McCarthy, David and Mikkola, Kalle and Thomas, Teruji (2017): Aggregation for potentially infinite populations without continuity or completeness.
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Abstract
We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling.
Item Type:  MPRA Paper 

Original Title:  Aggregation for potentially infinite populations without continuity or completeness 
Language:  English 
Keywords:  Social aggregation; discontinuous preferences and comparative likelihood relations; incomplete preferences and comparative likelihood relations; infinite populations; Harsanyi's social aggregation theorem; linear opinion pooling; partially ordered vector spaces 
Subjects:  D  Microeconomics > D6  Welfare Economics > D60  General D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement D  Microeconomics > D7  Analysis of Collective DecisionMaking > D70  General D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D83  Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness 
Item ID:  96751 
Depositing User:  Dr David McCarthy 
Date Deposited:  05 Nov 2019 17:30 
Last Modified:  05 Nov 2019 17:30 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/96751 
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Aggregation for general populations without continuity or completeness. (deposited 16 Aug 2017 15:55)
 Aggregation for potentially infinite populations without continuity or completeness. (deposited 05 Nov 2019 17:30) [Currently Displayed]