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

arXiv: https://arxiv.org/abs/2606.22711 · HTML: https://mlsanity.com/paper/2606.22711/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Software engineering coding agents, one of 16 directions in LLM agents and tool use.
- Builds on 3 of its 14 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Placed in

- LLM agents and tool use / [Software engineering coding agents](https://mlsanity.com/agents/software-engineering-coding-agents/)

## Builds on (most cited first, 3 of 3)

- [GitHub Copilot AI pair programmer: Asset or Liability?](https://mlsanity.com/paper/2206.15331/) (2022)
- [Quality Gatekeepers: Investigating the Effects ofCode Review Bots on Pull Request Activities](https://mlsanity.com/paper/2103.13547/) (2021)
- [Don't Disturb Me: Challenges of Interacting with SoftwareBots on Open Source Software Projects](https://mlsanity.com/paper/2103.13950/) (2021)

## Built on by (most cited first, 1 of 1)

- [Who Maintains Agent Skills? A Longitudinal Study of Human-Governed, AI-Assisted Skill Maintenance](https://mlsanity.com/paper/2609.05677/) (2026)

## Abstract (arXiv)

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.