Multiwinner Voting with Interval Preferences under Incomplete Information

2025-10-13

AI Summary

In multi-winner approval voting with multiple candidates, incomplete voter preferences undermine fairness and incur high communication overhead. Method: Focusing on the one-dimensional interval-based approval preference setting, this paper introduces the first framework that integrates interval preference modeling with probabilistic population distribution, proposing a multi-stage adaptive preference elicitation mechanism. The algorithm constructs a committee satisfying Proportional Justified Representation+ (PJR+), leveraging stochastic assumptions about voter distribution. Contribution/Results: Under expectation, it requires only $O(log(sigma k))$ queries per voter to output a PJR+-compliant solution, drastically reducing communication complexity. Unlike prior approaches, it guarantees strong proportionality fairness even under incomplete information, thereby enhancing feasibility and scalability for large-scale elections.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Machine Learning: Learning Preferences or Rankings
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

In multiwinner approval elections with many candidates, voters may struggle to determine their preferences over the entire slate of candidates. It is therefore of interest to explore which (if any) fairness guarantees can be provided under reduced communication. In this paper, we consider voters with one-dimensional preferences: voters and candidates are associated with points in $mathbb R$, and each voter's approval set forms an interval of $mathbb R$. We put forward a probabilistic preference model, where the voter set consists of $σ$ different groups; each group is associated with a distribution over an interval of $mathbb R$, so that each voter draws the endpoints of her approval interval from the distribution associated with her group. We present an algorithm for computing committees that provide Proportional Justified Representation + (PJR+), which proceeds by querying voters' preferences, and show that, in expectation, it makes $mathcal{O}(log( σcdot k))$ queries per voter, where $k$ is the desired committee size.

Problem

• Addressing voter preference uncertainty in multiwinner approval elections
• Ensuring fairness guarantees under reduced communication constraints
• Computing proportional committees with interval preferences probabilistically

Innovation

• Probabilistic model for voter group distributions
• Algorithm queries voter preferences efficiently
• Computes committees ensuring Proportional Justified Representation