I study the problem of obtaining a finite expected multi-utility representation for an incomplete preference relation over lotteries. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory and an additional necessary and sufficient axiom.

中文翻译：

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有限预期的多用途表示

我研究了针对彩票的不完全偏好关系获得有限预期的多用途表示的问题。结果表明，当奖赏空间是一个紧凑的度量空间时，只要满足期望效用理论的标准公理以及额外的必要和充分的公理，偏好关系就可以接受这种多效用表示。