Approximating optimal social choice under metric preferences

Anshelevich, Elliot; Bhardwaj, Onkar; Elkind, Edith; Postl, John; Skowron, Piotr

doi:10.1016/j.artint.2018.07.006

Cited by 106 publications

(338 citation statements)

References 24 publications

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“…From Figure 1 and 2, we can see that the distortion is minimized when τ = 1 + √ 2 in both settings. With only voter preferences being known, the best known deterministic distortion bounds are 3 for two candidates [1], and 4.236 for multiple candidates [25]. Interestingly, if we are also allowed to a choose a threshold τ , our results indicate that the optimal thing to do is to differentiate between candidates with lots of supporters who prefer them at least 1 + √ 2 times to other candidates, and candidates which have few such supporters.…”

Section: Distortionmentioning

confidence: 85%

“…Many insights were obtained for this setting, including that there are deterministic voting rules which obtain a distortion of at most a small constant (5 in [1], and more recently 4.236 in [25]), and that no deterministic rule can obtain a distortion of better than 3 given access to only ordinal information. 1 The fundamental assumption and motivation in the above work is that the strength or intensity of voter preferences is not possible to obtain, and thus we must do the best we can with only ordinal preferences. And indeed, knowing the exact strength of voter preferences is usually impossible.…”

Section: Introductionmentioning

confidence: 99%

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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: Distortionmentioning

confidence: 85%

Section: Introductionmentioning

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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“…In particular, Anshelevich et al (2015) study the same setting as Boutilier et al (2015), but in addition assume the preferences of voters are consistent with distances in a metric space. Approximating utilitarian social welfare given ordinal information has also been studied in mechanism design.…”

Section: Related Workmentioning

confidence: 99%

“…In addition to the aforementioned papers (Procaccia & Rosenschein, 2006;Boutilier et al, 2015), several other papers employ the notion of distortion to quantify how close one can get to maximizing utilitarian social welfare when only ordinal preferences are available (Caragiannis & Procaccia, 2011;Anshelevich, Bhardwaj, & Postl, 2015;Anshelevich & Postl, 2016;Anshelevich & Sekar, 2016). In particular, Anshelevich et al (2015) study the same setting as Boutilier et al (2015), but in addition assume the preferences of voters are consistent with distances in a metric space.…”

Section: Related Workmentioning

confidence: 99%

Subset Selection Via Implicit Utilitarian Voting

Caragiannis¹,

Nath²,

Procaccia³

et al. 2017

jair

101

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How should one aggregate ordinal preferences expressed by voters into a measurably superior social choice? A well-established approach -which we refer to as implicit utilitarian voting -assumes that voters have latent utility functions that induce the reported rankings, and seeks voting rules that approximately maximize utilitarian social welfare. We extend this approach to the design of rules that select a subset of alternatives. We derive analytical bounds on the performance of optimal (deterministic as well as randomized) rules in terms of two measures, distortion and regret. Empirical results show that regret-based rules are more compelling than distortion-based rules, leading us to focus on developing a scalable implementation for the optimal (deterministic) regret-based rule. Our methods underlie the design and implementation of RoboVote.org, a not-for-profit website that helps users make group decisions via AI-driven voting methods.

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“…However, this is not anymore the case if one uses the maximal lotteries randomised voting rule (Brandl et al, 2016). 2 (viii) Better welfare guarantees When considering cardinal preferences over outcomes, a probabilistic approach may achieve better approximation welfare guarantees while simultaneously achieving other axiomatic properties (Anshelevich et al, 2015;Anshelevich and Postl, 2016;Procaccia, 2010).…”

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confidence: 99%