The Attention Market: Interpreting Online Fair Re-ranking as Manifold Optimization under Walrasian Equilibrium

A new paper from Chen Xu, Wei Chu, Wenyu Hu, Fengran Mo, Jun Xu, and Maarten de Rijke proposes ManifoldRank, an online fair re-ranking algorithm that reframes information retrieval fairness through the lens of economic theory. The researchers reinterpret fair re-ranking as an "attentional market" governed by a Walrasian Equilibrium, where fairness is modeled as a taxation cost on the ranking process. This market-based formulation is coupled with manifold optimization, showing that seeking equilibrium is equivalent to performing gradient descent on a specific ranking manifold constructed by the market.

ManifoldRank adjusts gradients to align with the ranking manifold across different contextual settings. On the supply side, it incorporates gradient adjustments based on fairness requirements and associated costs. On the demand side, it empirically predicts an additional gradient adjustment term derived from ranking scores. The paper notes that different re-ranking settings induce distinct manifold geometries, and these intrinsic geometric differences dictate gradient landscapes and optimization trajectories. Experimental results across multiple datasets confirm ManifoldRank's effectiveness, addressing significant performance disparities observed among existing methods across 20 settings. The work was accepted at SIGIR'26.