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This paper is concerned with the problem of decision-making in systems that assist drivers in avoiding collisions. An important aspect of these systems is not only assisting the driver when needed but also not disturbing the driver with unnecessary interventions. Aimed at improving both of these properties, a probabilistic framework is presented for jointly evaluating the driver acceptance of an intervention and the necessity thereof to automatically avoid a collision. The intervention acceptance is modeled as high if it estimated that the driver judges the situation as critical, based on the driver's observations and predictions of the traffic situation. One advantage with the proposed framework is that interventions can be initiated at an earlier stage when the estimated driver acceptance is high. Using a simplified driver model, the framework is applied to a few different types of collision scenarios. The results show that the framework has appealing properties, both with respect to increasing the system benefit and to decreasing the risk of unnecessary interventions.