Approximating Optimal Social Choice under Metric Preferences

Anshelevich, Elliot; Bhardwaj, Onkar; Postl, John

doi:10.1609/aaai.v29i1.9308

Cited by 41 publications

(4 citation statements)

References 25 publications

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“…The distortion measures the inefficiency when a social choice rule (e.g., voting) is applied. Generally, voters with cardinal preferences [10,40]) or metric preferences [3,4,12]) are considered herein. As an embedding on a voter' ballot is allowed, Caragiannis and Procaccia [10] discussed the distortion of social choice when each voter's ballot receives an embedding, which maps the preference to the output ballot.…”

Section: Related Workmentioning

confidence: 99%

On the Efficiency of An Election Game of Two or More Parties: How Bad Can It Be?

Lin¹,

Lu²,

Chen³

2023

Preprint

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We extend our previous work on two-party election competition [Lin, Lu & Chen 2021] to the setting of three or more parties. An election campaign among two or more parties is viewed as a game of two or more players. Each of them has its own candidates as the pure strategies to play. People, as voters, comprise supporters for each party, and a candidate brings utility for the the supporters of each party. Each player nominates exactly one of its candidates to compete against the other party's. A candidate is assumed to win the election with higher odds if it brings more utility for all the people. The payoff of each player is the expected utility its supporters get. The game is egoistic if every candidate benefits her party's supporters more than any candidate from the competing party does. In this work, we first argue that the election game always has a pure-strategy Nash equilibrium when the winner is chosen by the hardmax function, while there exist game instances in the threeparty election game such that no pure-strategy Nash equilibrium exists even if the game is egoistic. Next, we propose two sufficient conditions for the egoistic election game to have a pure-strategy Nash equilibrium. Based on these conditions, we propose a fixed-parameter tractable algorithm to compute a pure-strategy Nash equilibrium of the egoistic election game. Finally, perhaps surprisingly, we show that the price of anarchy of the egoistic election game is upper bounded by the number of parties. Our findings suggest that the election becomes unpredictable when more than two parties are involved and, moreover, the social welfare deteriorates with the number of participating parties in terms of possibly increasing price of anarchy. This work alternatively explains why the two-party system is prevalent in democratic countries.

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Section: Related Workmentioning

confidence: 99%

On the Efficiency of An Election Game of Two or More Parties: How Bad Can It Be?

Lin¹,

Lu²,

Chen³

2023

Preprint

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“…Given a set of points X and a distance function d, the median m is defined to be the point minimizing the sum of distances. Following a long line of work Anshelevich, Filos-Ratsikas, and Voudouris 2022;Feldman, Fiat, and Golomb 2016;Goel, Krishnaswamy, and Munagala 2017;Kempe 2020;Munagala and Wang 2019), there now exists a deterministic algorithm with optimal metric distortion 3 (Gkatzelis, Halpern, and Shah 2020), which is also optimal (Anshelevich, Bhardwaj, and Postl 2015;Anshelevich et al 2018). Using randomization, Charikar et al (2023) recently achieved an important breakthrough, achieving a metric distortion of 2.753.…”

Section: Introductionmentioning

confidence: 99%

Low-Distortion Clustering with Ordinal and Limited Cardinal Information

Burkhardt,

Caragiannis,

Fehrs

et al. 2024

AAAI

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Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of n agents located in an underlying metric space, our goal is to partition them into k clusters, optimizing some social cost objective. The metric space is defined by a distance function d between the agent locations. Information about d is available only implicitly via n rankings, through which each agent ranks all other agents in terms of their distance from her. Still, even though no cardinal information (i.e., the exact distance values) is available, we would like to evaluate clustering algorithms in terms of social cost objectives that are defined using d. This is done using the notion of distortion, which measures how far from optimality a clustering can be, taking into account all underlying metrics that are consistent with the ordinal information available. Unfortunately, the most important clustering objectives (e.g., those used in the well-known k-median and k-center problems) do not admit algorithms with finite distortion. To sidestep this disappointing fact, we follow two alternative approaches: We first explore whether resource augmentation can be beneficial. We consider algorithms that use more than k clusters but compare their social cost to that of the optimal k-clusterings. We show that using exponentially (in terms of k) many clusters, we can get low (constant or logarithmic) distortion for the k-center and k-median objectives. Interestingly, such an exponential blowup is shown to be necessary. More importantly, we explore whether limited cardinal information can be used to obtain better results. Somewhat surprisingly, for k-median and k-center, we show that a number of queries that is polynomial in k and only logarithmic in n (i.e., only sublinear in the number of agents for the most relevant scenarios in practice) is enough to get constant distortion.

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“…The framework has also been extended to multiwinner voting (Caragiannis et al 2017) and participatory budgeting (Benadè et al 2017), under the assumption that the utility of an agent for a set of alternatives is the maximum and the sum of her utilities for the alternatives in the set, respectively. Anshelevich, Bhardwaj, and Postl (2015) built on this idea to propose the metric distortion framework, in which agents and alternatives are embedded in an underlying metric space, and the cost of an agent for an alternative is the distance between them. An agent still ranks the alternatives, but now in a non-decreasing order of their distance from her.…”

Section: Introductionmentioning

confidence: 99%