The role of subtractions and comparisons in comparative judgments involving numerical reference points

Experiments in which subjects are asked to decide which of two digits is closer in magnitude to a third raise problems for many theories of linear orders. Holyoak (1978), for example, performed a number of these reference point experiments and concluded that they posed serious difficulties for a number of leading models. In their place, he offered the distance ratio model in which the ease of the decision in a reference point task is a function of the ratio of the distances between each stimulus and the reference point. In the present article, three experiments are presented that bear on the adequacy of Holyoak's position. In the first two studies, we present evidence that an important assumption of the distance ratio model is incorrect. In the third experiment, we compare the empirical adequacy of the distance ratio model with our own subtraction model. This model treats the reference point task as a concatenation of two subtractions and a simple digit comparison. This comparison operation is equivalent to the magnitude comparison required in standard linear order experiments. Overall, the subtraction model gives a somewhat better account than the distance ratio.