# The Measurable Majority

arXiv: https://arxiv.org/abs/2606.23853 · HTML: https://mlsanity.com/paper/2606.23853/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 23 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 1 of 1)

- [Exploring the Landscape of Relational Syllogistic Logics](https://mlsanity.com/paper/1809.00656/) (2018)

## Built on by (most cited first, 1 of 1)

- [Measurable Majorities Are Not Finitely Axiomatizable](https://mlsanity.com/paper/2606.25954/) (2026)

## Abstract (arXiv)

This paper studies strict majority reasoning in finite electorates using so-called textitsocial decision frames: finite sets of voters equipped with distinguished families of coalitions interpreted as those voting blocs evaluated to form a strict majority. A coherence criterion for qualitative majority judgments is identified and shown to give an exact characterization for representability of strict majorities by finitely additive measures. In addition, a minimal natural logic for reasoning about strict majorities is shown to be sound and complete. These developments motivate examination of associated combinatorial questions concerning incoherence in finite families of sets; partial results and a conjecture are given. Finally, the results of this paper are applied to correct a classical representation theorem for weak qualitative probability structures due to Patrick Suppes and to establish a May-type characterization for ordinary strict majority rule for social decision frames.