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.''

翻译：公平分蛋糕是一个数学子领域，研究在若干参与者间公平分配资源的问题。所谓“蛋糕”作为一种对象，代表可在参与者间分配的任何资源。这一概念与监督式多标签分类相关联：任何数据集均可视为待分配的蛋糕，其中每个标签相当于获得数据份额的参与者。特别地，数据集上的任何高效分蛋糕方案都等价于一个最优决策函数。尽管我们并非首次揭示这种关联，但这一类比的重要影响似乎已被部分遗忘。我们重新审视这些经典结论，并论证如何将这种关联创造性地应用于机器学习公平性问题。理清可达成的公平决策集合是寻找最优公平解、满足公平性要求的基础步骤。通过运用分蛋糕理论的工具，我们得以描述最优公平决策的行为特征——反直觉的是，这些决策常表现出相当不公平的特性。具体而言，为满足公平性约束，有时以最优性之名，宁可故意犯错，拒绝给予社区内应得个体正标签，转而惠及同一社区内价值较低的个体。这种实践在文献中被称为“樱桃采摘”，并被描述为“公然不公平”。