Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Strategic Costs of Perceived Bias in Fair Selection

L. Elisa Celis, Lingxiao Huang, Milind Sohoni, Nisheeth K. Vishnoi

TL;DR

This paper analyzes how perceptual biases in the value of being selected can induce unequal pre-selection effort and representation in meritocratic systems. It introduces a two-group contest with valuation asymmetry, models post-selection value through group-specific distributions linked by a bias parameter $\rho$, and derives a unique Nash equilibrium in the large-population limit defined by a threshold $t$ solving $(1-\alpha)F_1(t)+\alpha F_2(t)=1-c$. The authors provide closed-form expressions for key metrics (representation, welfare, revenue) in the uniform-density case and show how these metrics monotone with $\rho$, $c$, and $\alpha$, enabling a cost-sensitive intervention design that trades off increased selectivity against reducing valuation bias. They also propose a practical calibration using JEE data to estimate the implied bias $\rho$ and illustrate policy implications, including when to expand access or improve perceived post-selection value. The work connects rational-choice and structural explanations of inequality, offering quantitative tools for designing fairer meritocratic systems in the presence of techno-social cues such as AI-guided guidance and algorithmic recommendations.

Abstract

Meritocratic systems, from admissions to hiring, aim to impartially reward skill and effort. Yet persistent disparities across race, gender, and class challenge this ideal. Some attribute these gaps to structural inequality; others to individual choice. We develop a game-theoretic model in which candidates from different socioeconomic groups differ in their perceived post-selection value--shaped by social context and, increasingly, by AI-powered tools offering personalized career or salary guidance. Each candidate strategically chooses effort, balancing its cost against expected reward; effort translates into observable merit, and selection is based solely on merit. We characterize the unique Nash equilibrium in the large-agent limit and derive explicit formulas showing how valuation disparities and institutional selectivity jointly determine effort, representation, social welfare, and utility. We further propose a cost-sensitive optimization framework that quantifies how modifying selectivity or perceived value can reduce disparities without compromising institutional goals. Our analysis reveals a perception-driven bias: when perceptions of post-selection value differ across groups, these differences translate into rational differences in effort, propagating disparities backward through otherwise "fair" selection processes. While the model is static, it captures one stage of a broader feedback cycle linking perceptions, incentives, and outcome--bridging rational-choice and structural explanations of inequality by showing how techno-social environments shape individual incentives in meritocratic systems.

Strategic Costs of Perceived Bias in Fair Selection

TL;DR

This paper analyzes how perceptual biases in the value of being selected can induce unequal pre-selection effort and representation in meritocratic systems. It introduces a two-group contest with valuation asymmetry, models post-selection value through group-specific distributions linked by a bias parameter , and derives a unique Nash equilibrium in the large-population limit defined by a threshold solving . The authors provide closed-form expressions for key metrics (representation, welfare, revenue) in the uniform-density case and show how these metrics monotone with , , and , enabling a cost-sensitive intervention design that trades off increased selectivity against reducing valuation bias. They also propose a practical calibration using JEE data to estimate the implied bias and illustrate policy implications, including when to expand access or improve perceived post-selection value. The work connects rational-choice and structural explanations of inequality, offering quantitative tools for designing fairer meritocratic systems in the presence of techno-social cues such as AI-guided guidance and algorithmic recommendations.

Abstract

Meritocratic systems, from admissions to hiring, aim to impartially reward skill and effort. Yet persistent disparities across race, gender, and class challenge this ideal. Some attribute these gaps to structural inequality; others to individual choice. We develop a game-theoretic model in which candidates from different socioeconomic groups differ in their perceived post-selection value--shaped by social context and, increasingly, by AI-powered tools offering personalized career or salary guidance. Each candidate strategically chooses effort, balancing its cost against expected reward; effort translates into observable merit, and selection is based solely on merit. We characterize the unique Nash equilibrium in the large-agent limit and derive explicit formulas showing how valuation disparities and institutional selectivity jointly determine effort, representation, social welfare, and utility. We further propose a cost-sensitive optimization framework that quantifies how modifying selectivity or perceived value can reduce disparities without compromising institutional goals. Our analysis reveals a perception-driven bias: when perceptions of post-selection value differ across groups, these differences translate into rational differences in effort, propagating disparities backward through otherwise "fair" selection processes. While the model is static, it captures one stage of a broader feedback cycle linking perceptions, incentives, and outcome--bridging rational-choice and structural explanations of inequality by showing how techno-social environments shape individual incentives in meritocratic systems.
Paper Structure (61 sections, 16 theorems, 107 equations, 15 figures, 1 algorithm)

This paper contains 61 sections, 16 theorems, 107 equations, 15 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Model and metrics
  4. Theoretical results: Nash equilibrium and metrics for large $n$
  5. Analysis: metric behavior and intervention design
  6. Proof of Theorem \ref{['thm:two_general']}: two-group contest
  7. Technical overview
  8. NE policy for the undifferentiated contest for finite $n$ and obstacle in extending it
  9. A conjectured NE policy in two-group contests for large $n$
  10. Proving convergence to the conjectured NE policy
  11. A comprehensive version of Theorem \ref{['thm:two_general']}: convergence form
  12. Proof of Theorem \ref{['thm:two_formal']}
  13. Proof of Lemma \ref{['lm:unique']}: solution uniqueness
  14. Bounding winning probability
  15. Proof that $A^{(n)}$ is approximate NE
  16. ...and 46 more sections

Key Result

Theorem 4.1

Let $\alpha, c\in (0,1)$. For $\ell = 1,2$, let $p_\ell$ be a density supported on a domain $\Omega_{\ell}\subseteq \mathbb{R}_{\geq 0}$. Let $p_a$ be a density supported on a domain $\Omega_a\subseteq \mathbb{R}_{\geq 0}$. Let $m: \mathbb{R}_{\geq 0} \rightarrow \mathbb{R}_{\geq 0}$ be a merit func and let policy $A$ be: each agent $i \in G_1$ uses the restriction $A_i = s|_{\Omega_1\times \Omega

Figures (15)

  • Figure 1: Evolution of group effort policies at iteration 500 for various $n$ with $\rho = 0.8$ and $c = 0.2$.
  • Figure 2: Plots of the representation ratio $r_{\mathcal{R}}(A)$ and the social welfare ratio $r_{\mathcal{S}}(A)$ as parameters $\rho$ and $c$ vary for Proposition \ref{['prop:uniform']}, with default settings of $(\rho, c, \alpha) = (0.8, 0.1, 0.5)$. A dotted line in these plots indicates the threshold at which $r_{\mathcal{R}}(A) = 0.8$ or $r_{\mathcal{S}}(A) = 0.8$.
  • Figure 3: Plots of $t$ versus $\rho$ for various $c$ with $\alpha = 0.5$ for the uniform distribution.
  • Figure 4: Explicit form of Problem \ref{['eq:intervention']}.
  • Figure 5: Plot of optimal interventions $(\Delta_\rho, \Delta_c)$ for various $\tau\in (0.671,1]$.
  • ...and 10 more figures

Theorems & Definitions (34)

  • Remark 3.1: Practical settings with group-based valuation bias
  • Definition 4.1: $\varepsilon$-Nash equilibrium lipton2003playing
  • Theorem 4.1: The two-group contest: Large $n$ limit
  • Theorem 4.2: Metrics and their monotonicity
  • Proposition 5.1: Metrics for uniform densities
  • Lemma 6.1: Unique solution
  • Definition 6.1: Threshold $n_t$
  • Definition 6.2: Threshold $\Delta_n$
  • Theorem 6.2: Two-group contest: Large $n$ limit
  • Lemma 6.3: Unique solution for multiple groups
  • ...and 24 more