We investigate risk attitudes when the underlying domain of payoffs is finite and the payoffs are, in general, not numerical. In such cases, the traditional notions of absolute risk attitudes, that are designed for convex domains of numerical payoffs, are not applicable. We introduce comparative notions of weak and strong risk attitudes that remain applicable. We examine how they are characterized within the rank-dependent utility model, thus including expected utility as a special case. In particular, we characterize strong comparative risk aversion under rank-dependent utility. This is our main result. From this and other findings, we draw two novel conclusions. First, under expected utility, weak and strong comparative risk aversion are characterized by the same condition over finite domains. By contrast, such is not the case under non-expected utility. Second, under expected utility, weak (respectively: strong) comparative risk aversion is characterized by the same condition when the utility functions have finite range and when they have convex range (alternatively, when the payoffs are numerical and their domain is finite or convex, respectively). By contrast, such is not the case under non-expected utility. Thus, considering comparative risk aversion over finite domains leads to a better understanding of the divide between expected and non-expected utility, more generally, the structural properties of the main models of decision-making under risk.

当收益的潜在领域是有限的并且收益通常不是数字时，我们会调查风险态度。在这种情况下，为数值收益的凸域设计的绝对风险态度的传统概念不适用。我们引入了仍然适用的弱风险和强风险态度的比较概念。我们研究了它们在依赖于等级的效用模型中的特征，因此将预期效用作为一个特例。特别是，我们在依赖等级的效用下表征了强烈的比较风险厌恶。这是我们的主要结果。从这一发现和其他发现中，我们得出了两个新的结论。首先，在预期效用下，弱和强比较风险规避的特点是有限域上的条件相同。相比之下，在非预期效用下，情况并非如此。其次，在预期效用下，弱（分别为：强）比较风险厌恶的特征在于，当效用函数具有有限范围和具有凸范围时（或者，当收益是数值并且它们的域是有限或凸的，分别）。相比之下，在非预期效用下情况并非如此。因此，考虑有限域上的比较风险规避可以更好地理解预期效用和非预期效用之间的区别，更一般地，风险下主要决策模型的结构特性。强）比较风险厌恶的特征在于，当效用函数具有有限范围和具有凸范围时（或者，当收益为数值且其域分别为有限或凸）时，比较风险厌恶的特征相同。相比之下，在非预期效用下情况并非如此。因此，考虑有限域上的比较风险规避可以更好地理解预期效用和非预期效用之间的区别，更一般地，风险下主要决策模型的结构特性。强）比较风险厌恶的特征在于，当效用函数具有有限范围和具有凸范围时（或者，当收益为数值且其域分别为有限或凸）时，比较风险厌恶的特征相同。相比之下，在非预期效用下情况并非如此。因此，考虑有限域上的比较风险规避可以更好地理解预期效用和非预期效用之间的区别，更一般地，风险下主要决策模型的结构特性。