For centuries, the mathematical aggregation of preferences by groups, organizations, or society itself has received keen interdisciplinary attention. Extensive theoretical work in economics and political science throughout the second half of the 20th century has highlighted the idea that competing notions of rational social choice intrinsically contradict each other. This has led some researchers to consider coherent democratic decision making to be a mathematical impossibility. Recent empirical work in psychology qualifies that view. This nontechnical review sketches a quantitative research paradigm for the behavioral investigation of mathematical social choice rules on real ballots, experimental choices, or attitudinal survey data. The article poses a series of open questions. Some classical work sometimes makes assumptions about voter preferences that are descriptively invalid. Do such technical assumptions lead the theory astray? How can empirical work inform the formulation of meaningful theoretical primitives? Classical “impossibility results” leverage the fact that certain desirable mathematical properties logically cannot hold in all conceivable electorates. Do these properties nonetheless hold true in empirical distributions of preferences? Will future behavioral analyses continue to contradict the expectations of established theory? Under what conditions do competing consensus methods yield identical outcomes and why do they do so?.
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