INTRODUCTION Imagine you are approaching a stop sign at an empty intersection. It is clear that no one else is on the road. You would like to pass right through, to save time, gasoline, and wear on your breaks. But you also worry about the small chance that a patrol officer may be watching, and you do not want a fine. In such a circumstance, would it ever make sense to base your decision—whether to skip or stop—on the flip of a coin?1 On a familiar picture associated with Bayesian decision theory (e.g., Savage 1954), such randomized decisions are rationally permissible only in cases where the options look equally attractive. For instance, the costs associated with stopping should be on a par with the prospect of either avoiding those costs or paying a fine, weighted by the appropriate probabilities. A number of authors have argued that situations like these—the case of Buridan’s donkey being the most famous—present us with positive reason to want access to a randomizing device in order to break the apparent symmetry (see Rescher 1959, and Ullman-Margalit and Morgenbesser 1977 and the large ensuing literature for critical discussion), though from a decision theoretic perspective any way of breaking the symmetry is acceptable, random or not. Some have declared such dilemmas to be extremely rare, if not inconceivable: there will always be some discernible difference between options, and further reflection will inevitably tip the balance.2 A moment’s thought will reveal either skipping or stopping as clearly the better option. Whatever one concludes about these issues, it is apparent that the rational role of randomization on this traditional picture is marginal at best. The sentiment was nicely summarized by economist Robert Aumann, who wrote: ‘Practically speaking, the idea that serious people would base important decisions on the flip of a coin is difficult to accept’ (Aumann, 1987, 15).

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为什么是随机的？

介绍 想象一下，您正接近一个空路口的停车标志。很明显，没有其他人在路上。您想直接通过，以节省时间、汽油和休息时的磨损。但是您也担心巡逻人员可能会看到的小机会，并且您不想要罚款。在这种情况下，将您的决定（是跳过还是停止）基于抛硬币是否有意义？1 根据与贝叶斯决策理论相关的熟悉图片（例如，Savage 1954），此类随机决策是合理的仅在选项看起来同样有吸引力的情况下才允许。例如，与停止相关的成本应该与避免这些成本或支付罚款的前景相当，按适当的概率加权。许多作者认为，像这样的情况——布里丹的驴是最著名的例子——为我们提供了想要访问随机化设备以打破表面对称性的积极理由（参见 Rescher 1959，以及 Ullman-Margalit 和Morgenbesser 1977 以及随后的大量批判性讨论文献），尽管从决策理论的角度来看，任何打破对称性的方式都是可以接受的，无论是否随机。一些人声称这种困境极为罕见，如果不是不可思议的话：选项之间总会有一些明显的差异，进一步的反思将不可避免地打破平衡。2 片刻的思考会发现跳过或停止显然是更好的选择。无论人们对这些问题得出什么结论，很明显，随机化对这种传统图片的合理作用充其量只是微不足道的。经济学家罗伯特·奥曼 (Robert Aumann) 很好地总结了这种情绪，他写道：“实际上，严肃的人会根据抛硬币做出重要决定的想法是难以接受的”(Aumann, 1987, 15)。