Lunch In Theory This Thursday (12:00, 9/18, GCS 502c)
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Devansh Gupta
Sep 17, 2025, 1:01:47 PMSep 17
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Hi all,
Please join us for Lunch in Theory this Thursday 9/18 at 12:00 in GCS 502c.
Reminder: please bring your own lunch, as lunch will not be provided.
This week we have Fatih Kizilkaya giving his quals and he will be speaking on metric distortion. Please find the title and abstract attached.
We look forward to having you all in the talk.
Best,
Devansh
Plurality Veto: A Simple Voting Rule Achieving Optimal Metric Distortion
Abstract:
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 show that a straightforward extension can be used to give a constructive proof of the more general Ranking-Matching Lemma of Gkatzelis et al.
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 expected distortion at most 3.
Abstract:
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 show that a straightforward extension can be used to give a constructive proof of the more general Ranking-Matching Lemma of Gkatzelis et al.
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 expected distortion at most 3.
Devansh Gupta
Sep 18, 2025, 3:02:32 PMSep 18
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Hi all,
Please find the zoom link attached for the talk today: https://usc.zoom.us/j/7808315301.
Best,
Devansh
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