Approval-Based Elections and Distortion of Voting Rules

Grzegorz, Pierczyński,; Skowron, Piotr

doi:10.24963/ijcai.2019/77

Cited by 14 publications

(16 citation statements)

References 15 publications

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“…Moving away from the unconstrained normalized se ing that we considered here, it would be very interesting to analyze the e ect of districts in the case of metric preferences [Anshelevich et al, 2018], a se ing that has received considerable a ention in the recent related literature on the distortion of voting rules without districts [Abramowitz et al, 2019;Anshelevich and Postl, 2017;Feldman et al, 2016;Goel et al, 2018Goel et al, , 2017Gross et al, 2017;Munagala and Wang, 2019;Pierczynski and Skowron, 2019]. Other important extensions include se ings in which the partitioning of voters into districts is further constrained by natural factors such as geological locations [Lewenberg et al, 2017] or connectivity in social networks [Lesser et al, 2017].…”

Section: Conclusion and Possible Extensionsmentioning

confidence: 99%

The distortion of distributed voting

Filos-Ratsikas

Micha

Voudouris

2020

Artificial Intelligence

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Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the voting process on the societal welfare for the outcome, by bounding the distortion of voting rules. Even though there has been signi cant progress towards this goal, almost all previous works have so far neglected the fact that in many scenarios (like presidential elections) voting is actually a distributed procedure. In this paper, we consider a se ing in which the voters are partitioned into disjoint districts and vote locally therein to elect local winning alternatives using a voting rule; the nal outcome is then chosen from the set of these alternatives. We prove tight bounds on the distortion of well-known voting rules for such distributed elections both from a worst-case perspective as well as from a best-case one. Our results indicate that the partition of voters into districts leads to considerably higher distortion, a phenomenon which we also experimentally showcase using real-world data.

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Section: Conclusion and Possible Extensionsmentioning

confidence: 99%

The distortion of distributed voting

Filos-Ratsikas

Micha

Voudouris

2020

Artificial Intelligence

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“…Exact preference strengths costs are normalized in some way, as in e.g., [5,6,7,9,11,12]. The second approach, which we take here, assumes all voters and candidates are points in a metric space [1,2,3,8,13,14,15,17,19,20,22,27,30].…”

Section: Two Candidates Multiple Candidatesmentioning

confidence: 99%

“…In particular, we consider voters and candidates which lie in an arbitrary unknown metric space. Our work follows a recent line of research in social choice which considers this setting [1,2,3,8,13,14,15,17,19,20,22,27,30]. The distance between each voter and the winning candidate is interpreted as the cost to that voter.…”

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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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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“…Another related recent piece of work is on approval-based voting, due to (Pierczyński and Skowron 2019), whoamong other results -analyze the distortion of approvalbased voting. They consider mechanisms in which voters approve all candidates within a given distance of themselves, not bounded by a number of candidates.…”

Section: Related Workmentioning

confidence: 99%

Communication, Distortion, and Randomness in Metric Voting

Kempe

2020

AAAI

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In distortion-based analysis of social choice rules over metric spaces, voters and candidates are jointly embedded in a metric space. Voters rank candidates by non-decreasing distance. The mechanism, receiving only this ordinal (comparison) information, must select a candidate approximately minimizing the sum of distances from all voters to the chosen candidate. It is known that while the Copeland rule and related rules guarantee distortion at most 5, the distortion of many other standard voting rules, such as Plurality, Veto, or k-approval, grows unboundedly in the number n of candidates.An advantage of Plurality, Veto, or k-approval with small k is that they require less communication from the voters; all deterministic social choice rules known to achieve constant distortion require voters to transmit their complete rankings of all candidates. This motivates our study of the tradeoff between the distortion and the amount of communication in deterministic social choice rules.We show that any one-round deterministic voting mechanism in which each voter communicates only the candidates she ranks in a given set of k positions must have distortion at least 2n-k/k; we give a mechanism achieving an upper bound of O(n/k), which matches the lower bound up to a constant. For more general communication-bounded voting mechanisms, in which each voter communicates b bits of information about her ranking, we show a slightly weaker lower bound of Ω(n/b) on the distortion.For randomized mechanisms, Random Dictatorship achieves expected distortion strictly smaller than 3, almost matching a lower bound of 3 − 2/n for any randomized mechanism that only receives each voter's top choice. We close this gap, by giving a simple randomized social choice rule which only uses each voter's first choice, and achieves expected distortion 3 − 2/n.

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Approval-Based Elections and Distortion of Voting Rules

Cited by 14 publications

References 15 publications

The distortion of distributed voting

The distortion of distributed voting

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

Communication, Distortion, and Randomness in Metric Voting

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