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<p>Intransitive indifference is a well-documented phenomenon in which the decision maker is forced to choose between alternatives with a subtle difference. In this paper, we establish a general model that extends the semiorder/interval order approach (e.g., Fishburn in J Math Psychol 7: 144–149, 1970a. <a href="https://doi.org/10.1016/0022-2496(70)90062-3">https://doi.org/10.1016/0022-2496(70)90062-3</a>; Luce in Econometrica 24: 178–191, 1956. <a href="https://doi.org/10.2307/1905751">https://doi.org/10.2307/1905751</a>) by adopting the set of lotteries as the domain of choice and a direction-dependent just-noticeable difference function. The model can distinguish two classes of intransitive indifference, that is, <i>imperfect discrimination</i>, which is relevant to previous studies on intransitive indifference, and <i>uncertainty about tastes</i>, which is relevant to incomplete preferences. The main theorem axiomatizes the essentially unique <i>expected utility with direction-dependent sensitivity</i> representation. The key axioms for this characterization are <i>irresolute independence</i>, wherein mixing alternatives with another alternative may change a strict preference to indifference while preserving indifference, and <i>strict preference convexity</i>, which derives the convexity of strict upper and lower contour sets. We also obtain two special cases of our model—one-directional and categorical sensitivity—which highlight the two classes of intransitive indifference, and discuss a possible change in the domain of choice to a vector space.</p>

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Intransitive indifference with direction-dependent sensitivity

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    2026年5月9日

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  • Nobuo Koida

摘要

Intransitive indifference is a well-documented phenomenon in which the decision maker is forced to choose between alternatives with a subtle difference. In this paper, we establish a general model that extends the semiorder/interval order approach (e.g., Fishburn in J Math Psychol 7: 144–149, 1970a. https://doi.org/10.1016/0022-2496(70)90062-3; Luce in Econometrica 24: 178–191, 1956. https://doi.org/10.2307/1905751) by adopting the set of lotteries as the domain of choice and a direction-dependent just-noticeable difference function. The model can distinguish two classes of intransitive indifference, that is, imperfect discrimination, which is relevant to previous studies on intransitive indifference, and uncertainty about tastes, which is relevant to incomplete preferences. The main theorem axiomatizes the essentially unique expected utility with direction-dependent sensitivity representation. The key axioms for this characterization are irresolute independence, wherein mixing alternatives with another alternative may change a strict preference to indifference while preserving indifference, and strict preference convexity, which derives the convexity of strict upper and lower contour sets. We also obtain two special cases of our model—one-directional and categorical sensitivity—which highlight the two classes of intransitive indifference, and discuss a possible change in the domain of choice to a vector space.