Expected utility theory often falls silent, even in cases where the correct rankings of options seems obvious. For instance, it fails to compare the Pasadena game to the Altadena game, despite the latter turning out better in every state. Decision theorists have attempted to fill these silences by proposing various extensions to expected utility theory. As I show in this paper, such extensions often fall silent too, even in cases where the correct ranking is intuitively obvious. But we can extend the theory further than has been done before—I offer a new extension, Invariant Value Theory, which deals neatly with those problem cases and also satisfies various desirable conditions. But other prima facie desirable conditions, including Independence, the theory violates. Is this a problem for the proposal? It may not be—in a new impossibility result, I show that no theory can satisfy Independence in full generality without violating several other conditions that together seem just as plausible.

中文翻译：

---

 令人困惑的期望


预期效用理论经常沉默，即使在正确的选项排名似乎很明显的情况下也是如此。例如，它未能将帕萨迪纳的比赛与阿尔塔迪纳的比赛进行比较，尽管后者在每个州的结果都更好。决策理论家试图通过提出对预期效用理论的各种扩展来填补这些沉默。正如我在这篇论文中所展示的，这样的扩展也经常会沉默，即使在直观上正确排名明显的情况下也是如此。但是我们可以比以前更进一步地扩展该理论 — 我提供了一个新的扩展，即不变值理论，它巧妙地处理了这些问题情况，也满足了各种理想的条件。但该理论违反了其他表面理想的条件，包括独立。这对提案来说是个问题吗？可能不是——在一个新的不可能性结果中，我表明，没有任何理论可以在不违反其他几个条件的情况下完全普遍地满足独立性，这些条件加在一起似乎同样合理。