2019/11/03 by David McCarthy, McCarthy, David, Kalle Mikkola +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Economics and business #Functional Equations Stability Results #Game Theory and Applications #Game Theory and Voting Systems #Opinion Dynamics and Social Influence #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.1911.00872
openalex publication_date 2019/11/03 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
We present an abstract social aggregation theorem. Society, and each\nindividual, has a preorder that may be interpreted as expressing values or\nbeliefs. The preorders are allowed to violate both completeness and continuity,\nand the population is allowed to be infinite. The preorders are only assumed to\nbe represented by functions with values in partially ordered vector spaces, and\nwhose product has convex range. This includes all preorders that satisfy strong\nindependence. Any Pareto indifferent social preorder is then shown to be\nrepresented by a linear transformation of the representations of the individual\npreorders. Further Pareto conditions on the social preorder correspond to\npositivity conditions on the transformation. When all the Pareto conditions\nhold and the population is finite, the social preorder is represented by a sum\nof individual preorder representations. We provide two applications. The first\nyields an extremely general version of Harsanyi's social aggregation theorem.\nThe second generalizes a classic result about linear opinion pooling.\n