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IMAGING ALL THE PEOPLE

Published online by Cambridge University Press:  10 June 2016

Hannes Leitgeb
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Abstract

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 first 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 commutes 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 causal decision theory, and a formal result from which the required commutativity property is derivable was supplied already by Gärdenfors (1982) in a different context. 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.

Type
Articles
Information
Episteme , Volume 14 , Issue 4 , December 2017 , pp. 463 - 479
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Copyright
Copyright © Cambridge University Press 2016 

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References

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