Imaging all the people

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

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 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.

• Item Type: Journal article
• EU-FP7/Horizon 2020 Grant Agreement Number: info:eu-repo/grantAgreement/EC/H2020/675415
• Form of publication: Postprint
• Faculties: Philosophy, Philosophy of Science and Religious Science; Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP); Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Diaphora: Logic and Paradox; ERC Grants > ERC Grant 675415: Diaphora: Philosophical Problems, Resilience and Persistent Disagreement
• Subjects: 100 Philosophy and Psychology > 100 Philosophy
• ISSN: 1750-0117
• Language: English