Abstract

We consider a model of individual preferences in which the preference of each individual is characterized by a stochastic vector (stochastic model of preferences). Using a sociological survey or analysis of user actions in an online social network, it is possible to obtain the probability distribution of individual preferences. The problem of finding the median preference—a vector that minimizes the expected distance to the preferences of individuals—is posed and solved. It is shown that knowing partial (marginal) distributions is sufficient to find the median preference. Illustrative examples of finding median preferences for the three-dimensional case are provided.

中文翻译：

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在随机模型中寻找个人偏好的中值问题

摘要

我们考虑一个个体偏好模型，其中每个个体的偏好由一个随机向量表征（偏好的随机模型）。通过对在线社交网络中用户行为的社会学调查或分析，可以获得个人偏好的概率分布。提出并解决了寻找中值偏好的问题——一个最小化与个人偏好的预期距离的向量。结果表明，了解部分（边际）分布足以找到中值偏好。提供了寻找三维案例的中值偏好的说明性示例。