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Symmetry axioms and perceived ambiguity

机译：对称公理和可理解的歧义

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Since at least de Finetti (Annales de l'lnstitut Henri Poincare 7:1-68,1937), preference symmetry assumptions have played an important role in models of decision making under uncertainty. In the current paper, we explore (1) the relationship between the symmetry assumption of Klibanoff et al. (KMS) (Econometrica 82:1945-1978, 2014) and alternative symmetry assumptions in the literature, and (2) assuming symmetry, the relationship between the set of relevant measures, shown by KMS (2014) to reflect only perceived ambiguity, and the set of measures (which we will refer to as the Bewley set) developed by Ghirardato et al. (J Econ Theory 118:133-173, 2004), Nehring (Ambiguity in the context of probabilistic beliefs, working paper, 2001, Bernoulli without Bayes: a theory of utility-sophisticated preference, working paper, 2007) and Ghirardato and Siniscalchi (A more robust definition of multiple priors, working paper, 2007, Econometrica 80:2827-2847, 2012). This Bewley set is the main alternative offered in the literature as possibly representing perceived ambiguity. Regarding symmetry assumptions, we show that, under relatively mild conditions, a variety of preference symmetry conditions from the literature [including that in KMS (2014)] are equivalent. In KMS (2014), we showed that, under symmetry, the Bewley set and the set of relevant measures are not always the same. Here, we establish a preference condition, No Half Measures, that is necessary and sufficient for the two to be the same under symmetry. This condition is rather stringent. Only when it is satisfied may the Bewley set be interpreted as reflecting only perceived ambiguity and not also taste aspects such as ambiguity aversion.
机译：自从至少de Finetti（Annales de l'Institut Henri Poincare 7：1-68,1937）开始，偏好对称假设就在不确定性下的决策模型中发挥了重要作用。在本文中，我们探索（1）Klibanoff等人的对称假设之间的关系。 （KMS）（Econometrica 82：1945-1978，2014）和文献中的其他对称性假设，以及（2）假设对称性，即KMS（2014）显示的仅反映感知到的歧义的一组相关度量之间的关系，以及Ghirardato等人开发的一组度量（我们将其称为Bewley集）。 （J Econ Theory 118：133-173，2004），Nehring（在概率信念背景下的歧义，工作论文，2001，Bernoulli Without Bayes：实用性复杂的偏好理论，工作论文，2007）和Ghirardato和Siniscalchi（多个先验的更可靠定义，工作文件，2007，Econometrica 80：2827-2847，2012）。 Bewley集是文献中提供的主要替代方法，可能代表了感知的歧义。关于对称性假设，我们表明，在相对温和的条件下，文献[包括KMS（2014）中]的各种偏好对称性条件是等效的。在KMS（2014）中，我们证明了对称性下的Bewley集和相关度量集并不总是相同的。在这里，我们建立了一个偏好条件，即“不采取半数措施”，这对于使两个对象在对称情况下相同是必要和充分的。此条件相当严格。仅当满足时，才可以将Bewley集解释为仅反映感知到的歧义，而不反映诸如歧义厌恶之类的方面。

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