Does the Competitive Component of Adversarial Self-Play Improve Legal Reasoning? A Controlled Negative Result

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arXiv:2608.01559v1 Announce Type: cross Abstract: Adversarial self-play is an appealing recipe for legal reasoning: have a student model draft an argument, have an adversary attack it, and reward the student when its argument survives the attack. We designed exactly such a training signal -- a verifiable "survival" reward in which both the student's cited authorities and the adversary's counter-authorities are checked by a citation verifier, so that survival is decided on verified grounds rather than rhetoric, and fabricated citations are automatically neutralized. We then asked a narrow but important question: does the competitive component itself -- the adversary and the survival reward -- add anything on top of an otherwise identical non-competitive training run? Across four independent tests -- a bootstrap comparison, a two-seed replication, a paired per-case adversarial-robustness comparison, and a blinded head-to-head judgment of generated arguments, plus a follow-up pilot with a deliberately strengthened self-play adversary -- the competitive component produced no reliable benefit. The blinded judgment gave a 49% win rate (binomial p approx. 1.000); the strengthened-adversary pilot gave a 50% win rate (32:32, p approx. 1.000). An early apparent +29% advantage reversed and proved to be a small-sample artifact. We report this as an honest negative result. The value of the paper is reproducibility and the sharing of concrete pitfalls: an initially promising metric that inverted on more data, and an adversarial-robustness metric that silently collapsed to plain recall …

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