Deterrence coalitions that collectively own their deterrence technology, need an institutional design to decide when to retaliate against an attack or incident. This choice of institutional design, formalized through a social choice function, introduces a tradeoff between credible deterrence and escalation risk. We study this tradeoff via a simple signalling model, and use it to construct an associated binary classification problem to determine institutional designs that perform well in a variety of environments. For a small coalition of four members, we compute and study the statistics of the empirical ROC curves associated to a variety of choice functions and probability distributions for retaliation and false positives.