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Ordinal Approximation for Social Choice, Matching, and Facility Location Problems given Candidate Positions [article]

Elliot Anshelevich, Wennan Zhu
2018 arXiv   pre-print
In this work we consider general facility location and social choice problems, in which sets of agents A and facilities F are located in a metric space, and our goal is to assign agents to facilities (  ...  We analyze many general problems including matching, k-center, and k-median, and present black-box reductions from omniscient approximation algorithms with approximation factor β to ordinal algorithms  ...  See for example [3, 4, 11, 16, 21, 23, 29] for the social choice setting, [1, [5] [6] [7] for matching and other graph problems, and [13] for facility location.  ... 
arXiv:1805.03103v1 fatcat:hi4ciebu3jaqfdvt2r7epsqugm

Resolving the Optimal Metric Distortion Conjecture [article]

Vasilis Gkatzelis, Daniel Halpern, Nisarg Shah
2020 arXiv   pre-print
A prominent motivation for this problem comes from voting theory, where V represents a set of voters, C represents a set of candidates, and the rankings correspond to ordinal preferences of the voters.  ...  We do so by proving a novel lemma about matching voters to candidates, which we refer to as the ranking-matching lemma.  ...  novel algorithms for problems such as matching, clustering, and facility location using only ordinal information.  ... 
arXiv:2004.07447v2 fatcat:gxlktxx7jrc3fn3uysp7z5dveu

Approximate Mechanism Design without Money

Ariel D. Procaccia, Moshe Tennenholtz
2013 ACM Transactions on Economics and Computation  
We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective  ...  functions: the social cost, and the maximum cost.  ...  Acknowledgments We thank Shahar Dobzinski and Ron Lavi for commenting on an ancient draft of this paper.  ... 
doi:10.1145/2542174.2542175 fatcat:xei6klroovhfrafsvhtra7sgru

Favorite-Candidate Voting for Eliminating the Least Popular Candidate in Metric Spaces [article]

Xujin Chen, Minming Li, Chenhao Wang
2019 arXiv   pre-print
Given the collection of favorite candidates, a mechanism for eliminating the least popular candidate finds a committee containing all candidates but the one to be eliminated.  ...  We design mechanisms for finding a committee to optimize the social value.  ...  An election in the social choice problem under consideration is a triple Γ = (Ω, M, a).  ... 
arXiv:1911.12109v1 fatcat:gggct625bbe6desgmxqnq3kkka

On Voting and Facility Location [article]

Michal Feldman, Amos Fiat, Iddan Golomb
2015 arXiv   pre-print
A question closely related to candidate selection is that of minimizing the sum of distances for facility location.  ...  While it may seem that Black's 1948 median algorithm is optimal for candidate selection on the line, this is not the case. We give matching upper and lower bounds for a variety of settings.  ...  Acknowledgements We would like to thank Alon Eden, Ilan Cohen, Ophir Friedler, Shai Vardi, Rachel Matichin, Sella Nevo, Guy Reiner, Lirong Xia and Elliot Anshelevich for interesting discussions.  ... 
arXiv:1512.05868v1 fatcat:7e5y52nncjg3bgddku3okmkhpm

Favorite-Candidate Voting for Eliminating the Least Popular Candidate in a Metric Space

Xujin Chen, Minming Li, Chenhao Wang
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Given the collection of favorite candidates, a mechanism for eliminating the least popular candidate finds a committee containing all candidates but the one to be eliminated.  ...  We design mechanisms for finding a committee to optimize the social value.  ...  An election in the social choice problem under consideration is a triple Γ = (Ω, M, a).  ... 
doi:10.1609/aaai.v34i02.5558 fatcat:7iqaxxoarfetnlvb6nzh332lc4

Metric Distortion of Social Choice Rules: Lower Bounds and Fairness Properties [article]

Ashish Goel, Anilesh Kollagunta Krishnaswamy, Kamesh Munagala
2017 arXiv   pre-print
Social choice rules have access to only the ordinal preferences of agents but not the latent cardinal costs that induce them.  ...  Using the concept of approximate majorization within the distortion framework, we prove that Copeland and Randomized Dictatorship achieve low constant factor fairness-ratios (5 and 3 respectively), which  ...  Such models, especially those with euclidean spaces, have also been commonly studied in the approximation algorithms literature on facility location problems [Arya et al., 2004, Drezner and Hamacher,  ... 
arXiv:1612.02912v2 fatcat:cqulsgce65gzjigb7c22caqhgi

Application-Oriented Computational Social Choice (Dagstuhl Seminar 19381)

Umberto Grandi, Stefan Napel, Rolf Niedermeier, Kristen Brent Venable, Michael Wagner
2020 Dagstuhl Reports  
work and open problems in short talks.  ...  , collective decision making, multi-agent systems, social choice License Creative Commons BY 3.0 Unported license © Computational social choice (COMSOC) combines models from political science and economics  ...  We address the problem of learning rankings in recommender systems under cold start and constrained settings. We presented our solution to the job recommendation task for ACM RecSys 2017 challenge.  ... 
doi:10.4230/dagrep.9.9.45 dblp:journals/dagstuhl-reports/GrandiNNV19 fatcat:hnmptiqktfeejejqwakbpyruqi

The Distortion of Distributed Metric Social Choice [article]

Elliot Anshelevich, Aris Filos-Ratsikas, Alexandros A. Voudouris
2021 arXiv   pre-print
We consider a social choice setting with agents that are partitioned into disjoint groups, and have metric preferences over a set of alternatives.  ...  choice must be made in a distributed way: The preferences of the agents within each group are first aggregated into a representative alternative for the group, and then these group representatives are  ...  as choosing public policies, allocations of resources, or the most appropriate position to locate a public facility.  ... 
arXiv:2107.05456v1 fatcat:2erh6ejcgbbnrptvmxkmfxgy5q

Core-Stable Committees under Restricted Domains [article]

Grzegorz Pierczyński, Piotr Skowron
2021 arXiv   pre-print
This model is relevant for a number of real-life scenarios including political elections, participatory budgeting, and facility-location.  ...  We show that for a number of restricted domains including voter-interval, candidate-interval, single-peaked, and single-crossing preferences the core is non-empty and can be found in polynomial time.  ...  Acknowldegments Grzegorz Pierczyński and Piotr Skowron were supported by Poland's National Science Center grant UMO-2019/35/B/ST6/02215.  ... 
arXiv:2108.01987v1 fatcat:d4yqddcr6ncdhi2vqwtvohljgi

Application of AHP/EVAMIX Method for Decision Making in the Industrial Environment

Veera P. Darji, Ravipudi V. Rao
2013 American Journal of Operations Research  
The novelty of the proposed methodology is its capability of dealing with both ordinal and cardinal information.  ...  This paper explores the applicability and capability of an outranking method known as Evaluation of Mixed Data (EVAMIX) method combined with Analytical Hierarchy Process (AHP) for selection of right alternative  ...  Higher the appraisal score better is the site for the thermal power plant location. The scores and ranking is given in Table 19 .  ... 
doi:10.4236/ajor.2013.36053 fatcat:2kxjrfqgjzc2tonmtwrh7zmice

Dimensionality, Coordination, and Robustness in Voting [article]

Ioannis Anagnostides, Dimitris Fotakis, Panagiotis Patsilinakos
2022 arXiv   pre-print
Finally, driven by applications in facility location games, we consider several refinements and extensions of the standard metric-setting.  ...  We also establish a nearly-matching lower bound, refining the construction of Skowron and Elkind.  ...  We are also grateful to Benny Moldovanu for pointing out related work on the subject of dimensionality in voting.  ... 
arXiv:2109.02184v2 fatcat:gj32f5thqrgcfignwthhkocefq

Metric Distortion Bounds for Randomized Social Choice [article]

Moses Charikar, Prasanna Ramakrishnan
2021 arXiv   pre-print
Consider the following social choice problem. Suppose we have a set of n voters and m candidates that lie in a metric space.  ...  Instead, it gets each voter's ordinal ranking of the candidates by distance.  ...  Another application is in the facility location problem [CG99, JMM + 03, CAPP19], where the voters correspond to customers and the candidates correspond to possible locations for a new facility (e.g.,  ... 
arXiv:2111.03694v1 fatcat:trehtwiqcjf5jnmcwgjdg7ixkq

Relating Metric Distortion and Fairness of Social Choice Rules [article]

Ashish Goel, Reyna Hulett, Anilesh K. Krishnaswamy
2018 arXiv   pre-print
Analogously, we can consider the worst-case fairness ratio of a social choice rule by comparing a useful notion of fairness (based on approximate majorization) for the chosen alternative to that of the  ...  We further extend the notions of distortion and fairness ratio to social choice rules choosing a set of alternatives.  ...  Such models, especially those using Euclidean spaces, have naturally also been studied in the approximation algorithms literature on facility location problems [5, 14] .  ... 
arXiv:1810.01092v1 fatcat:bf4klo2aijbzfkvklnjcjd4awa

Truthful Mechanisms for Matching and Clustering in an Ordinal World [article]

Elliot Anshelevich, Shreyas Sekar
2016 arXiv   pre-print
We study truthful mechanisms for matching and related problems in a partial information setting, where the agents' true utilities are hidden, and the algorithm only has access to ordinal preference information  ...  Our techniques yield universally truthful algorithms for a number of graph problems: a 1.76-approximation algorithm for Max-Weight Matching, 2-approximation algorithm for Max k-matching, a 6-approximation  ...  Acknowledgements This work was supported in part by NSF awards CCF-1527497 and CNS-1218374.  ... 
arXiv:1610.04069v2 fatcat:fs4z3cutxnacnbrgx6bw7vg2dq
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