Organizations: (†) Dept. of Mathematics, Indiana University, Bloomington. · (‡) Dept. of Computer Science & the Intel Investigations Lab, the City College of New York · the Graduate Center & Remote Sensing Earth Systems Institute, the City University of New York.
This paper studies strict majority reasoning in finite electorates using so-called 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.