Towards Fair Allocation in Social Commerce Platforms

TL;DR

This paper tackles fair allocation in social commerce by formulating product-to-re-seller assignments as a two-sided cardinality-constrained fair division problem. It shows that traditional fairness notions like EF1 and EQ1 may fail under these constraints and argues for Nash social welfare (NSW) as the practical objective, leading to a NP-hard problem (2S-CardNashOpt). To address scalability, the authors propose an MILP (NashMax) and two scalable greedy heuristics (GreedyNash and SeAl) that approximate NSW with minimal revenue loss. Empirical results on a large real-world Shopsy dataset and synthetic data demonstrate that the greedy methods achieve near-optimal NSW while satisfying all constraints, outperforming revenue-centric baselines in fairness metrics with modest revenue impact. The work provides a principled approach to fairness and exposure guarantees in social commerce, enabling practical deployment with provable fairness guarantees.

Abstract

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.

Figures (3)

• Figure 1: Producers connect with the customers directly in e-commerce platforms (left), whereas in social commerce, re-sellers facilitate this connection (right).
• Figure 2: Distributions of the re-sellers (left) and the average price of products sold by them in each cluster (right).
• Figure 3: The bar plot shows (a) an increase in fairness among re-sellers, (b) a decrease/increase in fairness among products, and (c) a decrease in revenue on comparing NashFair to RevMax w.r.t. variation in $L$. Recall that $L_1$ and $L_2$ are set as $L-\epsilon$ and $L+\epsilon$ respectively where $\epsilon=3$. (d-f) represent the same metrics but, w.r.t. $R1$. (g-h) Scalability: Running time (in seconds) comparison of SeAl, GreedyNash, and NashMax on synthetic dataset w.r.t. increase in the number of (g) products and (h) re-sellers.

Theorems & Definitions (16)

• Definition 1: Expertise Matrix ($E$)
• Definition 2: Utility ($W$)
• Definition 3: Equitability up to one item ($EQ1$)
• Proposition 1
• Theorem 1
• Theorem 2
• Definition 4: Envy-freeness up to one item ($EF1$)
• Proposition 2
• Theorem 3
• Theorem 4