Constitutional Governance in Metric Spaces

Ehud Shapiro and Nimrod Talmon

Papers from arXiv.org

Abstract: 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 \emph{constitutional governance in metric spaces}, integrating these stages into a protocol for constitutional governance. A community's \emph{legal corpus} comprises its \emph{laws} together with a \emph{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 \emph{public proposals} carrying \emph{supermajority public support}; a polynomial-time \emph{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.

Date: 2026-05, Revised 2026-07
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