Abstract

In many fields of decision making, choices have to be made from multiple alternatives, but stochastic dominance rules do not yield a complete ordering due to incomparability of some or all of the prospects. For ranking incomparable prospects, a “Utopia Index” measuring the proximity to a lower envelope of integrated distribution functions is proposed. Economic interpretations in terms of Expected Utility are provided for the envelope and deviations from it. The analysis generalizes the existing Almost Stochastic Dominance concept from pairwise comparison to a joint analysis of an arbitrary number of prospects. The limit distribution for the empirical counterpart of the index for a general class of dynamic processes is derived together with a consistent and feasible inference procedure based on subsampling techniques. Empirical applications to Chinese household income data and historical investment returns data show that, in every choice set, a single prospect is ranked above all alternatives at conventional significance levels, despite the incomparability problem.

摘要

在决策的许多领域中，必须从多种选择中做出选择，但是由于某些或所有前景的可比性，随机支配性规则无法产生完整的排序。为了对无与伦比的前景进行排名，提出了一种“乌托邦指数”，用于衡量与综合分布函数的较低范围的接近程度。提供了关于“预期效用”的经济解释，以解释信封的内容和与信封的偏差。该分析从成对比较到对任意数量前景的联合分析概括了现有的几乎随机优势概念。基于子采样技术，得出了针对一般动态过程类别的指数的经验对应项的极限分布以及一致且可行的推断过程。