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Leitgeb, Hannes (2016): Imaging all the people. In: Episteme, Vol. 14, No. 4: pp. 463-479 [PDF, 252kB]


It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out of this dilemma: adapting the method of update or learning such that linear pooling com- mutes with it. As it turns out, the resulting update scheme – (general) imaging on the evidence – is well-known from areas such as the study of conditionals and cau- sal decision theory, and a formal result from which the required commutativity property is derivable was supplied already by Gärdenfors (1982) in a different con- text. We end up determining under which conditions imaging would seem to be right method of update, and under which conditions, therefore, group update would not be affected by the commutativity dilemma.

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