The strict dominance principle that a wager always paying better than another is rationally preferable is one of the least controversial principles in decision theory. I shall show that (given the Axiom of Choice) there is a contradiction between strict dominance and plausible isomorphism or symmetry conditions, by showing how in several natural cases one can construct isomorphic wagers one of which strictly dominates the other. In particular, I will show that there is a pair of wagers on the outcomes of a uniform spinner which differ simply in where the zero degrees point of the spinner is defined to be but where one wager dominates the other. I shall also argue that someone who accepts Williamson’s famous argument that the probability of an infinite sequence of heads is zero should accept the symmetry conditions, and thus has reason to weaken the strict dominance principle, and I shall propose a restriction of the principle to “implementable” wagers. Our main result also has implications for social choice principles.

一个赌注总是比另一个赌注支付更高的严格支配原则在理性上是更可取的，这是决策理论中争议最小的原则之一。我将证明（给定选择公理）严格支配与似是而非的同构或对称条件之间存在矛盾，方法是展示在几种自然情况下如何构建其中一个严格支配另一个的同构赌注。特别是，我将证明有一对关于均匀微调器结果的赌注，它们的不同之处仅在于微调器的零度点被定义为一个赌注支配另一个赌注。我还将争辩说，接受威廉姆森著名论点（即无限次正面朝上的概率为零）的人应该接受对称条件，因此有理由削弱严格的支配原则，我将建议将该原则限制为“可实施”的赌注。我们的主要结果也对社会选择原则有影响。