# Constitutional Governance in Metric Spaces

arXiv: https://arxiv.org/abs/2605.13362 · HTML: https://mlsanity.com/paper/2605.13362/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 26 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 8 of 8)

- [Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation](https://mlsanity.com/paper/1806.06277/) (2018)
- [Metric Distortion of Social Choice Rules: Lower Bounds and Fairness Properties](https://mlsanity.com/paper/1612.02912/) (2016)
- [United for Change: Deliberative Coalition Formation to Change the Status Quo](https://mlsanity.com/paper/2001.08031/) (2020)
- [Reality-Aware Social Choice](https://mlsanity.com/paper/1710.10117/) (2017)
- [In the Beginning there were n Agents: Founding and Amending a Constitution](https://mlsanity.com/paper/2011.03111/) (2020)
- [Grassroots Federation: Fair Democratic Governance at Scale](https://mlsanity.com/paper/2505.02208/) (2025)
- [AI-Generated Compromises for Coalition Formation](https://mlsanity.com/paper/2506.06837/) (2025)
- [Complexity of Deliberative Coalition Formation](https://mlsanity.com/paper/2202.12594/) (2022)

## Abstract (arXiv)

Computational social choice and algorithmic decision theory offer rich aggregation theory but no end-to-end process for egalitarian self-governance: aggregation, deliberation, amendment, and consensus are each considered in isolation, with key metric-space aggregators being NP-hard. Here, we propose constitutional governance in metric spaces, integrating these stages into a protocol for constitutional governance. A community's legal corpus comprises its laws together with a constitution, each being a point in a metric space, with the constitution specifying the supermajority threshold required to amend it. Members vote to amend the legal corpus by proposing their ideal points, followed by rounds of submitting public proposals carrying supermajority public support; a polynomial-time aggregation rule scores each proposal, and a supported proposal whose score is positive and maximal for two rounds is adopted; if none is found the status quo is retained. Public proposals can be sourced from deliberation, vote aggregation, or AI mediation. With Constitutional Consensus, a community can run the constitutional governance protocol on members' personal computing devices (e.g., smartphones), achieving digital sovereignty. By drawing on metric-space aggregation, reality-aware social choice, supermajority amendment, constitutional consensus, deliberative coalition formation, and AI mediation, we provide a comprehensive framework for the constitutional governance of digital communities and organisations.