A Bayesian Framework for Human-AI Collaboration: Complementarity and Correlation Neglect

TL;DR

The paper addresses how AI recommendations influence human decisions when humans misinterpret correlations, by constructing a Bayesian framework with signals $H$ and $A$ and a loss $L$. It introduces a micro-founded information-overlap coefficient $\\lambda$ and decomposes AI impact into the marginal value $v(A|H)$ and a behavioral penalty from misspecification, showing that the joint value $v(H,A)$ can be subadditive under correlation neglect. A cue-based Gaussian model demonstrates that the incremental benefit of AI depends on both AI capability (captured by $\\tau_A$) and overlap, leading to phase transitions among augmentation, complementarity, and automation, with automation inevitable as AI improves if human use stagnates. The findings imply that practical deployment should focus on reducing correlation neglect and managing information overlap, as well as designing AI to target unexplained human information to expand the regime where augmentation or complementarity is possible.

Abstract

We develop a decision-theoretic model of human-AI interaction to study when AI assistance improves or impairs human decision-making. A human decision-maker observes private information and receives a recommendation from an AI system, but may combine these signals imperfectly. We show that the effect of AI assistance decomposes into two main forces: the marginal informational value of the AI beyond what the human already knows, and a behavioral distortion arising from how the human uses the AI's recommendation. Central to our analysis is a micro-founded measure of informational overlap between human and AI knowledge. We study an empirically relevant form of imperfect decision-making -- correlation neglect -- whereby humans treat AI recommendations as independent of their own information despite shared evidence. Under this model, we characterize how overlap and AI capabilities shape the Human-AI interaction regime between augmentation, impairment, complementarity, and automation, and draw key insights.

Figures (3)

• Figure 1: Conceptual model with cues split into two subsets (Section \ref{['sec:sampling_two_worlds']}). The AI can only access primitive cues in $\mathcal{S}_{\text{ai-acc}}$ and samples uniformly from this set.
• Figure 2: Expected loss as a function of AI capability $\tau_A$ in the conceptual model (Section \ref{['sec:conceptual']}). Shown are losses of human acting alone ($L_{\mathrm{H}}$, gray), AI acting alone ($L_{\mathrm{AI}}$, blue), and AI-assisted human who exhibits correlation neglect ($\widehat{L}_{\mathrm{H-AI}}$, red). Regime thresholds and the best-performing agent in each regime are labeled on the $x$-axis, with the smallest lost curve thickened. Each panel fixes $\tau_Y=1, \tau_H=1$ and $\lambda$.
• Figure 3: Phase diagram of agent-optimal regimes in the conceptual model (Section \ref{['sec:conceptual']}) when the human exhibits correlation neglect. The diagram varies AI capability $\tau_A$ ($x$-axis) and overlap coefficient $\lambda$ ($y$-axis): each $(\tau_A, \lambda)$ point corresponds to a unique joint distribution of signals $(Y,H,A)$. Regimes are labeled according to the best-performing agent: AI-assisted human (complementarity, red), human alone (impairment, gray), and AI alone (automation, blue). Threshold functions where two agents perform identically are shown as solid curves where they define regime boundaries, and dashed curves elsewhere. Each panel in Figure \ref{['fig:loss-three-panels']} shows loss functions along a horizontal slice of this diagram. The figure fixes $\tau_Y=1$ and $\tau_H=1$.

Theorems & Definitions (22)

• Example 1: AI-Assisted Clinical Diagnosis
• Definition 1: Value of Information
• Example 2: Regression
• Example 3: Classification
• Definition 2: Marginal Value of Information
• Proposition 1
• Theorem 1: Complementarity Gap
• Lemma 1: Decomposition Lemma
• Proposition 2: Overlap stabilization under random sampling
• Proposition 3: Comparative statics