Relative attention across features predicts that common features increase geometric similarity

The human mind relies on similarity to organize the world around it. A geometric approach to similarity, which assumes that two objects' similarity decreases with the sum of their feature value differences, has been particularly influential. Yet, geometric similarities are claimed to consider only differing features but ignore common features, which is inconsistent with human similarity judgments that get larger with additional common features (the common features effect). This paper shows that a relative attention mechanism, as it is implemented in current cognitive models based on geometric similarities, can naturally predict the common features effect by weighting each feature value difference with the share of attention allocated to the feature. Additional common features draw away attention from the already present features, which entails that the differences between objects with respect to already present features receive less weight, resulting in a higher similarity. The ability of the geometric similarity theory with relative attention to predict the common features effect is illustrated for data from Gati and Tversky (1984) and for data from a new pairwise similarity judgment experiment.