Although anti-terrorism policy should be based on a normative treatment of risk that incorporates likelihoods of attack, policy makers’ anti-terror decisions may be influenced by the blame they expect from failing to prevent attacks. We show that people’s anti-terror budget priorities before a perceived attack and blame judgments after a perceived attack are associated with the attack’s severity and how upsetting it is but largely independent of its likelihood. We also show that anti-terror budget priorities are influenced by directly highlighting the likelihood of the attack, but because of outcome biases, highlighting the attack’s prior likelihood has no influence on judgments of blame, severity, or emotion after an attack is perceived to have occurred. Thus, because of accountability effects, we propose policy makers face a dilemma: prevent terrorism using normative methods that incorporate the likelihood of attack or prevent blame by preventing terrorist attacks the public find most blameworthy.