Counterfactual regret minimization (CFR) is a family of algorithms of no-regret learning dynamics capable of solving large-scale imperfect information games. There has been a notable lack of work on making CFR more computationally efficient. We propose implementing this algorithm as a series of dense and sparse matrix and vector operations, thereby making it highly parallelizable for a graphical processing unit. Our experiments show that our implementation performs up to about 352.5 times faster than OpenSpiel's Python implementation and up to about 22.2 times faster than OpenSpiel's C++ implementation and the speedup becomes more pronounced as the size of the game being solved grows.
{"title":"GPU-Accelerated Counterfactual Regret Minimization","authors":"Juho Kim","doi":"arxiv-2408.14778","DOIUrl":"https://doi.org/arxiv-2408.14778","url":null,"abstract":"Counterfactual regret minimization (CFR) is a family of algorithms of\u0000no-regret learning dynamics capable of solving large-scale imperfect\u0000information games. There has been a notable lack of work on making CFR more\u0000computationally efficient. We propose implementing this algorithm as a series\u0000of dense and sparse matrix and vector operations, thereby making it highly\u0000parallelizable for a graphical processing unit. Our experiments show that our\u0000implementation performs up to about 352.5 times faster than OpenSpiel's Python\u0000implementation and up to about 22.2 times faster than OpenSpiel's C++\u0000implementation and the speedup becomes more pronounced as the size of the game\u0000being solved grows.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the constraint of a no regret follower, will the players in a two-player Stackelberg game still reach Stackelberg equilibrium? We first show when the follower strategy is either reward-average or transform-reward-average, the two players can always get the Stackelberg Equilibrium. Then, we extend that the players can achieve the Stackelberg equilibrium in the two-player game under the no regret constraint. Also, we show a strict upper bound of the follower's utility difference between with and without no regret constraint. Moreover, in constant-sum two-player Stackelberg games with non-regret action sequences, we ensure the total optimal utility of the game remains also bounded.
{"title":"ReLExS: Reinforcement Learning Explanations for Stackelberg No-Regret Learners","authors":"Xiangge Huang, Jingyuan Li, Jiaqing Xie","doi":"arxiv-2408.14086","DOIUrl":"https://doi.org/arxiv-2408.14086","url":null,"abstract":"With the constraint of a no regret follower, will the players in a two-player\u0000Stackelberg game still reach Stackelberg equilibrium? We first show when the\u0000follower strategy is either reward-average or transform-reward-average, the two\u0000players can always get the Stackelberg Equilibrium. Then, we extend that the\u0000players can achieve the Stackelberg equilibrium in the two-player game under\u0000the no regret constraint. Also, we show a strict upper bound of the follower's\u0000utility difference between with and without no regret constraint. Moreover, in\u0000constant-sum two-player Stackelberg games with non-regret action sequences, we\u0000ensure the total optimal utility of the game remains also bounded.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"204 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tatiana Belova, Yuriy Dementiev, Fedor V. Fomin, Petr A. Golovach, Artur Ignatiev
The present bias is a well-documented behavioral trait that significantly influences human decision-making, with present-biased agents often prioritizing immediate rewards over long-term benefits, leading to suboptimal outcomes in various real-world scenarios. Kleinberg and Oren (2014) proposed a popular graph-theoretical model of inconsistent planning to capture the behavior of present-biased agents. In this model, a multi-step project is represented by a weighted directed acyclic task graph, where the agent traverses the graph based on present-biased preferences. We use the model of Kleinberg and Oren to address the principal-agent problem, where a principal, fully aware of the agent's present bias, aims to modify an existing project by adding or deleting tasks. The challenge is to create a modified project that satisfies two somewhat contradictory conditions. On one hand, the present-biased agent should select specific tasks deemed important by the principal. On the other hand, if the anticipated costs in the modified project become too high for the agent, there is a risk of the agent abandoning the entire project, which is not in the principal's interest. To tackle this issue, we leverage the tools of parameterized complexity to investigate whether the principal's strategy can be efficiently identified. We provide algorithms and complexity bounds for this problem.
{"title":"How to guide a present-biased agent through prescribed tasks?","authors":"Tatiana Belova, Yuriy Dementiev, Fedor V. Fomin, Petr A. Golovach, Artur Ignatiev","doi":"arxiv-2408.13675","DOIUrl":"https://doi.org/arxiv-2408.13675","url":null,"abstract":"The present bias is a well-documented behavioral trait that significantly\u0000influences human decision-making, with present-biased agents often prioritizing\u0000immediate rewards over long-term benefits, leading to suboptimal outcomes in\u0000various real-world scenarios. Kleinberg and Oren (2014) proposed a popular\u0000graph-theoretical model of inconsistent planning to capture the behavior of\u0000present-biased agents. In this model, a multi-step project is represented by a\u0000weighted directed acyclic task graph, where the agent traverses the graph based\u0000on present-biased preferences. We use the model of Kleinberg and Oren to address the principal-agent\u0000problem, where a principal, fully aware of the agent's present bias, aims to\u0000modify an existing project by adding or deleting tasks. The challenge is to\u0000create a modified project that satisfies two somewhat contradictory conditions.\u0000On one hand, the present-biased agent should select specific tasks deemed\u0000important by the principal. On the other hand, if the anticipated costs in the\u0000modified project become too high for the agent, there is a risk of the agent\u0000abandoning the entire project, which is not in the principal's interest. To tackle this issue, we leverage the tools of parameterized complexity to\u0000investigate whether the principal's strategy can be efficiently identified. We\u0000provide algorithms and complexity bounds for this problem.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate a model of sequential decision-making where a single alternative is chosen at each round. We focus on two objectives-utilitarian welfare (Util) and egalitarian welfare (Egal)-and consider the computational complexity of the associated maximization problems, as well as their compatibility with strategyproofness and proportionality. We observe that maximizing Util is easy, but the corresponding decision problem for Egal is NP-complete even in restricted cases. We complement this hardness result for Egal with parameterized complexity analysis and an approximation algorithm. Additionally, we show that, while a mechanism that outputs a Util outcome is strategyproof, all deterministic mechanisms for computing Egal outcomes fail a very weak variant of strategyproofness, called non-obvious manipulability (NOM). However, we show that when agents have non-empty approval sets at each timestep, choosing an Egal-maximizing outcome while breaking ties lexicographically satisfies NOM. Regarding proportionality, we prove that a proportional (PROP) outcome can be computed efficiently, but finding an outcome that maximizes Util while guaranteeing PROP is NP-hard. We also derive upper and lower bounds on the price of proportionality with respect to Util and Egal.
{"title":"Temporal Elections: Welfare, Strategyproofness, and Proportionality","authors":"Edith Elkind, Tzeh Yuan Neoh, Nicholas Teh","doi":"arxiv-2408.13637","DOIUrl":"https://doi.org/arxiv-2408.13637","url":null,"abstract":"We investigate a model of sequential decision-making where a single\u0000alternative is chosen at each round. We focus on two objectives-utilitarian\u0000welfare (Util) and egalitarian welfare (Egal)-and consider the computational\u0000complexity of the associated maximization problems, as well as their\u0000compatibility with strategyproofness and proportionality. We observe that\u0000maximizing Util is easy, but the corresponding decision problem for Egal is\u0000NP-complete even in restricted cases. We complement this hardness result for\u0000Egal with parameterized complexity analysis and an approximation algorithm.\u0000Additionally, we show that, while a mechanism that outputs a Util outcome is\u0000strategyproof, all deterministic mechanisms for computing Egal outcomes fail a\u0000very weak variant of strategyproofness, called non-obvious manipulability\u0000(NOM). However, we show that when agents have non-empty approval sets at each\u0000timestep, choosing an Egal-maximizing outcome while breaking ties\u0000lexicographically satisfies NOM. Regarding proportionality, we prove that a\u0000proportional (PROP) outcome can be computed efficiently, but finding an outcome\u0000that maximizes Util while guaranteeing PROP is NP-hard. We also derive upper\u0000and lower bounds on the price of proportionality with respect to Util and Egal.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jakub Cerny, Chun Kai Ling, Darshan Chakrabarti, Jingwen Zhang, Gabriele Farina, Christian Kroer, Garud Iyengar
We introduce Contested Logistics Games, a variant of logistics problems that account for the presence of an adversary that can disrupt the movement of goods in selected areas. We model this as a large two-player zero-sum one-shot game played on a graph representation of the physical world, with the optimal logistics plans described by the (possibly randomized) Nash equilibria of this game. Our logistics model is fairly sophisticated, and is able to handle multiple modes of transport and goods, accounting for possible storage of goods in warehouses, as well as Leontief utilities based on demand satisfied. We prove computational hardness results related to equilibrium finding and propose a practical double-oracle solver based on solving a series of best-response mixed-integer linear programs. We experiment on both synthetic and real-world maps, demonstrating that our proposed method scales to reasonably large games. We also demonstrate the importance of explicitly modeling the capabilities of the adversary via ablation studies and comparisons with a naive logistics plan based on heuristics.
{"title":"Contested Logistics: A Game-Theoretic Approach","authors":"Jakub Cerny, Chun Kai Ling, Darshan Chakrabarti, Jingwen Zhang, Gabriele Farina, Christian Kroer, Garud Iyengar","doi":"arxiv-2408.13057","DOIUrl":"https://doi.org/arxiv-2408.13057","url":null,"abstract":"We introduce Contested Logistics Games, a variant of logistics problems that\u0000account for the presence of an adversary that can disrupt the movement of goods\u0000in selected areas. We model this as a large two-player zero-sum one-shot game\u0000played on a graph representation of the physical world, with the optimal\u0000logistics plans described by the (possibly randomized) Nash equilibria of this\u0000game. Our logistics model is fairly sophisticated, and is able to handle\u0000multiple modes of transport and goods, accounting for possible storage of goods\u0000in warehouses, as well as Leontief utilities based on demand satisfied. We\u0000prove computational hardness results related to equilibrium finding and propose\u0000a practical double-oracle solver based on solving a series of best-response\u0000mixed-integer linear programs. We experiment on both synthetic and real-world\u0000maps, demonstrating that our proposed method scales to reasonably large games.\u0000We also demonstrate the importance of explicitly modeling the capabilities of\u0000the adversary via ablation studies and comparisons with a naive logistics plan\u0000based on heuristics.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A proper mechanism design can help federated learning (FL) to achieve good social welfare by coordinating self-interested clients through the learning process. However, existing mechanisms neglect the network effects of client participation, leading to suboptimal incentives and social welfare. This paper addresses this gap by exploring network effects in FL incentive mechanism design. We establish a theoretical model to analyze FL model performance and quantify the impact of network effects on heterogeneous client participation. Our analysis reveals the non-monotonic nature of FL network effects. To leverage such effects, we propose a model trading and sharing (MTS) framework that allows clients to obtain FL models through participation or purchase. To tackle heterogeneous clients' strategic behaviors, we further design a socially efficient model trading and sharing (SEMTS) mechanism. Our mechanism achieves social welfare maximization solely through customer payments, without additional incentive costs. Experimental results on an FL hardware prototype demonstrate up to 148.86% improvement in social welfare compared to existing mechanisms.
{"title":"Social Welfare Maximization for Federated Learning with Network Effects","authors":"Xiang Li, Yuan Luo, Bing Luo, Jianwei Huang","doi":"arxiv-2408.13223","DOIUrl":"https://doi.org/arxiv-2408.13223","url":null,"abstract":"A proper mechanism design can help federated learning (FL) to achieve good\u0000social welfare by coordinating self-interested clients through the learning\u0000process. However, existing mechanisms neglect the network effects of client\u0000participation, leading to suboptimal incentives and social welfare. This paper\u0000addresses this gap by exploring network effects in FL incentive mechanism\u0000design. We establish a theoretical model to analyze FL model performance and\u0000quantify the impact of network effects on heterogeneous client participation.\u0000Our analysis reveals the non-monotonic nature of FL network effects. To\u0000leverage such effects, we propose a model trading and sharing (MTS) framework\u0000that allows clients to obtain FL models through participation or purchase. To\u0000tackle heterogeneous clients' strategic behaviors, we further design a socially\u0000efficient model trading and sharing (SEMTS) mechanism. Our mechanism achieves\u0000social welfare maximization solely through customer payments, without\u0000additional incentive costs. Experimental results on an FL hardware prototype\u0000demonstrate up to 148.86% improvement in social welfare compared to existing\u0000mechanisms.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The classic house allocation problem involves assigning $m$ houses to $n$ agents based on their utility functions, ensuring each agent receives exactly one house. A key criterion in these problems is satisfying fairness constraints such as envy-freeness. We extend this problem by considering agents with arbitrary weights, focusing on the concept of weighted envy-freeness, which has been extensively studied in fair division. We present a polynomial-time algorithm to determine whether weighted envy-free allocations exist and, if so, to compute one. Since weighted envy-free allocations do not always exist, we also investigate the potential of achieving such allocations through the use of subsidies. We provide several characterizations for weighted envy-freeable allocations (allocations that can be turned weighted envy-free by introducing subsidies) and show that they do not always exist, which is different from the unweighted setting. Furthermore, we explore the existence of weighted envy-freeable allocations in specific scenarios and outline the conditions under which they exist.
{"title":"Weighted Envy-Freeness in House Allocation","authors":"Sijia Dai, Yankai Chen, Xiaowei Wu, Yicheng Xu, Yong Zhang","doi":"arxiv-2408.12523","DOIUrl":"https://doi.org/arxiv-2408.12523","url":null,"abstract":"The classic house allocation problem involves assigning $m$ houses to $n$\u0000agents based on their utility functions, ensuring each agent receives exactly\u0000one house. A key criterion in these problems is satisfying fairness constraints\u0000such as envy-freeness. We extend this problem by considering agents with\u0000arbitrary weights, focusing on the concept of weighted envy-freeness, which has\u0000been extensively studied in fair division. We present a polynomial-time\u0000algorithm to determine whether weighted envy-free allocations exist and, if so,\u0000to compute one. Since weighted envy-free allocations do not always exist, we\u0000also investigate the potential of achieving such allocations through the use of\u0000subsidies. We provide several characterizations for weighted envy-freeable\u0000allocations (allocations that can be turned weighted envy-free by introducing\u0000subsidies) and show that they do not always exist, which is different from the\u0000unweighted setting. Furthermore, we explore the existence of weighted\u0000envy-freeable allocations in specific scenarios and outline the conditions\u0000under which they exist.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Arrow's celebrated Impossibility Theorem asserts that an election rule, or Social Welfare Function (SWF), between three or more candidates meeting a set of strict criteria cannot exist. Maskin suggests that Arrow's conditions for SWFs are too strict. In particular he weakens the "Independence of Irrelevant Alternatives" condition (IIA), which states that if in two elections, each voter's binary preference between candidates $c_i$ and $c_j$ is the same, then the two results must agree on their preference between $c_i$ and $c_j$. Instead, he proposes a modified IIA condition (MIIA). Under this condition, the result between $c_i$ and $c_j$ can be affected not just by the order of $c_i$ and $c_j$ in each voter's ranking, but also the number of candidates between them. More candidates between $c_i$ and $c_j$ communicates some information about the strength of a voter's preference between the two candidates, and Maskin argues that it should be admissible evidence in deciding on a final ranking. We construct SWFs for three-party elections which meet the MIIA criterion along with other sensibility criteria, but are far from being Borda elections (where each voter assigns a score to each candidate linearly according to their ranking). On the other hand, we give cases in which any SWF must be the Borda rule.
{"title":"Non-Borda elections under relaxed IIA conditions","authors":"Gabriel Gendler","doi":"arxiv-2408.12661","DOIUrl":"https://doi.org/arxiv-2408.12661","url":null,"abstract":"Arrow's celebrated Impossibility Theorem asserts that an election rule, or\u0000Social Welfare Function (SWF), between three or more candidates meeting a set\u0000of strict criteria cannot exist. Maskin suggests that Arrow's conditions for\u0000SWFs are too strict. In particular he weakens the \"Independence of Irrelevant\u0000Alternatives\" condition (IIA), which states that if in two elections, each\u0000voter's binary preference between candidates $c_i$ and $c_j$ is the same, then\u0000the two results must agree on their preference between $c_i$ and $c_j$.\u0000Instead, he proposes a modified IIA condition (MIIA). Under this condition, the\u0000result between $c_i$ and $c_j$ can be affected not just by the order of $c_i$\u0000and $c_j$ in each voter's ranking, but also the number of candidates between\u0000them. More candidates between $c_i$ and $c_j$ communicates some information\u0000about the strength of a voter's preference between the two candidates, and\u0000Maskin argues that it should be admissible evidence in deciding on a final\u0000ranking. We construct SWFs for three-party elections which meet the MIIA criterion\u0000along with other sensibility criteria, but are far from being Borda elections\u0000(where each voter assigns a score to each candidate linearly according to their\u0000ranking). On the other hand, we give cases in which any SWF must be the Borda\u0000rule.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces the new concept of (follower) satisfaction in Stackelberg games and compares the standard Stackelberg game with its satisfaction version. Simulation results are presented which suggest that the follower adopting satisfaction generally increases leader utility. This important new result is proven for the case where leader strategies to commit to are restricted to be deterministic (pure strategies). The paper then addresses the application of regret based algorithms to the Stackelberg problem. Although it is known that the follower adopts a no-regret position in a Stackelberg solution, this is not generally the case for the leader. The report examines the convergence behaviour of unconditional and conditional regret matching (RM) algorithms in the Stackelberg setting. The paper shows that, in the examples considered, that these algorithms either converge to any pure Nash equilibria for the simultaneous move game, or to some mixed strategies which do not have the "no-regret" property. In one case, convergence of the conditional RM algorithm over both players to a solution "close" to the Stackelberg case was observed. The paper argues that further research in this area, in particular when applied in the satisfaction setting could be fruitful.
{"title":"Satisfaction and Regret in Stackelberg Games","authors":"Langford White, Duong Nguyen, Hung Nguyen","doi":"arxiv-2408.11340","DOIUrl":"https://doi.org/arxiv-2408.11340","url":null,"abstract":"This paper introduces the new concept of (follower) satisfaction in\u0000Stackelberg games and compares the standard Stackelberg game with its\u0000satisfaction version. Simulation results are presented which suggest that the\u0000follower adopting satisfaction generally increases leader utility. This\u0000important new result is proven for the case where leader strategies to commit\u0000to are restricted to be deterministic (pure strategies). The paper then\u0000addresses the application of regret based algorithms to the Stackelberg\u0000problem. Although it is known that the follower adopts a no-regret position in\u0000a Stackelberg solution, this is not generally the case for the leader. The\u0000report examines the convergence behaviour of unconditional and conditional\u0000regret matching (RM) algorithms in the Stackelberg setting. The paper shows\u0000that, in the examples considered, that these algorithms either converge to any\u0000pure Nash equilibria for the simultaneous move game, or to some mixed\u0000strategies which do not have the \"no-regret\" property. In one case, convergence\u0000of the conditional RM algorithm over both players to a solution \"close\" to the\u0000Stackelberg case was observed. The paper argues that further research in this\u0000area, in particular when applied in the satisfaction setting could be fruitful.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"204 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider committee election of $k geq 3$ (out of $m geq k+1$) candidates, where the voters and the candidates are associated with locations on the real line. Each voter's cardinal preferences over candidates correspond to her distance to the candidate locations, and each voter's cardinal preferences over committees is defined as her distance to the nearest candidate elected in the committee. We consider a setting where the true distances and the locations are unknown. We can nevertheless have access to degraded information which consists of an order of candidates for each voter. We investigate the best possible distortion (a worst-case performance criterion) wrt. the social cost achieved by deterministic committee election rules based on ordinal preferences submitted by $n$ voters and few additional distance queries. We show that for any $k geq 3$, the best possible distortion of any deterministic algorithm that uses at most $k-3$ distance queries cannot be bounded by any function of $n$, $m$ and $k$. We present deterministic algorithms for $k$-committee election with distortion of $O(n)$ with $O(k)$ distance queries and $O(1)$ with $O(k log n)$ distance queries.
{"title":"On the Distortion of Committee Election with 1-Euclidean Preferences and Few Distance Queries","authors":"Dimitris Fotakis, Laurent Gourvès, Panagiotis Patsilinakos","doi":"arxiv-2408.11755","DOIUrl":"https://doi.org/arxiv-2408.11755","url":null,"abstract":"We consider committee election of $k geq 3$ (out of $m geq k+1$)\u0000candidates, where the voters and the candidates are associated with locations\u0000on the real line. Each voter's cardinal preferences over candidates correspond\u0000to her distance to the candidate locations, and each voter's cardinal\u0000preferences over committees is defined as her distance to the nearest candidate\u0000elected in the committee. We consider a setting where the true distances and\u0000the locations are unknown. We can nevertheless have access to degraded\u0000information which consists of an order of candidates for each voter. We\u0000investigate the best possible distortion (a worst-case performance criterion)\u0000wrt. the social cost achieved by deterministic committee election rules based\u0000on ordinal preferences submitted by $n$ voters and few additional distance\u0000queries. We show that for any $k geq 3$, the best possible distortion of any\u0000deterministic algorithm that uses at most $k-3$ distance queries cannot be\u0000bounded by any function of $n$, $m$ and $k$. We present deterministic\u0000algorithms for $k$-committee election with distortion of $O(n)$ with $O(k)$\u0000distance queries and $O(1)$ with $O(k log n)$ distance queries.","PeriodicalId":501316,"journal":{"name":"arXiv - CS - Computer Science and Game Theory","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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