In the standard 'trolley problem', respondents must decide whether to save a condemned group of individuals by sacrificing a safe bystander. Although respondents often are willing to sacrifice the bystander in some circumstances (e.g., by pulling a lever), they are loath to sacrifice the bystander in others (e.g., by pushing the bystander off a footbridge). This difference in responding has been explained via a Dual Process theory of moral judgements (DPT). DPT, however, is a classic boxes-and-arrows model that only makes directional predictions. Meehl (1967, Philosophy of Science, 34, 103) cautioned against theories that only make directional predictions, explaining that they are notoriously difficult to falsify. Meehl (1967, Philosophy of Science, 34, 103) argued that researchers should follow the lead of Physics and develop computational models that make functional and point predictions. Here, we use a value-based, computational cognitive model of decision-making (Psychological Value Theory) to predict precisely both the speed and kind of response in trolley-like problems in three experiments. We show that this model accounts for the changes in choices across variations of the trolley problem with a response bias parameter.