This paper presents a random utility maximization model for individuals selecting discrete quantities from a set of n alternatives. Multiple alternatives with positive quantities may be selected. Diminishing marginal utility to quantity of each alternative is modeled via order statistics of independent Gumbel random variables. The model is parsimonious and tractable, admitting closed-form expressions for choice probabilities. As such, the model is amenable to maximum likelihood estimation of structural parameters from observed choices.

Probability functions recover binary logit probabilities under binary choice and a maximum quantity of one unit, and probability is monotonic in the quantity of each alternative. The monotonic property likely restricts the application of the model to a narrow range of settings. The property is a manifestation of a recursive relationship among Gumbel order statistic probabilities. This relationship and related properties may lead to new models for capturing important complexities in a tractable manner.

本文提出了一个随机效用最大化模型，供个人从一组n 个备选方案中选择离散量。可以选择多个具有正数量的备选方案。通过独立 Gumbel 随机变量的阶数统计，对每个备选方案的边际效用递减进行建模。该模型简约且易于处理，允许使用封闭形式的选择概率表达式。因此，该模型适用于根据观察到的选择对结构参数进行最大似然估计。

概率函数恢复二元选择和一个单位的最大数量下的二元 logit 概率，并且概率在每个备选方案的数量上是单调的。单调属性可能将模型的应用限制在狭窄的设置范围内。该性质是 Gumbel 阶统计概率之间递归关系的体现。这种关系和相关属性可能会导致新模型以易于处理的方式捕获重要的复杂性。