Algorithms are increasingly used to guide consequential decisions, such as who should be granted bail or be approved for a loan. Motivated by growing empirical evidence, regulators are concerned about the possibility that the errors of these algorithms differ sharply across subgroups of the population. What are the tradeoffs between accuracy and fairness, and how do these tradeoffs depend on the inputs to the algorithm? We propose a model in which a designer chooses an algorithm that maps observed inputs into decisions, and introduce a fairness-accuracy Pareto frontier. We identify how the algorithm's inputs govern the shape of this frontier, showing (for example) that access to group identity reduces the error for the worse-off group everywhere along the frontier. We then apply these results to study an "input-design" problem where the designer controls the algorithm's inputs (for example, by legally banning an input), but the algorithm itself is chosen by another agent. We show that: (1) all designers strictly prefer to allow group identity if and only if the algorithm's other inputs satisfy a condition we call group-balance; (2) all designers strictly prefer to allow any input (including potentially biased inputs such as test scores) so long as group identity is permitted as an input, but may prefer to ban it when group identity is not.
{"title":"Algorithmic Design: Fairness Versus Accuracy","authors":"Annie Liang, Jay Lu, Xiaosheng Mu","doi":"10.1145/3490486.3538237","DOIUrl":"https://doi.org/10.1145/3490486.3538237","url":null,"abstract":"Algorithms are increasingly used to guide consequential decisions, such as who should be granted bail or be approved for a loan. Motivated by growing empirical evidence, regulators are concerned about the possibility that the errors of these algorithms differ sharply across subgroups of the population. What are the tradeoffs between accuracy and fairness, and how do these tradeoffs depend on the inputs to the algorithm? We propose a model in which a designer chooses an algorithm that maps observed inputs into decisions, and introduce a fairness-accuracy Pareto frontier. We identify how the algorithm's inputs govern the shape of this frontier, showing (for example) that access to group identity reduces the error for the worse-off group everywhere along the frontier. We then apply these results to study an \"input-design\" problem where the designer controls the algorithm's inputs (for example, by legally banning an input), but the algorithm itself is chosen by another agent. We show that: (1) all designers strictly prefer to allow group identity if and only if the algorithm's other inputs satisfy a condition we call group-balance; (2) all designers strictly prefer to allow any input (including potentially biased inputs such as test scores) so long as group identity is permitted as an input, but may prefer to ban it when group identity is not.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133184066","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}
Most algorithmic studies on multi-agent information design have focused on the restricted situation of optimal public signaling with no inter-agent externalities; only a few exceptions investigated special game classes such as zero-sum games and second-price auctions. This paper initiates the algorithmic information design of both public and private signaling in a fundamental class of games with negative externalities, i.e., atomic singleton congestion games, with a wide range of applications in scheduling, routing, and network design, etc. For both public and private signaling, we show that the optimal information design can be efficiently computed when the number of resources is a constant. To our knowledge, this is the first set of efficient exact algorithms for information design in succinctly representable many-player games. Our results hinge on novel techniques such as developing certain reduced forms to compactly characterize equilibria in public signaling or to represent players' marginal beliefs in private signaling. When there are many resources, we show computational intractability results. Here, we introduce a new notion of (equilibrium)-obliviously NP-hardness, which rules out any possibility of computing a good signaling scheme, irrespective of the equilibrium selection. full version of this paper can be accessed from the following link: https://arxiv.org/pdf/2109.12445.pdf
{"title":"Algorithmic Information Design in Multi-Player Games: Possibilities and Limits in Singleton Congestion","authors":"Chenghan Zhou, T. Nguyen, Haifeng Xu","doi":"10.1145/3490486.3538238","DOIUrl":"https://doi.org/10.1145/3490486.3538238","url":null,"abstract":"Most algorithmic studies on multi-agent information design have focused on the restricted situation of optimal public signaling with no inter-agent externalities; only a few exceptions investigated special game classes such as zero-sum games and second-price auctions. This paper initiates the algorithmic information design of both public and private signaling in a fundamental class of games with negative externalities, i.e., atomic singleton congestion games, with a wide range of applications in scheduling, routing, and network design, etc. For both public and private signaling, we show that the optimal information design can be efficiently computed when the number of resources is a constant. To our knowledge, this is the first set of efficient exact algorithms for information design in succinctly representable many-player games. Our results hinge on novel techniques such as developing certain reduced forms to compactly characterize equilibria in public signaling or to represent players' marginal beliefs in private signaling. When there are many resources, we show computational intractability results. Here, we introduce a new notion of (equilibrium)-obliviously NP-hardness, which rules out any possibility of computing a good signaling scheme, irrespective of the equilibrium selection. full version of this paper can be accessed from the following link: https://arxiv.org/pdf/2109.12445.pdf","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133423954","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 a methodology for selecting seeds to maximize contagion using a coarse categorization of individuals. Within a large and flexible class of random graph models, I show how to compute a seed multiplier for each category---the average number of new infections a seed generates---and I propose randomly seeding the category with the highest multiplier. Relative to existing methods for targeted seeding, my approach requires far less computing power---the problem scales with the number of categories, not the number of individuals---and far less data---all we need are estimates for the first two moments of the degree distribution within each category and aggregated relational data on connections between individuals in different categories. I validate the methodology through simulations using real network data.
{"title":"Seeding a Simple Contagion","authors":"E. Sadler","doi":"10.1145/3490486.3538359","DOIUrl":"https://doi.org/10.1145/3490486.3538359","url":null,"abstract":"This paper introduces a methodology for selecting seeds to maximize contagion using a coarse categorization of individuals. Within a large and flexible class of random graph models, I show how to compute a seed multiplier for each category---the average number of new infections a seed generates---and I propose randomly seeding the category with the highest multiplier. Relative to existing methods for targeted seeding, my approach requires far less computing power---the problem scales with the number of categories, not the number of individuals---and far less data---all we need are estimates for the first two moments of the degree distribution within each category and aggregated relational data on connections between individuals in different categories. I validate the methodology through simulations using real network data.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132080591","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 study the design of a class of incentive mechanisms that can effectively prevent cheating in a strategic classification and regression problem. A conventional strategic classification or regression problem is modeled as a Stackelberg game, or a principal-agent problem between the designer of a classifier (the principal) and individuals subject to the classifier's decisions (the agents), potentially from different demographic groups. The former benefits from the accuracy of its decisions, whereas the latter may have an incentive to game the algorithm into making favorable but erroneous decisions. While prior works tend to focus on how to design an algorithm to be more robust to such strategic maneuvering, this study focuses on an alternative, which is to design incentive mechanisms to shape the utilities of the agents and induce effort that genuinely improves their skills, which in turn benefits both parties in the Stackelberg game. Specifically, the principal and the mechanism provider (which could also be the principal itself) move together in the first stage, publishing and committing to a classifier and an incentive mechanism. The agents are (simultaneous) second movers and best respond to the published classifier and incentive mechanism. When an agent's strategic action merely changes its observable features, it hurts the performance of the algorithm. However, if the action leads to improvement in the agent's true label, it not only helps the agent achieve better decision outcomes, but also preserves the performance of the algorithm. We study how a subsidy mechanism can induce improvement actions, positively impact a number of social well-being metrics, such as the overall skill levels of the agents (efficiency) and positive or true positive rate differences between different demographic groups (fairness).
{"title":"Incentive Mechanisms for Strategic Classification and Regression Problems","authors":"Kun Jin, Xueru Zhang, Mohammad Mahdi Khalili","doi":"10.1145/3490486.3538300","DOIUrl":"https://doi.org/10.1145/3490486.3538300","url":null,"abstract":"We study the design of a class of incentive mechanisms that can effectively prevent cheating in a strategic classification and regression problem. A conventional strategic classification or regression problem is modeled as a Stackelberg game, or a principal-agent problem between the designer of a classifier (the principal) and individuals subject to the classifier's decisions (the agents), potentially from different demographic groups. The former benefits from the accuracy of its decisions, whereas the latter may have an incentive to game the algorithm into making favorable but erroneous decisions. While prior works tend to focus on how to design an algorithm to be more robust to such strategic maneuvering, this study focuses on an alternative, which is to design incentive mechanisms to shape the utilities of the agents and induce effort that genuinely improves their skills, which in turn benefits both parties in the Stackelberg game. Specifically, the principal and the mechanism provider (which could also be the principal itself) move together in the first stage, publishing and committing to a classifier and an incentive mechanism. The agents are (simultaneous) second movers and best respond to the published classifier and incentive mechanism. When an agent's strategic action merely changes its observable features, it hurts the performance of the algorithm. However, if the action leads to improvement in the agent's true label, it not only helps the agent achieve better decision outcomes, but also preserves the performance of the algorithm. We study how a subsidy mechanism can induce improvement actions, positively impact a number of social well-being metrics, such as the overall skill levels of the agents (efficiency) and positive or true positive rate differences between different demographic groups (fairness).","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132096735","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}
Tomer Ezra, M. Feldman, N. Gravin, Zhihao Gavin Tang
Online algorithms for secretary matching in bipartite weighted graphs have been studied extensively in recent years. We generalize this study to secretary matching in general weighted graphs, for both vertex and edge arrival models. Under vertex arrival, vertices arrive online in a uniformly random order; upon the arrival of a vertex v, the weights of edges from v to all previously arriving vertices are revealed, and the algorithm decides which of these edges, if any, to include in the matching. We provide a tight 5/12-competitive algorithm for this setting. Interestingly, it outperforms the best possible algorithm for secretary matching in bipartite graphs with 1-sided arrival, which cannot be better than 1/e-competitive. Under edge arrival, edges arrive online in a uniformly random order; upon the arrival of an edge e, its weight is revealed, and the algorithm decides whether to include it in the matching or not. For this setting we provide a 1/4-competitive algorithm, which improves upon the state of the art bound.
{"title":"General Graphs are Easier than Bipartite Graphs: Tight Bounds for Secretary Matching","authors":"Tomer Ezra, M. Feldman, N. Gravin, Zhihao Gavin Tang","doi":"10.1145/3490486.3538290","DOIUrl":"https://doi.org/10.1145/3490486.3538290","url":null,"abstract":"Online algorithms for secretary matching in bipartite weighted graphs have been studied extensively in recent years. We generalize this study to secretary matching in general weighted graphs, for both vertex and edge arrival models. Under vertex arrival, vertices arrive online in a uniformly random order; upon the arrival of a vertex v, the weights of edges from v to all previously arriving vertices are revealed, and the algorithm decides which of these edges, if any, to include in the matching. We provide a tight 5/12-competitive algorithm for this setting. Interestingly, it outperforms the best possible algorithm for secretary matching in bipartite graphs with 1-sided arrival, which cannot be better than 1/e-competitive. Under edge arrival, edges arrive online in a uniformly random order; upon the arrival of an edge e, its weight is revealed, and the algorithm decides whether to include it in the matching or not. For this setting we provide a 1/4-competitive algorithm, which improves upon the state of the art bound.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116196948","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}
Amanda Kube, Sanmay Das, P. Fowler, Yevgeniy Vorobeychik
We examine justice in data-aided decisions in the context of a scarce societal resource allocation problem. Non-experts (recruited on Amazon Mechanical Turk) have to determine which homeless households to serve with limited housing assistance. We empirically elicit decision-maker preferences for whether to prioritize more vulnerable households or households who would best take advantage of more intensive interventions. We present three main findings. (1) When vulnerability or outcomes are quantitatively conceptualized and presented, humans (at a single point in time) are remarkably consistent in making either vulnerability- or outcome-oriented decisions. (2) Prior exposure to quantitative outcome predictions has a significant effect and changes the preferences of human decision-makers from vulnerability-oriented to outcome-oriented about one-third of the time. (3) Presenting algorithmically-derived risk predictions in addition to household descriptions reinforces decision-maker preferences. Among the vulnerability-oriented, presenting the risk predictions leads to a significant increase in allocations to the more vulnerable household, whereas among the outcome-oriented it leads to a significant decrease in allocations to the more vulnerable household. These findings emphasize the importance of explicitly aligning data-driven decision aids with system-wide allocation goals.
{"title":"Just Resource Allocation? How Algorithmic Predictions and Human Notions of Justice Interact","authors":"Amanda Kube, Sanmay Das, P. Fowler, Yevgeniy Vorobeychik","doi":"10.1145/3490486.3538305","DOIUrl":"https://doi.org/10.1145/3490486.3538305","url":null,"abstract":"We examine justice in data-aided decisions in the context of a scarce societal resource allocation problem. Non-experts (recruited on Amazon Mechanical Turk) have to determine which homeless households to serve with limited housing assistance. We empirically elicit decision-maker preferences for whether to prioritize more vulnerable households or households who would best take advantage of more intensive interventions. We present three main findings. (1) When vulnerability or outcomes are quantitatively conceptualized and presented, humans (at a single point in time) are remarkably consistent in making either vulnerability- or outcome-oriented decisions. (2) Prior exposure to quantitative outcome predictions has a significant effect and changes the preferences of human decision-makers from vulnerability-oriented to outcome-oriented about one-third of the time. (3) Presenting algorithmically-derived risk predictions in addition to household descriptions reinforces decision-maker preferences. Among the vulnerability-oriented, presenting the risk predictions leads to a significant increase in allocations to the more vulnerable household, whereas among the outcome-oriented it leads to a significant decrease in allocations to the more vulnerable household. These findings emphasize the importance of explicitly aligning data-driven decision aids with system-wide allocation goals.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124321340","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}
Bargaining is ubiquitous. How can people bargain better? We train a reinforcement learning agent to bargain optimally in "Best Offer" listings on eBay, and we characterize its behavior in a manner that humans can use. As a buyer, the agent starts lower than human buyers and bargains longer. As the seller, the agent interprets offers as signals---of the buyer's willingness to pay and of the item's desirability---that human sellers ignore. Simple strategies derived from these agents purchase more items for lower prices than human buyers and sell more items for higher prices than human sellers.
{"title":"The Science of the Deal: Optimal Bargaining on eBay Using Deep Reinforcement Learning","authors":"Etan A. Green, E. B. Plunkett","doi":"10.1145/3490486.3538373","DOIUrl":"https://doi.org/10.1145/3490486.3538373","url":null,"abstract":"Bargaining is ubiquitous. How can people bargain better? We train a reinforcement learning agent to bargain optimally in \"Best Offer\" listings on eBay, and we characterize its behavior in a manner that humans can use. As a buyer, the agent starts lower than human buyers and bargains longer. As the seller, the agent interprets offers as signals---of the buyer's willingness to pay and of the item's desirability---that human sellers ignore. Simple strategies derived from these agents purchase more items for lower prices than human buyers and sell more items for higher prices than human sellers.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117020594","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}
M. Braverman, M. Derakhshan, Antonio Molina Lovett
In this paper, we study max-weight stochastic matchings on online bipartite graphs under both vertex and edge arrivals. We focus on designing polynomial time approximation algorithms with respect to the online benchmark, which was first considered by Papadimitriou, Pollner, Saberi, and Wajc [EC'21]. In the vertex arrival version of the problem, the goal is to find an approximate max-weight matching of a given bipartite graph when the vertices in one part of the graph arrive online in a fixed order with independent chances of failure. Whenever a vertex arrives we should decide, irrevocably, whether to match it with one of its unmatched neighbors or leave it unmatched forever. There has been a long line of work designing approximation algorithms for different variants of this problem with respect to the offline benchmark (prophet). Papadimitriou et al., however, propose the alternative online benchmark and show that considering this new benchmark allows them to improve the 0.5 approximation ratio, which is the best ratio achievable with respect to the offline benchmark. They provide a 0.51-approximation algorithm which was later improved to 0.526 by Saberi and Wajc [ICALP'21]. The main contribution of this paper is designing a simple algorithm with a significantly improved approximation ratio of (1-1/e) for this problem. We also consider the edge arrival version in which, instead of vertices, edges of the graph arrive in an online fashion with independent chances of failure. Designing approximation algorithms for this problem has also been studied extensively with the best approximation ratio being 0.337 with respect to the offline benchmark. This paper, however, is the first to consider the online benchmark for the edge arrival version of the problem. For this problem, we provide a simple algorithm with an approximation ratio of 0.5 with respect to the online benchmark.
{"title":"Max-Weight Online Stochastic Matching: Improved Approximations Against the Online Benchmark","authors":"M. Braverman, M. Derakhshan, Antonio Molina Lovett","doi":"10.1145/3490486.3538315","DOIUrl":"https://doi.org/10.1145/3490486.3538315","url":null,"abstract":"In this paper, we study max-weight stochastic matchings on online bipartite graphs under both vertex and edge arrivals. We focus on designing polynomial time approximation algorithms with respect to the online benchmark, which was first considered by Papadimitriou, Pollner, Saberi, and Wajc [EC'21]. In the vertex arrival version of the problem, the goal is to find an approximate max-weight matching of a given bipartite graph when the vertices in one part of the graph arrive online in a fixed order with independent chances of failure. Whenever a vertex arrives we should decide, irrevocably, whether to match it with one of its unmatched neighbors or leave it unmatched forever. There has been a long line of work designing approximation algorithms for different variants of this problem with respect to the offline benchmark (prophet). Papadimitriou et al., however, propose the alternative online benchmark and show that considering this new benchmark allows them to improve the 0.5 approximation ratio, which is the best ratio achievable with respect to the offline benchmark. They provide a 0.51-approximation algorithm which was later improved to 0.526 by Saberi and Wajc [ICALP'21]. The main contribution of this paper is designing a simple algorithm with a significantly improved approximation ratio of (1-1/e) for this problem. We also consider the edge arrival version in which, instead of vertices, edges of the graph arrive in an online fashion with independent chances of failure. Designing approximation algorithms for this problem has also been studied extensively with the best approximation ratio being 0.337 with respect to the offline benchmark. This paper, however, is the first to consider the online benchmark for the edge arrival version of the problem. For this problem, we provide a simple algorithm with an approximation ratio of 0.5 with respect to the online benchmark.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124050052","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 voting rule decides on a probability distribution over a set of m alternatives, based on rankings of those alternatives provided by agents. We assume that agents have cardinal utility functions over the alternatives, but voting rules have access to only the rankings induced by these utilities. We evaluate how well voting rules do on measures of social welfare and of proportional fairness, computed based on the hidden utility functions. In particular, we study the distortion of voting rules, which is a worst-case measure. It is an approximation ratio comparing the utilitarian social welfare of the optimum outcome to the social welfare produced by the outcome selected by the voting rule, in the worst case over possible input profiles and utility functions that are consistent with the input. The previous literature has studied distortion with unit-sum utility functions (which are normalized to sum to 1), and left a small asymptotic gap in the best possible distortion. Using tools from the theory of fair multi-winner elections, we propose the first voting rule which achieves the optimal distortion Θ(√m) for unit-sum utilities. Our voting rule also achieves optimum Θ(√m) distortion for a larger class of utilities, including unit-range and approval (0/1) utilities. We then take a similar worst-case approach to a quantitative measure of the fairness of a voting rule, called proportional fairness. Informally, it measures whether the influence of cohesive groups of agents on the voting outcome is proportional to the group size. We show that there is a voting rule which, without knowledge of the utilities, can achieve an O(log m)-approximation to proportional fairness, which is the best possible approximation. As a consequence of its proportional fairness, we show that this voting rule achieves O(log m) distortion with respect to the Nash welfare, and selects a distribution that is approximately stable by being an O(log m)-approximation to the core, making it interesting for applications in participatory budgeting.
{"title":"Optimized Distortion and Proportional Fairness in Voting","authors":"Soroush Ebadian, Dominik Peters, Nisarg Shah","doi":"10.1145/3490486.3538339","DOIUrl":"https://doi.org/10.1145/3490486.3538339","url":null,"abstract":"A voting rule decides on a probability distribution over a set of m alternatives, based on rankings of those alternatives provided by agents. We assume that agents have cardinal utility functions over the alternatives, but voting rules have access to only the rankings induced by these utilities. We evaluate how well voting rules do on measures of social welfare and of proportional fairness, computed based on the hidden utility functions. In particular, we study the distortion of voting rules, which is a worst-case measure. It is an approximation ratio comparing the utilitarian social welfare of the optimum outcome to the social welfare produced by the outcome selected by the voting rule, in the worst case over possible input profiles and utility functions that are consistent with the input. The previous literature has studied distortion with unit-sum utility functions (which are normalized to sum to 1), and left a small asymptotic gap in the best possible distortion. Using tools from the theory of fair multi-winner elections, we propose the first voting rule which achieves the optimal distortion Θ(√m) for unit-sum utilities. Our voting rule also achieves optimum Θ(√m) distortion for a larger class of utilities, including unit-range and approval (0/1) utilities. We then take a similar worst-case approach to a quantitative measure of the fairness of a voting rule, called proportional fairness. Informally, it measures whether the influence of cohesive groups of agents on the voting outcome is proportional to the group size. We show that there is a voting rule which, without knowledge of the utilities, can achieve an O(log m)-approximation to proportional fairness, which is the best possible approximation. As a consequence of its proportional fairness, we show that this voting rule achieves O(log m) distortion with respect to the Nash welfare, and selects a distribution that is approximately stable by being an O(log m)-approximation to the core, making it interesting for applications in participatory budgeting.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126798269","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}
Rediet Abebe, Nicole Immorlica, J. Kleinberg, Brendan Lucier, Ali Shirali
The tendency for individuals to form social ties with others who are similar to themselves, known as homophily, is one of the most robust sociological principles. Since this phenomenon can lead to patterns of interactions that segregate people along different demographic dimensions, it can also lead to inequalities in access to information, resources, and opportunities. As we consider potential interventions that might alleviate the effects of segregation, we face the challenge that homophily constitutes a pervasive and organic force that is difficult to push back against. Designing effective interventions can therefore benefit from identifying counterbalancing social processes that might be harnessed to work in opposition to segregation. In this work, we show that triadic closure---another common phenomenon that posits that individuals with a mutual connection are more likely to be connected to one another---can be one such process. In doing so, we challenge a long-held belief that triadic closure and homophily work in tandem. By analyzing several fundamental network models using popular integration measures, we demonstrate the desegregating potential of triadic closure. We further empirically investigate this effect on real-world dynamic networks, surfacing observations that mirror our theoretical findings. We leverage these insights to discuss simple interventions that can help reduce segregation in settings that exhibit an interplay between triadic closure and homophily. We conclude with a discussion on qualitative implications for the design of interventions in settings where individuals arrive in an online fashion, and the designer can influence the initial set of connections.
{"title":"On the Effect of Triadic Closure on Network Segregation","authors":"Rediet Abebe, Nicole Immorlica, J. Kleinberg, Brendan Lucier, Ali Shirali","doi":"10.1145/3490486.3538322","DOIUrl":"https://doi.org/10.1145/3490486.3538322","url":null,"abstract":"The tendency for individuals to form social ties with others who are similar to themselves, known as homophily, is one of the most robust sociological principles. Since this phenomenon can lead to patterns of interactions that segregate people along different demographic dimensions, it can also lead to inequalities in access to information, resources, and opportunities. As we consider potential interventions that might alleviate the effects of segregation, we face the challenge that homophily constitutes a pervasive and organic force that is difficult to push back against. Designing effective interventions can therefore benefit from identifying counterbalancing social processes that might be harnessed to work in opposition to segregation. In this work, we show that triadic closure---another common phenomenon that posits that individuals with a mutual connection are more likely to be connected to one another---can be one such process. In doing so, we challenge a long-held belief that triadic closure and homophily work in tandem. By analyzing several fundamental network models using popular integration measures, we demonstrate the desegregating potential of triadic closure. We further empirically investigate this effect on real-world dynamic networks, surfacing observations that mirror our theoretical findings. We leverage these insights to discuss simple interventions that can help reduce segregation in settings that exhibit an interplay between triadic closure and homophily. We conclude with a discussion on qualitative implications for the design of interventions in settings where individuals arrive in an online fashion, and the designer can influence the initial set of connections.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123325503","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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