For collision avoidance systems to be accepted by human drivers, it is important to keep the rate of unnecessary interventions very low. This is challenging since the decision to intervene or not is based on incomplete and uncertain information. The contribution of this paper is a decision making strategy for collision avoidance systems which allows the system to occasionally postpone a decision in order to collect more information. The problem is formulated in the framework of statistical decision theory, and the core of the algorithm is to run a preposterior analysis to estimate the benefit of deciding with the additional information. A final decision is made by comparing this benefit with the cost of delaying the intervention. The proposed approach is evaluated in simulation at a two-way stop road intersection for stop sign violation scenarios. The results show that the ability to postpone decisions leads to a significant reduction of false alarms and does not impair the ability of the collision avoidance system to prevent accidents.