Multiwinner Voting with Spatial Preferences under Incomplete Information

2026-07-01

AI Summary

This work addresses the challenge of eliciting voter preferences in multiwinner elections, where voters struggle to fully evaluate a large candidate pool, yet existing proportionality guarantees—such as Extended Justified Representation (EJR+)—assume complete approval ballots. Under the axis-aligned random rectangle voting (ARRV) spatial preference model, the authors propose a dimension-agnostic “verify-or-fallback” framework that recovers an EJR+-satisfying committee using only a single tolerance query per voter on one issue. The method achieves this with an expected $O(d \log dk)$ number of queries, independent of the total number of candidates. By integrating spatial preference modeling, planar querying, and modular algorithm design, the approach provides end-to-end theoretical guarantees under known, unknown, and smoothed distributions, substantially reducing the information acquisition cost while preserving strong fairness properties.

Abstract

In multiwinner elections with many candidates, as in participatory budgeting or large-scale recommendation, voters cannot plausibly evaluate every candidate, yet standard proportional-fairness guarantees such as EJR+ are stated for fully specified approval ballots. We ask whether strong proportional representation can still be guaranteed while eliciting only a little from each voter. We study this in a spatial model, the Axis-aligned Random Rectangle Voter (ARRV) model, in which candidates occupy a $d$-dimensional issue space and each voter approves an axis-aligned hyper-rectangle: a tolerance interval on every issue. Preferences are revealed only through Planar queries, each comparing a voter's tolerance to a candidate on a single issue. We give an algorithm returning an EJR+ committee for any distribution over rectangular preferences, using only $\mathcal{O}(d\log dk)$ Planar queries per voter in expectation given a sufficiently large electorate, independent of the number of candidates $m$, where $d$ is the number of issues and $k$ the committee size. The algorithm rests on a dimension-agnostic verify-or-fallback framework whose query cost is governed by two properties supplied by interchangeable modules. We describe such modules, yielding end-to-end guarantees for known, unknown, and smooth distributions.

Problem

• multiwinner voting
• proportional representation
• incomplete information
• spatial preferences
• preference elicitation

Innovation

• Multiwinner Voting
• Spatial Preferences
• Proportional Fairness
• Query Complexity
• EJR+