Representation with Incomplete Votes

TL;DR

This paper addresses the challenge of fairly representing participant opinions in online civic discussions when votes are incomplete, proposing an adaptive algorithm that ensures fair outcomes efficiently and effectively.

Contribution

It introduces an adaptive voting algorithm for incomplete approval votes, ensuring fair representation and demonstrating practical effectiveness with real data.

Findings

The adaptive algorithm guarantees fair representation with incomplete votes.

Non-adaptive algorithms are impractical due to information requirements.

Empirical results show the algorithm's effectiveness in real-world data.

Abstract

Platforms for online civic participation rely heavily on methods for condensing thousands of comments into a relevant handful, based on whether participants agree or disagree with them. These methods should guarantee fair representation of the participants, as their outcomes may affect the health of the conversation and inform impactful downstream decisions. To that end, we draw on the literature on approval-based committee elections. Our setting is novel in that the approval votes are incomplete since participants will typically not vote on all comments. We prove that this complication renders non-adaptive algorithms impractical in terms of the amount of information they must gather. Therefore, we develop an adaptive algorithm that uses information more efficiently by presenting incoming participants with statements that appear promising based on votes by previous participants. We prove that this method satisfies commonly used notions of fair representation, even when participants only vote on a small fraction of comments. Finally, an empirical evaluation using real data shows that the proposed algorithm provides representative outcomes in practice.