It is well-established that there is a fundamental phenomenological distinction between intentional events and non-intentional events. Different approaches have been proposed for assessing risk from intentional events, including a conditional screening approach ignoring the probability of attack, probabilistic risk analysis, game theoretic modelling, and a semi-quantitative approach highlighting the knowledge dimension and surprises. In the present paper, we review and compare these four approaches in terms of how they assess the effect of risk reducing measures. The potential theft of paintings from an art museum is used as an illustrating example. The comparison illustrates how the different fundamental assumptions underlying these approaches influence the baseline conclusions made regarding risk reducing measures. A scheme for assessing assumptions and their justification is suggested, linked to the semi-quantitative approach and showing how this approach can contribute to the structuring and evaluation of the decision basis provided by the other approaches.