A Mathematical Framework for AI-Human Integration in Work

The rapid rise of Generative AI (GenAI) tools has sparked debate over their role in complementing or replacing human workers across job contexts. We present a mathematical framework that models jobs, workers, and worker-job fit, introducing a novel decomposition of skills into decision-level and action-level subskills to reflect the complementary strengths of humans and GenAI. We analyze how changes in subskill abilities affect job success, identifying conditions for sharp transitions in success probability. We also establish sufficient conditions under which combining workers with complementary subskills significantly outperforms relying on a single worker. This explains phenomena such as productivity compression, where GenAI assistance yields larger gains for lower-skilled workers. We demonstrate the framework's practicality using data from O*NET and Big-Bench Lite, aligning real-world data with our model via subskill-division methods. Our results highlight when and how GenAI complements human skills, rather than replacing them.

The growing presence of Generative AI (GenAI) tools in the workplace has raised questions about whether these systems will replace human workers or enhance their capabilities. This paper introduces a mathematical framework to study this question systematically. The key idea is to break down job skills into two parts: decision-level skills (where humans typically excel) and action-level skills (where GenAI often performs better).Using this structure, we examine how a worker’s ability in these subskills affects their chances of completing a job successfully. We discover that small improvements in ability can lead to sudden, dramatic increases in success—especially when combining workers with complementary strengths. This helps explain real-world findings that AI tools often boost the performance of lower-skilled workers more than higher-skilled ones, a phenomenon known as "productivity compression."We support our theoretical insights with data from U.S. job databases and AI benchmarks, and show how this framework can be used to evaluate human-AI teams, guide worker upskilling, and improve hiring or task allocation decisions. Overall, the work highlights that GenAI is best viewed not as a replacement for humans, but as a collaborator that can amplify human strengths.