Abstract
For a large society conceived as an infinite set of individuals, a probabilistic rule of aggregation is introduced and defined as a probability distribution over the infinite set of individual utilities. Then, two generalizations of Harsanyi (1955) possibility result are established for large societies (Theorems 1–2), one for an arbitrary space of acts and the other for a finite dimensional one.
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Notes
A vnm individual is an individual whose preferences satisfy all vnm axioms.
Note that the integration notion refers to the coordinate-wise integration.
More generally, the closure of any set A is thereafter denoted by \(\overline{A}\).
This follows also from Theorem 5.35 in (Aliprantis and Border 2006).
We are particularly indebted to Marcus Pivato who suggested this interpretation.
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This research has been conducted as part of the project LabEx mmedii.
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Askoura, Y., Billot, A. A probabilistic aggregation rule for large societies. Econ Theory Bull 6, 251–262 (2018). https://doi.org/10.1007/s40505-017-0132-5
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DOI: https://doi.org/10.1007/s40505-017-0132-5