When you are indifferent between two options, it’s rationally permissible to take either. One way to decide between two such options is to flip a fair coin, taking one option if it lands heads and the other if it lands tails. Is it rationally permissible to employ such a tie-breaking procedure? Intuitively, yes. However, if you are genuinely risk-averse—in particular, if you adhere to risk-weighted expected utility theory (Buchak in Risk and rationality, Oxford University Press, 2013) and have a strictly convex risk-function—the answer will often be no: the REU of deciding by coin-flip will be lower than the REU of choosing one of the options outright (so long as at least one of the options is a nondegenerate gamble). This turns out to be a significant worry for risk-weighted expected utility theory. I argue that it adds real bite to established worries about diachronic consistency afflicting views, like risk-weighted expected utility theory, that violate Independence. And that, while these worries might be surmountable, surmounting them comes at a price.

当你对两种选择无动于衷时，理性地允许选择任何一种。在两个这样的选项之间做出决定的一种方法是抛一枚公平的硬币，如果正面朝上则选择一个选项，如果反面则选择另一个选项。采用这种打破平局的程序是否合理？直觉上，是的。然而，如果你真的厌恶风险——特别是，如果你坚持风险加权预期效用理论（Buchak in Risk and rationality，牛津大学出版社，2013 年）并且具有严格的凸风险函数——答案通常是否：通过掷硬币决定的 REU 将低于直接选择其中一个选项的 REU（只要至少一个选项是非退化赌博）。事实证明，这是风险加权预期效用理论的一个重大担忧。我认为，它确实增加了对历时一致性影响观点的既定担忧，比如风险加权预期效用理论，这些观点违反了独立性。而且，虽然这些担忧可能是可以克服的，但克服它们是有代价的。