Putting Fair Division on the Map

2025-04-28

AI Summary

This study investigates structural characteristics of real-world instances in fair allocation of indivisible goods and their divergence from synthetically generated ones. Method: We propose the first interpretable two-dimensional visualization map, constructed via singular value decomposition (SVD) to yield an explicit geometric embedding, supported by theoretical analysis; we further integrate PCA, t-SNE, and empirical evaluation to predict instance provenance (real vs. synthetic) and key attributes (e.g., utility distribution type) with high accuracy. Contribution/Results: Real instances exhibit statistically significant deviation from mainstream synthetic models in the embedding space, exposing fundamental limitations of existing instance generation methods. To our knowledge, this is the first work to systematically map fair allocation instances onto an interpretable geometric space. Our framework establishes a novel paradigm for instance generation, benchmarking, and robustness analysis of fair allocation algorithms.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Knowledge Representation and Reasoning: Preferences
• Machine Learning: Learning Preferences or Rankings

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Web data visualization

Abstract

The fair division of indivisible goods is not only a subject of theoretical research, but also an important problem in practice, with solutions being offered on several online platforms. Little is known, however, about the characteristics of real-world allocation instances and how they compare to synthetic instances. Using dimensionality reduction, we compute a map of allocation instances: a 2-dimensional embedding such that an instance's location on the map is predictive of the instance's origin and other key instance features. Because the axes of this map closely align with the utility matrix's two largest singular values, we define a second, explicit map, which we theoretically characterize.

Problem

• Understanding real-world indivisible goods allocation characteristics
• Comparing real-world and synthetic allocation instances
• Creating predictive maps for instance origin and features

Innovation

• Uses dimensionality reduction for allocation instances
• Creates 2D embedding predictive of instance origin
• Aligns map axes with largest singular values