# Representation with Incomplete Votes

arXiv: https://arxiv.org/abs/2211.15608 · HTML: https://mlsanity.com/paper/2211.15608/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2022.

## Built on by (most cited first, 13 of 13)

- [Social Choice Should Guide AI Alignment in Dealing with Diverse Human Feedback](https://mlsanity.com/paper/2404.10271/) (2024)
- [Generative Social Choice](https://mlsanity.com/paper/2309.01291/) (2023)
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- [Generative Social Choice: The Next Generation](https://mlsanity.com/paper/2505.22939/) (2025)
- [Computing Voting Rules with Elicited Incomplete Votes](https://mlsanity.com/paper/2402.11104/) (2024)
- [Adaptive political surveys and GPT-4: Tackling the cold start problem with simulated user interactions](https://mlsanity.com/paper/2503.09311/) (2025)
- [Representative Ranking for Deliberation in the Public Sphere](https://mlsanity.com/paper/2503.18962/) (2025)
- [A Linear Theory of Multi-Winner Voting](https://mlsanity.com/paper/2503.03082/) (2025)
- [Artificial Delegates Resolve Fairness Issues in Perpetual Voting with Partial Turnout](https://mlsanity.com/paper/2506.21186/) (2025)
- [Linear Social Choice with Few Queries: A Moment-Based Approach](https://mlsanity.com/paper/2603.19510/) (2026)
- [Probably Approximately Consensus: On the Learning Theory of Finding Common Ground](https://mlsanity.com/paper/2604.21811/) (2026)
- [Fairness in the Multi-Secretary Problem](https://mlsanity.com/paper/2511.23097/) (2025)
- [AI of the People, by the People, for the People: A Social Choice Approach to Collective Control of Artificial Intelligence](https://mlsanity.com/paper/2605.16291/) (2026)

## Abstract (arXiv)

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.