Social commerce platforms are emerging businesses where producers sell products through re-sellers who advertise the products to other customers in their social network. Due to the increasing popularity of this business model, thousands of small producers and re-sellers are starting to depend on these platforms for their livelihood; thus, it is important to provide fair earning opportunities to them. The enormous product space in such platforms prohibits manual search, and motivates the need for recommendation algorithms to effectively allocate product exposure and, consequently, earning opportunities. In this work, we focus on the fairness of such allocations in social commerce platforms and formulate the problem of assigning products to re-sellers as a fair division problem with indivisible items under two-sided cardinality constraints, wherein each product must be given to at least a certain number of re-sellers and each re-seller must get a certain number of products. Our work systematically explores various well-studied benchmarks of fairness -- including Nash social welfare, envy-freeness up to one item (EF1), and equitability up to one item (EQ1) -- from both theoretical and experimental perspectives. We find that the existential and computational guarantees of these concepts known from the unconstrained setting do not extend to our constrained model. To address this limitation, we develop a mixed-integer linear program and other scalable heuristics that provide near-optimal approximation of Nash social welfare in simulated and real social commerce datasets. Overall, our work takes the first step towards achieving provable fairness alongside reasonable revenue guarantees on social commerce platforms.

翻译：社交电商平台是一种新兴商业模式，生产者通过转销商向社交网络中的其他客户推广产品。随着该商业模式的日益普及，数千名小型生产者和转销商开始依赖这些平台谋生，因此为其提供公平的收益机会至关重要。此类平台上庞大的产品空间使得手动搜索难以实现，亟需推荐算法来有效分配产品曝光机会，进而影响收益分配。本研究聚焦于社交电商平台中这种分配的公平性问题，将产品分配给转销商的问题形式化为一种在双边基数约束下的不可分割物品公平分配问题——每个产品必须分配给至少一定数量的转销商，且每个转销商必须获得一定数量的产品。我们从理论和实验两个维度系统探索了多种公认的公平基准，包括纳什社会福利、至多一项物品的无嫉妒性（EF1）以及至多一项物品的公平性（EQ1）。研究发现，这些概念在无约束环境下已知的存在性和计算性保证无法扩展到我们的约束模型中。为解决这一局限，我们开发了混合整数线性规划及其他可扩展的启发式算法，能够在模拟数据集和真实社交电商数据上实现纳什社会福利的近优近似。总体而言，本研究首次在保障社交电商平台合理收益的同时，向可证明的公平分配迈出了第一步。