Plurality Veto: A Simple Voting Rule Achieving Optimal Metric Distortion

06/14/2022
by   Fatih Erdem Kizilkaya, et al.
0

The metric distortion framework posits that n voters and m candidates are jointly embedded in a metric space such that voters rank candidates that are closer to them higher. A voting rule's purpose is to pick a candidate with minimum total distance to the voters, given only the rankings, but not the actual distances. As a result, in the worst case, each deterministic rule picks a candidate whose total distance is at least three times larger than that of an optimal one, i.e., has distortion at least 3. A recent breakthrough result showed that achieving this bound of 3 is possible; however, the proof is non-constructive, and the voting rule itself is a complicated exhaustive search. Our main result is an extremely simple voting rule, called Plurality Veto, which achieves the same optimal distortion of 3. Each candidate starts with a score equal to his number of first-place votes. These scores are then gradually decreased via an n-round veto process in which a candidate drops out when his score reaches zero. One after the other, voters decrement the score of their bottom choice among the standing candidates, and the last standing candidate wins. We give a one-paragraph proof that this voting rule achieves distortion 3. This rule is also immensely practical, and it only makes two queries to each voter, so it has low communication overhead. We also generalize Plurality Veto into a class of randomized voting rules in the following way: Plurality veto is run only for k < n rounds; then, a candidate is chosen with probability proportional to his residual score. This general rule interpolates between Random Dictatorship (for k=0) and Plurality Veto (for k=n-1), and k controls the variance of the output. We show that for all k, this rule has distortion at most 3.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/20/2019

Approval-Based Elections and Distortion of Voting Rules

We consider elections where both voters and candidates can be associated...
research
05/31/2023

Generalized Veto Core and a Practical Voting Rule with Optimal Metric Distortion

We revisit the recent breakthrough result of Gkatzelis et al. on (single...
research
11/17/2019

An Analysis Framework for Metric Voting based on LP Duality

Distortion-based analysis has established itself as a fruitful framework...
research
09/28/2019

Voting for Distortion Points in Geometric Processing

Low isometric distortion is often required for mesh parameterizations. A...
research
06/30/2023

Breaking the Metric Voting Distortion Barrier

We consider the following well studied problem of metric distortion in s...
research
06/20/2023

Nearly Optimal Committee Selection For Bias Minimization

We study the model of metric voting proposed by Feldman et al. [2020]. I...
research
05/31/2021

Optimal Algorithms for Multiwinner Elections and the Chamberlin-Courant Rule

We consider the algorithmic question of choosing a subset of candidates ...

Please sign up or login with your details

Forgot password? Click here to reset