When two possible causes of an outcome are under consideration, contingency information concerns each possible combination of presence and absence of the two causes with occurrences and nonoccurrences of the outcome. White (2008) proposed that such judgements could be predicted by a weighted averaging model integrating these kinds of contingency information. The weights in the model are derived from the hypothesis that causal judgements seek to meet two main aims, accounting for occurrences of the outcome and estimating the strengths of the causes. Here it is shown that the model can explain many but not all relevant published findings. The remainder can be explained by reasoning about interactions between the two causes, by scenario-specif...