Randomized Social Choice Functions Under Metric Preferences

Anshelevich, Elliot; Postl, John

doi:10.1613/jair.5340

Cited by 96 publications

(208 citation statements)

References 25 publications

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“…Randomized vs Deterministic Mechanisms In this paper we restrict our attention to deterministic social choice rules, instead of randomized ones as in e.g., [2,11,17,22], for several reasons. First, consider looking at our mechanisms from a social choice perspective, i.e., as voting rules that need to be adopted by organizations and used in practice.…”

Section: Two Candidates Multiple Candidatesmentioning

confidence: 99%

Awareness of Voter Passion Greatly Improves the Distortion of Metric Social Choice

Abramowitz

Anshelevich

Zhu

2019

Lecture Notes in Computer Science

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We develop new voting mechanisms for the case when voters and candidates are located in an arbitrary unknown metric space, and the goal is to choose a candidate minimizing social cost: the total distance from the voters to this candidate. Previous work has often assumed that only ordinal preferences of the voters are known (instead of their true costs), and focused on minimizing distortion: the quality of the chosen candidate as compared with the best possible candidate. In this paper, we instead assume that a (very small) amount of information is known about the voter preference strengths, not just about their ordinal preferences. We provide mechanisms with much better distortion when this extra information is known as compared to mechanisms which use only ordinal information. We quantify tradeoffs between the amount of information known about preference strengths and the achievable distortion. We further provide advice about which type of information about preference strengths seems to be the most useful. Finally, we conclude by quantifying the ideal candidate distortion, which compares the quality of the chosen outcome with the best possible candidate that could ever exist, instead of only the best candidate that is actually in the running.

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Section: Two Candidates Multiple Candidatesmentioning

confidence: 99%

Awareness of Voter Passion Greatly Improves the Distortion of Metric Social Choice

Abramowitz

Anshelevich

Zhu

2019

Lecture Notes in Computer Science

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“…Anshelevich and Postl [2] consider randomized social choice rules. The output of such rules is a probability distribution over the set of alternatives rather than a single winning alternative.…”

Section: Related Workmentioning

confidence: 99%

“…However, they may change the probability of the occurrences of events r i = 1 and r j = 1. Let r i and r j be the new indicator variables corresponding to v i and v j , after one of the displacements and let and let δ c k be the value of δ c for the k'th type of displacement (i ∈ [2]). By straightforward calculus, we can show that:…”

Section: Otherwisementioning

confidence: 99%

On the Distortion Value of the Elections with Abstention

Ghodsi

Latifian

Seddighin

2019

AAAI

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In Spatial Voting Theory, distortion is a measure of how good the winner is. It is proved that no deterministic voting mechanism can guarantee a distortion better than 3, even for simple metrics such as a line. In this study, we wish to answer the following question: how does the distortion value change if we allow less motivated agents to abstain from the election?We consider an election with two candidates and suggest an abstention model, which is a more general form of the abstention model proposed by Kirchgässner [15]. We define the concepts of the expected winner and the expected distortion to evaluate the distortion of an election in our model. Our results fully characterize the distortion value and provide a rather complete picture of the model.

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“…Any deterministic rule cannot distinguish I 1 from I 2 , so the winner will be the same in both instances. Thus, in one of them, we will get the ab-distortion of 1 Proof. Let c w be the winner and c o be the optimal candidate.…”

Section: Inmentioning

confidence: 99%

Approval-Based Elections and Distortion of Voting Rules

Grzegorz

Skowron

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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We consider elections where both voters and candidates can be associated with points in a metric space and voters prefer candidates that are closer to those that are farther away. It is often assumed that the optimal candidate is the one that minimizes the total distance to the voters. Yet, the voting rules often do not have access to the metric space M and only see preference rankings induced by M . Consequently, they often are incapable of selecting the optimal candidate. The distortion of a voting rule measures the worst-case loss of the quality being the result of having access only to preference rankings. We extend the idea of distortion to approval-based preferences. First, we compute the distortion of Approval Voting. Second, we introduce the concept of acceptability-based distortion-the main idea behind is that the optimal candidate is the one that is acceptable to most voters. We determine acceptability-distortion for a number of rules, including Plurality, Borda, k-Approval, Veto, the Copeland's rule, Ranked Pairs, the Schulze's method, and STV.

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Randomized Social Choice Functions Under Metric Preferences

Cited by 96 publications

References 25 publications

Awareness of Voter Passion Greatly Improves the Distortion of Metric Social Choice

Awareness of Voter Passion Greatly Improves the Distortion of Metric Social Choice

On the Distortion Value of the Elections with Abstention

Approval-Based Elections and Distortion of Voting Rules

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