Instrument Validity as an Audit for Algorithmic Collective Action

We study encouragement experiments in which a group coordinates its treatment take-up. A one-sided population discrepancy $V(P)$ is the sharp lower bound on the share of defiers. The bound is zero exactly when the defiers' potential-outcome measures are dominated by the compliers', so detectability depends on outcome distributions as well as group size. In a discretized Gaussian simulation, the complier-LATE set widens with the defier share under outcome mimicry but is non-monotone under separation. With a $29\%$ defier share, the Wald estimand is $-0.45$ when the complier effect is $1.0$; $V(P)=0.0022$ and a moment-inequality test rejects in $18\%$ of $n=200{,}000$ replications. The first stage is $0.01$ in the same design. We therefore report the monotonicity inequalities together with instrument strength.