# Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation

arXiv: https://arxiv.org/abs/1806.06277 · HTML: https://mlsanity.com/paper/1806.06277/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2018.

## Built on by (most cited first, 7 of 7)

- [Byzantine-Robust Decentralized Learning via ClippedGossip](https://mlsanity.com/paper/2202.01545/) (2022)
- [Foundations for Grassroots Democratic Metaverse](https://mlsanity.com/paper/2203.04090/) (2022)
- [AI-Generated Compromises for Coalition Formation](https://mlsanity.com/paper/2506.06837/) (2025)
- [Probably Approximately Consensus: On the Learning Theory of Finding Common Ground](https://mlsanity.com/paper/2604.21811/) (2026)
- [Embeddings for Preferences, Not Semantics](https://mlsanity.com/paper/2605.08360/) (2026)
- [AI-Generated Compromises for Coalition Formation: Modeling, Simulation, and a Textual Case Study](https://mlsanity.com/paper/2512.05983/) (2025)
- [Constitutional Governance in Metric Spaces](https://mlsanity.com/paper/2605.13362/) (2026)

## Abstract (arXiv)

We present a unifying framework encompassing many social choice settings. Viewing each social choice setting as voting in a suitable metric space, we consider a general model of social choice over metric spaces, in which---similarly to the spatial model of elections---each voter specifies an ideal element of the metric space. The ideal element functions as a vote, where each voter prefers elements that are closer to her ideal element. But it also functions as a proposal, thus making all participants equal not only as voters but also as proposers. We consider Condorcet aggregation and a continuum of solution concepts, ranging from minimizing the sum of distances to minimizing the maximum distance. We study applications of the abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters, and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making.