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Regular preorders and behavioral indifference

机译：规律的预购和行为冷漠

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摘要

In this article, we discuss some aspects of Eliaz and Ok 's (Games Econ Behav 56:61-86, 2006) choice theoretical foundations of incomplete preferences. Our aim is to clarify some aspects of their regularity condition for preorders, showing that, as far as rationalization of a choice correspondence alone is concerned, no further restriction is imposed by requiring the preorder to be regular. However, if one is also interested in capturing other observable aspects of the individual's choice procedure, such as Eliaz and Ok's notion of c-incomparability or the notion of behavioral indifference introduced in this paper, then the only option is to use a regular preorder. We also argue that their weak axiom of revealed non-inferiority (WARNI) is too strong a property if our aim is to characterize the rationalizability of a choice correspondence by a (possibly incomplete) preorder. Finally, as we have mentioned above, we introduce the notion of behavioral indifference and argue, not only that Eliaz and Ok's notion of c-incomparability (observable incomparability) can be derived from it, but also that it has a wider range of applicability than their notion of observable incomparability.
机译：在本文中，我们讨论了Eliaz和Ok的某些方面（不完全偏好的选择理论基础）（Games Econ Behav 56：61-86，2006）。我们的目的是弄清它们对预购商品的规律性条件的某些方面，表明仅就选择对应关系的合理化而言，不要求预购商品为正规商品就不会施加进一步的限制。但是，如果也有兴趣捕捉个人选择过程的其他可观察方面，例如本文介绍的Eliaz和Ok的c-不可比性概念或行为冷漠概念，那么唯一的选择就是使用常规的预购订单。我们还争辩说，如果我们的目标是通过（可能是不完整的）预购来表征选择对应关系的合理性，那么他们的显性非劣性（WARNI）的弱公理就太强大了。最后，如上所述，我们引入了行为冷漠的概念，并认为，不仅可以从中推导出Eliaz和Ok的c-可比性（可观察到的可比性）概念，而且它的适用范围比他们可观察到的不可比性的概念。

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