Explaining Rankings with Hidden Group Bonuses

2026-05-28

AI Summary

This work addresses the problem of ranking explanation when sensitive attributes are hidden yet influence rankings through group-specific bonuses. Existing methods fail under this setting due to their assumption of fully observable features. The paper formally defines and investigates ranking explanation with latent group bonuses, proving the problem is NP-hard in general but admits a polynomial-time algorithm when both feature dimensionality and the number of groups are fixed. To tackle this challenge, the authors propose a joint inference framework that integrates linear scoring models, constraint satisfaction, and discrete optimization. Experiments on both real-world and synthetic datasets demonstrate that the method effectively recovers the underlying hidden group bonus structure and provides high-fidelity explanations for observed rankings.

Abstract

Determining a linear utility function that correlates with observed candidate rankings is a foundational problem with applications in domains such as admissions, hiring, and recommendation systems, e.g., [Storandt and Funke, AAAI'19, Zhang et al., KDD'23, Wang et al., ICDE'24 (best paper award), Chen and Wong, VLDB'24]. Traditionally, these models assume full visibility into the feature sets used to determine the utility score. However, real-world scenarios often involve sensitive attributes that are hidden or partially observed, yet may influence outcomes through additive bonuses designed to promote fairness, as in [Gale and Marian, ICDE'24]. Motivated by such practical concerns, we study a variant of the ranking explanation problem where sensitive features are unobserved but may influence candidate rankings through group-specific linear boosts. We present a formal framework for modeling this problem and develop an algorithmic solution that leverages constraint satisfaction and automated reasoning techniques to jointly infer the linear scoring parameters and latent group bonuses consistent with the observed rankings. We further show that determining a satisfying linear function with group-specific bonuses is \textsf{NP}-hard in general, but when the feature dimension and the number of groups are constant, the problem admits a polynomial-time solution. Our approach is the first to address this nuanced variant, which captures key real-world challenges in fair ranking and admission systems. We perform extensive experiments on both real-world and synthetic datasets, demonstrating that our method effectively recovers hidden bonus structures and provides faithful explanations of observed ranking outcomes.

Problem

• ranking explanation
• hidden sensitive attributes
• group bonuses
• fairness
• linear utility function

Innovation

• hidden group bonuses
• ranking explanation
• fairness-aware ranking
• constraint satisfaction
• latent attribute inference