Suppose that a decision-maker’s aim, under certainty, is to maximize some continuous value, such as lifetime income or continuous social welfare. Can such a decision-maker rationally satisfy what has been called ‘continuity for easy cases’ while at the same time satisfying what seems to be a widespread intuition against the full-blown continuity axiom of expected utility theory? In this note I argue that the answer is ‘no’: given transitivity and a weak trade-off principle, continuity for easy cases violates the anti-continuity intuition. I end the note by exploring an even weaker continuity condition that is consistent with the aforementioned intuition.

中文翻译：

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连续性和灾难性风险

假设决策者的目标在确定性下是最大化某些连续价值，例如终生收入或连续社会福利。这样的决策者能否理性地满足所谓的“简单案例的连续性”，同时满足似乎是反对预期效用理论的成熟连续性公理的普遍直觉？在这篇笔记中，我认为答案是否定的：鉴于传递性和弱权衡原则，简单情况的连续性违反了反连续性直觉。我通过探索与上述直觉一致的更弱的连续性条件来结束注释。