Electing a committee with dominance constraints

We consider the problem of electing a committee of k candidates, subject to constraints as to which committees are admissible for constitutional, conventional, or practical reasons. In our framework, the candidates are given labels as an abstraction of a politician’s religion, a film’s genre, a song...

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Bibliographic Details
Published in:Annals of operations research Vol. 318; no. 2; pp. 985 - 1000
Main Author: Ianovski, Egor
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2022
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Business and Management
Candidates
Combinatorics
Committees
Constraints
Elections
Game theory
Operations research
Operations Research/Decision Theory
Original Research
Polynomials
Preferences
Social choice
Theory of Computation
Voting
Russia
Multiwinner elections
Computational social choice
Voting
Diversity constraints
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary:We consider the problem of electing a committee of k candidates, subject to constraints as to which committees are admissible for constitutional, conventional, or practical reasons. In our framework, the candidates are given labels as an abstraction of a politician’s religion, a film’s genre, a song’s language, or other attribute, and the election outcome is constrained by interval constraints (constraints of the form “Between 3 and 5 candidates with label X”) and dominance constraints (“At least as many candidates with label X as with label Y”). The goal is to select a committee that is as good as possible among those that satisfy the constraints. The difficulty is that in the standard social choice framework we do not have a quantifiable notion of “goodness”, only a voting rule that tells us which committee is the best. In this paper we argue how the logic underlying separable and best- k rules can be extended into an ordering of committees from best to worst, and study the question of how to select the best valid committee with respect to this order. The problem is NP -hard, but we show the existence of a polynomial time solution in the case of tree-like constraints, and a fixed-parameter tractable algorithm for the general case.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-021-04128-7