC) rules. Due to the simplicity of approval preferences, ABC rules are widely suitable for practical use.  ...  The goal of this book is to present fundamental concepts and results for ABC voting and to discuss the recent advances in computational social choice.  ...  Acknowledgments First and foremost, we would like to thank Piotr Faliszewski for extensive feedback and discussions that significantly improved this book.  ... 
arXiv:2007.01795v4 fatcat:pef6zcg3fnalln55b3ixlbasl4

Approximation and Parameterized Complexity of Minimax Approval Voting [article]

Marek Cygan, Łukasz Kowalik, Arkadiusz Socała, Krzysztof Sornat
2016 arXiv   pre-print
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  ...  Motivated by this, we then show a parameterized approximation scheme, running in time O^((3/ϵ)^2d), which is essentially tight assuming ETH.  ...  goal is to maximize the total satisfaction), Proportional Approval Voting (PAV: like SAV, but satisfaction of an agent whose j approved candidates are selected is the j-th harmonic number H j ), Reweighted  ... 
arXiv:1607.07906v1 fatcat:zq63yrsslnewlc4cuvfwspmemm

Proportionality Degree of Multiwinner Rules [article]

Piotr Skowron
2019 arXiv   pre-print
For example, we find that Proportional Approval Voting (PAV) has better proportionality guarantees than its sequential counterpart, and that Phragmén's Sequential Rule is worse than Sequential PAV.  ...  We study multiwinner elections with approval-based preferences.  ...  Proportional Approval Voting (PAV). PAV is the λ PAV -Thiele rule for λ PAV (i) = 1 /i.  ... 
arXiv:1810.08799v2 fatcat:ehfz5mtjqzeiddfoncy3rudn24

MEASURING THE DIFFERENCE BETWEEN WHITE VOTING AND POLLING ON INTERRACIAL MARRIAGE

Micah Altman, Philip A. Klinkner
2006 Du Bois Review: Social Science Research on Race  
Estimated proportion of White voters voting against constitutional reform, as a proportion of total White vote for and against reform.17 These results indicate that in South Carolina approximately  ...  very tight).  ...  enough bounds on w that both the EI-W regressions for SC and for the bulk of AL are well within the region of estimates expected to be "approximately unbiased".  ... 
doi:10.1017/s1742058x06060218 fatcat:j5ba7fuxnncc3i56yqntohyftu

Proportionality in Approval-Based Elections With a Variable Number of Winners

Rupert Freeman, Anson Kahng, David M. Pennock
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
to AS even for large numbers of candidates.  ...  We then prove that a natural randomized rule achieves a 29/32 approximation to AS.  ...  We also thank our anonymous IJCAI and workshop reviewers for their thorough and insightful feedback. Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  ... 
doi:10.24963/ijcai.2020/19 dblp:conf/ijcai/FreemanKP20 fatcat:aepkwbn4xrgrjmolwdfodyfugu

Decentralised Update Selection with Semi-Strategic Experts [article]

Georgios Amanatidis, Georgios Birmpas, Philip Lazos, Francisco J. Marmolejo-Cossío
2022 arXiv   pre-print
In particular, we develop an approval voting inspired selection mechanism through which the experts approve or disapprove the different updates according to their perception of the quality of each alternative  ...  Contrary to most existing voting approaches, we use the input of a set of motivated experts of varying levels of expertise.  ...  Acknowledgements We would like to thank Nikos Karagiannidis for many enlightening meetings, helping us formulate the model in early versions of this work.  ... 
arXiv:2205.08407v1 fatcat:4eh3x5irrzhklohw6iuwohxs7e

Individual Representation in Approval-Based Committee Voting

Markus Brill, Jonas Israel, Evi Micha, Jannik Peters
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
When selecting multiple candidates based on approval preferences of agents, the proportional representation of agents' opinions is an important and well-studied desideratum.  ...  We show that checking whether an IR outcome exists is computationally intractable, and we verify that all common approval-based voting rules may fail to provide IR even in cases where this is possible.  ...  Acknowledgments We would like to thank Nisarg Shah and the anonymous reviewers for their helpful comments.  ... 
doi:10.1609/aaai.v36i5.20418 fatcat:bw6extrlp5do5pnhb75m6c373m

Tight Approximation Guarantees for Concave Coverage Problems [article]

Siddharth Barman, Omar Fawzi, Paul Fermé
2021 arXiv   pre-print
., IJCAI, 2020] on multi-winner approval-based voting for geometrically dominant rules.  ...  Our result goes beyond these special cases and we illustrate it with applications to distributed resource allocation problems, welfare maximization problems and approval-based voting for general rules.  ...  B.1 Proportional Approval Voting j i=1 1 i α ϕ (1) ≃ 0.7965 . . . Prop. A.13 Proportional Approval Voting capped at 3 min{j,3} i=1 1 i α ϕ (1) ≃ 0.7910 . . . Prop.  ... 
arXiv:2010.00970v3 fatcat:w6gmqg6dcvhh5pltelgdfut564
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