Aggregation Consistency in collective decision-making under uncertainty

Stéphane Gonzalez () and Le-Nhat-Linh Huynh ()
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Stéphane Gonzalez: GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique
Le-Nhat-Linh Huynh: GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - UL2 - Université Lumière - Lyon 2 - UJM - Université Jean Monnet - Saint-Étienne - UJM EPE - Université Jean Monnet (EPSCPE) - EM - EMLyon Business School - CNRS - Centre National de la Recherche Scientifique

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Abstract: We consider a society where agents derive utility from social alternatives, and these utilities may vary across states. Each individual is endowed with their own aggregation operator, which aggregates their utilities across states for each alternative. Aggregation Consistency requires that, if the same set of alternatives is selected for the utility profile in each state, it remains selected for the aggregated utility profile. We combine this property with standard conditions on the social choice correspondence and on individual aggregation operators. We show that Aggregation Consistency forces all individuals to have the same aggregation operator and determines both the form of this function and that of the social choice correspondence. Aggregation operators are weighted quasi-arithmetic means, while the social choice correspondence selects the alternatives maximizing a sum of transformed utilities, where the same transformation determines the quasi-arithmetic means. When weights are interpreted as probabilities, this common transformation connects individual behavior under risk with social aggregation: it determines both individual attitudes toward risk and society's attitude toward inequality.

Date: 2026-10-02
Note: View the original document on HAL open archive server: https://hal.science/hal-05775990v1
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