Instability of ex post aggregation in the bolker–jeffrey framework and related instability phenomena

Erkenntnis 55 (2):239-270 (2001)
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Abstract

Suppose n Bayesian agents need to make a decision as a group. The groupas a whole is also supposed to be a Bayesian agent whose probabilities andutilities are derived or aggregated in reasonable ways from the probabilitiesand utilities of the group members. The aggregation could beex ante, i.e., interms of expected utilities, or it could be ex post, i.e., in terms of utilitiesonly, or in terms of utilities and probabilities separately. This study exploresthe ex post approach. Using the Bolker/Jeffrey framework, we show thatex post aggregation is subject to an instability phenomenon. That is, it mayhappen that the group preference between actions ``flips back and forth'''' dependingon the level of detail in which the decision problem is described. Structurally verysimilar phenomena also occur elsewhere in social choice theory, in statistics (Simpson''sParadox), and in voting theory (Ostrogorski''s Paradox).

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Mathias Risse
Harvard University

Citations of this work

Bayesian Group Belief.Franz Dietrich - 2010 - Social Choice and Welfare 35 (4):595-626.

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References found in this work

The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
Laws and Symmetry.Bas C. Van Fraassen - 1989 - Oxford, England: Oxford University Press.
The Logic of Decision.Richard C. Jeffrey - 1965 - New York, NY, USA: University of Chicago Press.

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