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Delegation and Verification Under AI

Lingxiao Huang, Wenyang Xiao, Nisheeth K. Vishnoi

TL;DR

These results identify a structural mechanism by which AI reshapes institutional worker quality and amplifies quality disparities between workers with different verification reliability, and induces *phase transitions*, where arbitrarily small differences in verification ability lead to sharply different behaviors.

Abstract

As AI systems enter institutional workflows, workers must decide whether to delegate task execution to AI and how much effort to invest in verifying AI outputs, while institutions evaluate workers using outcome-based standards that may misalign with workers' private costs. We model delegation and verification as the solution to a rational worker's optimization problem, and define worker quality by evaluating an institution-centered utility (distinct from the worker's objective) at the resulting optimal action. We formally characterize optimal worker workflows and show that AI induces *phase transitions*, where arbitrarily small differences in verification ability lead to sharply different behaviors. As a result, AI can amplify workers with strong verification reliability while degrading institutional worker quality for others who rationally over-delegate and reduce oversight, even when baseline task success improves and no behavioral biases are present. These results identify a structural mechanism by which AI reshapes institutional worker quality and amplifies quality disparities between workers with different verification reliability.

Delegation and Verification Under AI

TL;DR

These results identify a structural mechanism by which AI reshapes institutional worker quality and amplifies quality disparities between workers with different verification reliability, and induces *phase transitions*, where arbitrarily small differences in verification ability lead to sharply different behaviors.

Abstract

As AI systems enter institutional workflows, workers must decide whether to delegate task execution to AI and how much effort to invest in verifying AI outputs, while institutions evaluate workers using outcome-based standards that may misalign with workers' private costs. We model delegation and verification as the solution to a rational worker's optimization problem, and define worker quality by evaluating an institution-centered utility (distinct from the worker's objective) at the resulting optimal action. We formally characterize optimal worker workflows and show that AI induces *phase transitions*, where arbitrarily small differences in verification ability lead to sharply different behaviors. As a result, AI can amplify workers with strong verification reliability while degrading institutional worker quality for others who rationally over-delegate and reduce oversight, even when baseline task success improves and no behavioral biases are present. These results identify a structural mechanism by which AI reshapes institutional worker quality and amplifies quality disparities between workers with different verification reliability.
Paper Structure (76 sections, 15 theorems, 78 equations, 6 figures, 2 tables)

This paper contains 76 sections, 15 theorems, 78 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related work.
  3. Our contributions.
  4. Model
  5. Action space and workflow.
  6. Worker utility.
  7. Institutional utility.
  8. Worker quality.
  9. Reliability and task success.
  10. Execution efficiency and cost.
  11. Theoretical results
  12. Characterization of worker action.
  13. Worker quality under AI assistance.
  14. Interventions and extensions.
  15. Overview of the proofs
  16. ...and 61 more sections

Key Result

Theorem 3.1

Fix the task profile, AI characteristics, and baseline worker characteristics. Let $t \ge 0$ be a threshold such that $\Delta(t)=0$. There exist continuous functions $\psi_0: [t,\infty) \rightarrow \mathbb{R}_{\ge 0}$, monotonically increasing, and $\psi_1: [0,t] \rightarrow \mathbb{R}_{\ge 0}$, mon Then the optimal action $(d^\star, s^\star)$ takes the following form:

Figures (6)

  • Figure 1: A flow chart for the workflow under AI assistance with worker action $(d,s)\in [0,1]^2$.
  • Figure 2: Plots illustrating the worker action and quality regimes characterized in Theorems \ref{['thm:action']}, \ref{['thm:quality']}, and \ref{['thm:region']} as functions of abilities $(\alpha,\beta)$, under the default parameter setting $(b_W, \ell_W, b_I, \ell_I, \xi, \tau, p_a, C_a, p_w) = (8, 6, 14, 12, 0.3, 6.4, 0.65, 0, 0.75),$ and the functional choices $C_v(s)=s$, $C_w(\beta)=5(1-\beta)$, and $\phi(s;\alpha)=1-\frac{1}{1+2\alpha s}$. Discussion on the choice of parameters and functions, and closed-form expressions for key quantities—including $(d^\star, s^\star)$ and the boundaries $\psi_0$, $\psi_1$, $\psi$, and $\psi_\tau$—are provided in Section \ref{['sec:simulation']}.
  • Figure 3: Plots illustrating the effects of interventions from the worker side and the institutional side as functions of abilities $(\alpha,\beta)$, under the default parameter setting $(b_W, \ell_W, b_I, \ell_I, \xi, \tau, p_a, C_a, p_w) = (8, 6, 14, 12, 0.3, 6.4, 0.65, 0, 0.75),$ and the functional choices $C_v(s)=s$, $C_w(\beta)=5(1-\beta)$, $\phi(s;\alpha)=1-\frac{1}{1+2\alpha s}$, and $h_1(x) = h_2(x) = x$. In Figure \ref{['fig:worker_intervention']}, we restrict the domain to $[0,0.5]\times[0,0.8]$ for clarity. In Figures \ref{['fig:high_AI']} and \ref{['fig:high_gain']}, we analyze how worker quality varies under a more capable AI and under a larger marginal gain, respectively.
  • Figure 4: Plots illustrating the worker quality regimes with heterogeneous task difficulty as functions of abilities $(\alpha,\beta)$, under the default parameter setting $(b_W, \ell_W, b_I, \ell_I, \xi, \tau, C_a) = (8, 6, 14, 12, 0.3, 6.4, 0),$ and the functional choices $p_w(h) = 1 - 0.5h$, $p_a(h) = 1-0.7h$, $C_v(s;h)=(0.5+h)s$, $C_w(\beta; h)=10(1-\beta)h$, and $\phi(s;\alpha)=1-\frac{1}{1+2\alpha s}$.
  • Figure 5: Plots illustrating the worker action and quality regimes under miscalibrated beliefs about AI capability as functions of abilities $(\alpha,\beta)$, under the default parameter setting $(b_W, \ell_W, b_I, \ell_I, \xi, \tau, p_a, C_a, p_w, \widehat{p}_a) = (8, 6, 14, 12, 0.3, 6.4, 0.65, 0, 0.75, 0.7),$ and the functional choices $C_v(s)=s$, $C_w(\beta)=5(1-\beta)$, and $\phi(s;\alpha)=1-\frac{1}{1+2\alpha s}$.
  • ...and 1 more figures

Theorems & Definitions (23)

  • Remark 2.1: Structural properties of delegation with verification
  • Theorem 3.1: Worker optimal action
  • Proposition 3.4: Worker quality difference
  • Theorem 3.5: Worker quality improvement v.s. no AI
  • Theorem 3.6: Worker upgraded v.s. downgraded
  • Lemma 3.7: Effects of $\alpha$ and $\beta$ on $f_W$
  • Lemma 3.8: Effects of $\alpha$ and $\beta$ on $\Phi$
  • Lemma 3.9: Effect of $\alpha$ on $f_I(s^\star) d^\star$
  • Lemma 3.10: Effects of $\alpha,\beta$ on $Q$
  • Theorem 5.2: Restatement of Theorem \ref{['thm:action']}
  • ...and 13 more