
Improved Metric Distortion for Deterministic Social Choice Rules
In this paper, we study the metric distortion of deterministic social ch...
read it

Communication, Distortion, and Randomness in Metric Voting
In distortionbased analysis of social choice rules over metric spaces, ...
read it

MetricDistortion Bounds under Limited Information
In this work we study the metric distortion problem in voting theory und...
read it

An Analysis Framework for Metric Voting based on LP Duality
Distortionbased analysis has established itself as a fruitful framework...
read it

Optimal Algorithms for Multiwinner Elections and the ChamberlinCourant Rule
We consider the algorithmic question of choosing a subset of candidates ...
read it

Dimensionality, Coordination, and Robustness in Voting
We study the performance of voting mechanisms from a utilitarian standpo...
read it

Awareness of Voter Passion Greatly Improves the Distortion of Metric Social Choice
We develop new voting mechanisms for the case when voters and candidates...
read it
Resolving the Optimal Metric Distortion Conjecture
We study the following metric distortion problem: there are two finite sets of points, V and C, that lie in the same metric space, and our goal is to choose a point in C whose total distance from the points in V is as small as possible. However, rather than having access to the underlying distance metric, we only know, for each point in V , a ranking of its distances to the points in C. We propose algorithms that choose a point in C using only these rankings as input and we provide bounds on their distortion (worstcase approximation ratio). A prominent motivation for this problem comes from voting theory, where V represents a set of voters, C represents a set of candidates, and the rankings correspond to ordinal preferences of the voters. A major conjecture in this framework is that the optimal deterministic algorithm has distortion 3. We resolve this conjecture by providing a polynomialtime algorithm that achieves distortion 3, matching a known lower bound. We do so by proving a novel lemma about matching rankings of candidates to candidates, which we refer to as the rankingmatching lemma. This lemma induces a family of novel algorithms, which may be of independent interest, and we show that a special algorithm in this family achieves distortion 3. We also provide more refined, parameterized, bounds using the notion of αdecisiveness, which quantifies the extent to which a voter may prefer her top choice relative to all others. Finally, we introduce a new randomized algorithm with improved distortion compared to known results, and also provide improved lower bounds on the distortion of all deterministic and randomized algorithms.
READ FULL TEXT
Comments
There are no comments yet.