Gaming the Metric, Not the Harm: Certifying Safety Audits against Strategic Platform Manipulation

2026-05-07

AI Summary

This work addresses the risk that online platforms may strategically generate semantically equivalent content variants to manipulate compliance metrics, creating a “gaming” problem where apparent metric improvements mask unmitigated harms. The authors model moderation protocols as transformation graphs and introduce a semantic envelope metric, theoretically proving it to be the pointwise minimal solution within the class of conservative repairs. They further develop a hierarchical certification mechanism that guarantees effective constraint of true harm under any policy. Experimental evaluation—combining finite-state mixed-strategy enumeration, SMT solving (using Z3 and cvc5), and bounded single-player MDP verification in PRISM-games—demonstrates that conventional metrics often exhibit significant violations and gaming gaps, whereas the semantic envelope metric remains violation-free across all test instances, effectively resisting strategic manipulation.

Abstract

Online-safety regulation under the UK Online Safety Act and the EU Digital Services Act increasingly treats scalar metrics as compliance evidence. Once announced, such a metric also becomes an optimization target: a strategic platform can improve its score by routing recommendations through semantically equivalent content variants, without reducing true harm. We ask when such an audit metric can still certify a genuine reduction in harm. The protocol is modeled as a published transformation graph whose connected components form semantic classes, and the metric itself is treated as a security object. Three results follow. First, any metric that scores variants directly is manipulable as soon as two equivalent variants in a harmful class disagree in score. Second, the semantic-envelope lift, which assigns each variant the maximum score in its class, is the unique pointwise minimum among conservative classwise-constant repairs. Third, a class-stratified certificate, $H^\star(x) \le (1/\hatα) M_{\mathrm{Env}(m)}(x) + \barη$, holds for every platform strategy, with $\barη$ absorbing annotation and protocol error. We check the claims at three levels: exhaustive enumeration on a finite-state grid of mixed strategies, an SMT encoding in Z3 cross-replayed in cvc5, and a bounded single-player MDP encoded in PRISM-games. The fragile metric fails manipulation invariance and cannot support the same useful predeclared class-coverage certificate; under the envelope-level certificate, it produces large violations at every tested instance, with a large mean gaming gap across random catalogs at a fixed audit budget. The semantic-envelope metric exhibits no such violation in the tested instances.

Problem

• metric manipulation
• online safety regulation
• semantic equivalence
• audit certification
• strategic platform behavior

Innovation

• semantic-envelope
• audit metric
• strategic manipulation
• harm certification
• compliance verification