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<p>This paper scrutinizes the roles played by both subjective and objective probabilities in the representation of preferences under uncertainty. On the one hand, the <i>subjective</i> probability appears in the Choquet expected utility (CEU) preference in which the capacity can be decomposed into a unique probability and a unique strictly increasing distortion function. We call this preference the <i>rank-dependent subjective expected utility</i> (RDSEU). On the other hand, the <i>objective</i> probabilities appear in the domain of the preference consisting of the lottery acts (or the AA-acts). Given these two kinds of probabilities, this paper achieves two objectives. First, we axiomatize the RDSEU with the domain given by the AA-acts by invoking Dana (Scott, <CitationRef CitationID="CR27">1964</CitationRef>) decomposition theorem. Second, supposing that the domains of all the relevant preferences are the AA-acts, we prove that if the preference is represented by the CEU, then it is probabilistically sophisticated (PS) if and only if it is the subjective expected utility (SEU), which implies that, within the class of the CEU preferences, the SEU is the only class of the PS preferences. This shows that if the axioms are imposed over the entire AA-acts, a fairly severe restriction must be assumed on the form of preference representation.</p>

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The roles of subjective/objective probabilities in representation of preferences under uncertainty

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Satoshi Nakada,
  • Hiroyuki Ozaki

摘要

This paper scrutinizes the roles played by both subjective and objective probabilities in the representation of preferences under uncertainty. On the one hand, the subjective probability appears in the Choquet expected utility (CEU) preference in which the capacity can be decomposed into a unique probability and a unique strictly increasing distortion function. We call this preference the rank-dependent subjective expected utility (RDSEU). On the other hand, the objective probabilities appear in the domain of the preference consisting of the lottery acts (or the AA-acts). Given these two kinds of probabilities, this paper achieves two objectives. First, we axiomatize the RDSEU with the domain given by the AA-acts by invoking Dana (Scott, 1964) decomposition theorem. Second, supposing that the domains of all the relevant preferences are the AA-acts, we prove that if the preference is represented by the CEU, then it is probabilistically sophisticated (PS) if and only if it is the subjective expected utility (SEU), which implies that, within the class of the CEU preferences, the SEU is the only class of the PS preferences. This shows that if the axioms are imposed over the entire AA-acts, a fairly severe restriction must be assumed on the form of preference representation.