Related papers: Improved Metric Distortion via Threshold Approvals
In this work we consider general facility location and social choice problems, in which sets of agents $\mathcal{A}$ and facilities $\mathcal{F}$ are located in a metric space, and our goal is to assign agents to facilities (as well as…
In the single winner determination problem, we have n voters and m candidates and each voter j incurs a cost c(i, j) if candidate i is chosen. Our objective is to choose a candidate that minimizes the expected total cost incurred by the…
Agents that learn to select optimal actions represent a prominent focus of the sequential decision-making literature. In the face of a complex environment or constraints on time and resources, however, aiming to synthesize such an optimal…
We consider the one-sided matching problem, where n agents have preferences over n items, and these preferences are induced by underlying cardinal valuation functions. The goal is to match every agent to a single item so as to maximize the…
In this note, we uncover three connections between the metric distortion problem and voting methods and axioms from the social choice literature.
It is challenging to quantify numerical preferences for different objectives in a multi-objective decision-making problem. However, the demonstrations of a user are often accessible. We propose an algorithm to infer linear preference…
We study higher statistical moments of Distortion for randomized social choice in a metric implicit utilitarian model. The Distortion of a social choice mechanism is the expected approximation factor with respect to the optimal utilitarian…
We study the utilitarian distortion of social choice mechanisms under the recently proposed learning-augmented framework where some (possibly unreliable) predicted information about the preferences of the agents is given as input. In…
We study the problem of fair $k$-committee selection under an egalitarian objective. Given $n$ agents partitioned into $m$ groups (\eg, demographic quotas), the goal is to aggregate their preferences to form a committee of size $k$ that…
In Spatial Voting Theory, distortion is a measure of how good the winner is. It is proved that no deterministic voting mechanism can guarantee a distortion better than $3$, even for simple metrics such as a line. In this study, we wish to…
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…
{\em Distortion} is a well-established notion for quantifying the loss of social welfare that may occur in voting. As voting rules take as input only ordinal information, they are essentially forced to neglect the exact values the agents…
We consider the fair division of indivisible items among $n$ agents with additive non-negative normalized valuations, with the goal of obtaining high value guarantees, that is, close to the proportional share for each agent. We prove that…
The notion of distortion in social choice problems has been defined to measure the loss in efficiency -- typically measured by the utilitarian social welfare, the sum of utilities of the participating agents -- due to having access only to…
We consider the facility location problem in a metric space, focusing on the case of three agents. We show that selecting the reported location of each agent with probability proportional to the distance between the other two agents results…
We consider a problem where agents have private positions on a line, and public approval preferences over two facilities, and their cost is the maximum distance from their approved facilities. The goal is to decide the facility locations to…
We study the performance of voting mechanisms from a utilitarian standpoint, under the recently introduced framework of metric-distortion, offering new insights along three main lines. First, if $d$ represents the doubling dimension of the…
In voting with ranked ballots, each agent submits a strict ranking of the form $a \succ b \succ c \succ d$ over the alternatives, and the voting rule decides on the winner based on these rankings. Although this ballot format has desirable…
We study single-candidate voting embedded in a metric space, where both voters and candidates are points in the space, and the distances between voters and candidates specify the voters' preferences over candidates. In the voting, each…
The metric distortion of a randomized social choice function (RSCF) quantifies its worst-case approximation ratio to the optimal social cost when the voters' costs for alternatives are given by distances in a metric space. This notion has…