Ordinal Approximation for Social Choice, Matching, and Facility Location Problems given Candidate Positions

by   Elliot Anshelevich, et al.

In this work we consider general facility location and social choice problems, in which sets of agents A and facilities F are located in a metric space, and our goal is to assign agents to facilities (as well as choose which facilities to open) in order to optimize the social cost. We form new algorithms to do this in the presence of only ordinal information, i.e., when the true costs or distances from the agents to the facilities are unknown, and only the ordinal preferences of the agents for the facilities are available. The main difference between our work and previous work in this area is that while we assume that only ordinal information about agent preferences in known, we know the exact locations of the possible facilities F. Due to this extra information about the facilities, we are able to form powerful algorithms which have small distortion, i.e., perform almost as well as omniscient algorithms but use only ordinal information about agent preferences. For example, we present natural social choice mechanisms for choosing a single facility to open with distortion of at most 3 for minimizing both the total and the median social cost; this factor is provably the best possible. We analyze many general problems including matching, k-center, and k-median, and present black-box reductions from omniscient approximation algorithms with approximation factor β to ordinal algorithms with approximation factor 1+2β; doing this gives new ordinal algorithms for many important problems, and establishes a toolkit for analyzing such problems in the future.


page 1

page 2

page 3

page 4


Improved Metric Distortion via Threshold Approvals

We consider a social choice setting in which agents and alternatives are...

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

We develop new voting mechanisms for the case when voters and candidates...

Sequential Deliberation for Social Choice

In large scale collective decision making, social choice is a normative ...

Truthful Mechanisms for Matching and Clustering in an Ordinal World

We study truthful mechanisms for matching and related problems in a part...

Blind, Greedy, and Random: Ordinal Approximation Algorithms for Matching and Clustering

We study Matching and other related problems in a partial information se...

Approximation and Heuristic Algorithms for Probabilistic Physical Search on General Graphs

We consider an agent seeking to obtain an item, potentially available at...

Please sign up or login with your details

Forgot password? Click here to reset