Beyond Simpson's Paradox: A Cascade of Confounders in AI Agent Pull-Request Co-Authorship

2026-06-21

AI Summary

This study addresses the observed lower merge rate of pull requests (PRs) co-authored by AI coding agents and humans in aggregated data, which may stem from confounding bias. Through a stratified causal analysis of 33,596 PRs, the authors uncover a multi-layered confounding cascade involving agent identity, repository selection, and PR structure—giving rise to Simpson’s paradox. By employing repository fixed effects, within-group comparisons, and controls for PR structural features, they demonstrate that once these confounders are adequately accounted for, the apparent positive effect of co-authorship on merge probability becomes statistically insignificant. This suggests the original association is largely a product of selection bias and structural artifacts. The work underscores the necessity of jointly controlling for both repository- and PR-level variables in cross-agent evaluations to avoid spurious conclusions.

Abstract

Pooled across five AI coding agents, pull requests (PRs) with a human Co-Authored-By trailer merge less often than purely-autonomous ones (53.8% vs. 79.8%) -- yet this aggregate finding is a textbook Simpson's Paradox. Stratifying 33,596 PRs from the AIDev dataset by agent identity reverses the conclusion: Copilot and Devin show large positive within-agent gaps (+41.2 and +33.5 pp, both p<0.001), while Cursor, Claude Code, and Codex show small effects whose cross-sectional 95% CIs span zero. The paradox is driven entirely by agent composition: Codex, which dominates 64.9% of the dataset, achieves high merge rates while rarely using co-authorship. But Simpson's Paradox is only the first layer of a cascade of confounders: within-repo controls eliminate Devin's gap (+33.5 to +1.6 pp, p=0.73); a commit-count control further halves Copilot's within-repo gap (+36.2 to +24.4 pp); restricted to multi-commit PRs, the Copilot within-repo effect dissolves to +4.8 pp (p=0.59). No agent retains a clear co-authorship effect once both repository selection and PR structure are controlled. Our findings caution against reporting agent-pooled statistics without stratification and demonstrate that cross-sectional co-authorship associations are largely selection and PR-structure artefacts rather than evidence of a causal benefit.

Problem

• Simpson's Paradox
• confounding
• AI coding agents
• pull-request co-authorship
• selection bias

Innovation

• Simpson's Paradox
• confounding
• AI coding agents
• pull-request co-authorship
• causal inference