Approval-Based Committee Voting under Incomplete Information

TL;DR

This paper explores approval-based committee voting when voters have incomplete preferences, analyzing the computational complexity of determining possible and necessary winners and representation under various models of incomplete information.

Contribution

It introduces models of incomplete voter preferences and studies the complexity of fundamental voting problems under these models for classic approval-based rules.

Findings

Complexity results for possible and necessary winner problems.

Analysis of proportional representation axioms under incomplete preferences.

Applicability to scenarios with partial voter evaluations.

Abstract

We investigate approval-based committee voting with incomplete information about the approval preferences of voters. We consider several models of incompleteness where each voter partitions the set of candidates into approved, disapproved, and unknown candidates, possibly with ordinal preference constraints among candidates in the latter category. This captures scenarios where voters have not evaluated all candidates and/or it is unknown where voters draw the threshold between approved and disapproved candidates. We study the complexity of some fundamental computational problems for a number of classic approval-based committee voting rules including Proportional Approval Voting and Chamberlin-Courant. These problems include determining whether a given set of candidates is a possible or necessary winning committee and whether a given candidate is possibly or necessarily a member of the winning committee. We also consider proportional representation axioms and the problem of deciding whether a given committee is possibly or necessarily representative.