The voting paradox occurs when a democratic society seeking to aggregate individual preferences into a social preference reaches an intransitive ordering. However it is not widely known that the paradox may also manifest for an individual aggregating over attributes of risky objects to form a preference over those objects. When this occurs, the relation ‘stochastically greater than’ is not always transitive and so transitivity need not hold between those objects. We discuss the impact of other decision paradoxes to address a series of philosophical and economic arguments against intransitive (cyclical) choice, before concluding that intransitive choices can be justified.

中文翻译：

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投票悖论……只有一个选民？风险下选择传递性的含义

当一个民主社会试图将个人偏好聚合成一个社会的偏好达到不及物排序。然而，并不为人所知的是，这个悖论也可能表现为个人聚合风险对象的属性以形成对这些对象的偏好。当这种情况发生时，“随机大于”的关系并不总是传递性的，因此传递性不需要在这些对象之间保持。我们讨论了其他决策悖论的影响，以解决一系列反对不及物（循环）选择的哲学和经济论据，然后得出结论，不及物选择可以被证明是合理的。