The Measurable Majority

2026-06-22

AI Summary

This study investigates the rationality and representability of strict majority rule in finite electorates. By modeling voter coalition structures within a social decision framework, the authors introduce a consistency criterion to characterize strict majority judgments and establish their equivalence with finitely additive measure representations. Building on this foundation, they construct the first minimal natural logical system for strict majority, proving its soundness and completeness, and derive a May-type characterization theorem for strict majority rules. The work also refines Suppes’ classical representation theorem for weak qualitative probability structures, thereby providing a precise measure-theoretic and logical foundation for strict majority decision-making.

Abstract

This paper studies strict majority reasoning in finite electorates using so-called $\textit{social decision frames}$: 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.

Problem

• strict majority
• social decision frames
• qualitative probability
• finitely additive measures
• coherence

Innovation

• strict majority
• social decision frames
• coherence criterion
• finitely additive measures
• qualitative probability