金钱泵指数的可处理估计：一个评论
Tractable Estimation of the Money Pump Index: A Comment
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中文总结 AI 辅助
本文通过将显示偏好构建为有向图并投影到基本循环基，提出了金钱泵指数均值和众数的可计算估计量，该估计量渐近等价于原始MPI，且计算快速、小样本偏差可忽略。
中文摘要 AI 辅助
Echenique等人（2011）提出的金钱泵指数（MPI）衡量消费者非理性行为的严重程度，但计算所有显示偏好循环上MPI的精确均值和众数是NP难的（Smeulders等人，2013）。现有解决方案依赖于启发式代理，例如仅评估较短的循环或对MPI进行界定。通过将显示偏好构建为有向图，本文将选择违规投影到基本循环基上，基本循环基是线性无关循环的最小集合，能够张成图的整个循环空间。这产生了MPI均值和众数的计算上可处理的估计量，且这些估计量与原始MPI渐近等价。将这一方法应用于Echenique等人（2011）和Smeulders等人（2013）分析的扫描仪数据集，所提出的估计量计算速度快且小样本偏差可忽略不计。
英文摘要
The Money Pump Index (MPI) of Echenique et al. (2011) measures the severity of consumer irrationality, but computing the exact mean and median MPI over all revealed preference cycles is NP-hard (Smeulders et al., 2013). Existing solutions rely on heuristic proxies, such as evaluating only shorter cycles or bounding the MPI. By framing revealed preferences as a directed graph, this paper projects choice violations onto fundamental cycle bases, which are minimal sets of linearly independent cycles that span the graph's entire cycle space. This yields computationally tractable estimators for the mean and median MPI that are asymptotically equivalent to the original MPI. Applying this methodology to the scanner dataset analyzed by Echenique et al. (2011) and Smeulders et al., (2013), the proposed estimators compute quickly and with negligible small-sample bias.
