Quantifying Feedback-Loop Bias in Two-Sided Marketplaces: The Role of Ratings, Reviews, and Reputation Mechanisms

Abstract

Two-sided marketplaces commonly rely on ratings, reviews, and reputation scores to reduce information asymmetry between participants. These signals are rarely passive summaries; they are often inputs to ranking, search, recommendation, and eligibility rules that shape who is seen, who matches, and who transacts. When reputational signals affect exposure and exposure affects the future stream of signals, a feedback loop arises in which early stochasticity can be amplified into persistent disparities. This paper formalizes feedback-loop bias as the discrepancy between outcomes that would arise under exposure that is conditionally independent of signal noise and outcomes under platform policies that couple exposure to noisy reputational states. A continuous-time stochastic model links true latent quality, transaction intensity, rating generation, review text informativeness, and platform ranking functions. The analysis decomposes bias into components attributable to selection on unobservables, endogenous sampling of raters, and nonlinear score aggregation. Identification strategies are developed for observational and experimental data, including randomized perturbations to ranking, instrumental variation in exposure, and panel approaches with seller fixed effects and shrinkage priors. Numerical methods are proposed for solving the induced distributional dynamics, including diffusion approximations and finite element discretizations of the associated Fokker--Planck equations. The framework yields estimands for amplification, persistence, and welfare-relevant distortion, and it supports mechanism design objectives that trade off efficiency, exploration, and disparity under explicit constraints.