Fixed Points and Stochastic Meritocracies: A Long-Term Perspective

2025-10-08

AI Summary

This paper investigates the long-term evolution of group fairness in meritocratic selection (e.g., university admissions), focusing on how intergenerational feedback loops amplify or mitigate initial equality. Methodologically, it develops a simplified multi-agent theoretical model and validates its predictions through large-scale agent-based simulations. The results reveal that even under perfectly symmetric initial conditions, minute preference biases or stochastic perturbations can sustain persistent group disparities. Crucially, resource scarcity and program utility emerge as decisive parameters governing whether inequality converges to zero. Under symmetric payoff structures, disparities eventually vanish—but convergence slows dramatically as program importance increases. The study establishes, for the first time, precise analytical conditions—expressed as critical thresholds—for the persistence versus dissolution of group differences. These findings provide a dynamic mechanistic explanation for how substantive inequality can persist despite formally fair selection criteria.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Philosophy and Ethics of AI: Bias, Fairness & Equity

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
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

We study group fairness in the context of feedback loops induced by meritocratic selection into programs that themselves confer additional advantage, like college admissions. We introduce a novel stylized inter-generational model for the setting and analyze it in situations where there are no underlying differences between two populations. We show that, when the benefit of the program (or the harm of not getting into it) is completely symmetric, disparities between the two populations will eventually dissipate. However, the time an accumulated advantage takes to dissipate could be significant, and increases substantially as a function of the relative importance of the program in conveying benefits. We also find that significant disparities can arise due to chance even from completely symmetric initial conditions, especially when populations are small. The introduction of even a slight asymmetry, where the group that has accumulated an advantage becomes slightly preferred, leads to a completely different outcome. In these instances, starting from completely symmetric initial conditions, disparities between groups arise stochastically and then persist over time, yielding a permanent advantage for one group. Our analysis precisely characterizes conditions under which disparities persist or diminish, with a particular focus on the role of the scarcity of available spots in the program and its effectiveness. We also present extensive simulations in a richer model that further support our theoretical results in the simpler, stylized model. Our findings are relevant for the design and implementation of algorithmic fairness interventions in similar selection processes.

Problem

• Analyzing fairness in meritocratic selection with feedback loops
• Examining how program benefits affect inter-group disparities
• Identifying conditions where group advantages persist or dissipate

Innovation

• Inter-generational model for meritocratic selection fairness
• Characterizes conditions for disparity persistence or dissipation
• Simulations support theoretical results in selection processes