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On the multiplicative law of subjective probability

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  • Mitsunobu MIYAKE

Abstract

This note elaborates on Luce and Narens' (1978) axiomatic derivation of subjective probability, which generically satisfies the multiplicative law by removing requirement for the derived subjective probability to be non-atomic. For the two original sample spaces, we add the sample space defined by the direct product of the original sample spaces and the sample space of the auxiliary experiment. As a main result, the necessary and sufficient conditions are provided for the likelihood relation on the events of the sample spaces to be represented by the subjective probability satisfying the law with respect to the direct product, allowing atoms in the original sample spaces.

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  • Mitsunobu MIYAKE, 2024. "On the multiplicative law of subjective probability," TERG Discussion Papers 481, Graduate School of Economics and Management, Tohoku University.
    • Handle: RePEc:toh:tergaa:481
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    File URL: http://hdl.handle.net/10097/00135611
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