Majority judgment: Measuring, ranking, and electing

Abstract

Traditional social choice theory is fundamentally constrained by its reliance on ordinal rankings, which inevitably encounter the logical inconsistencies identified by Arrow’s impossibility theorem. By shifting the paradigm from ranking to evaluation, social choice can be placed on a more robust mathematical and practical foundation. This transition is achieved through majority judgment, a method wherein voters or judges evaluate each candidate or competitor independently using a common language of qualitative grades. The collective result is determined by the majority-grade, defined as the median of all evaluations assigned to a candidate. This mechanism satisfies the criterion of independence of irrelevant alternatives and avoids the cycles and paradoxes associated with Condorcet methods. Furthermore, the use of median-based aggregation makes the system uniquely resistant to strategic manipulation; since the median is an order function, voters cannot influence the outcome by “gaming” their grades to extreme values. Empirical data from political elections and professional competitions in fields such as sports and œnology demonstrate that this approach captures a more accurate representation of the collective will than traditional plurality or point-summing systems. It permits the expression of both intensity of preference and consensus, providing a consistent method for measuring and ranking without the inherent contradictions of the ordinal model. – AI-generated abstract.