Fair cake-cutting is a mathematical subfield that studies the problem of fairly dividing a resource among a number of participants. The so-called ``cake,'' as an object, represents any resource that can be distributed among players. This concept is connected to supervised multi-label classification: any dataset can be thought of as a cake that needs to be distributed, where each label is a player that receives its share of the dataset. In particular, any efficient cake-cutting solution for the dataset is equivalent to an optimal decision function. Although we are not the first to demonstrate this connection, the important ramifications of this parallel seem to have been partially forgotten. We revisit these classical results and demonstrate how this connection can be prolifically used for fairness in machine learning problems. Understanding the set of achievable fair decisions is a fundamental step in finding optimal fair solutions and satisfying fairness requirements. By employing the tools of cake-cutting theory, we have been able to describe the behavior of optimal fair decisions, which, counterintuitively, often exhibit quite unfair properties. Specifically, in order to satisfy fairness constraints, it is sometimes preferable, in the name of optimality, to purposefully make mistakes and deny giving the positive label to deserving individuals in a community in favor of less worthy individuals within the same community. This practice is known in the literature as cherry-picking and has been described as ``blatantly unfair.''

公平蛋糕切分是一种研究如何公平地将资源划分给多个参与者的数学子领域。本研究阐述了公平蛋糕切分与监督多标签分类之间的联系，以及其在机器学习中解决公平性问题的潜力。研究发现，为了满足公平性要求，有时为了最优性，会故意犯错，并在同一社群中偏爱不值得的个体而拒绝给予值得的个体正面标签，这被称为“挑大梁”或“彰显不公平”。

蛋糕上的樱桃：公平不是一个优化问题