Modeling judgment of sequentially presented categories using weighting and sampling without replacement

In a series of experiments, Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874–1886, 2011) studied relative-frequency judgments of items drawn from two distinct categories. The experiments showed that the judged frequencies of categories of sequentially encountered stimuli are affected by the properties of the experienced sequences. Specifically, a first-run effect was observed, whereby people overestimated the frequency of a given category when that category was the first repeated category to occur in the sequence. Here, we (1) interpret these findings as reflecting the operation of a judgment heuristic sensitive to sequential patterns, (2) present mathematical definitions of the sequences used in Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874–1886, 2011), and (3) present a mathematical formalization of the first-run effect—the judgments-relative-to-patterns model—to account for the judged frequencies of sequentially encountered stimuli. The model parameter w accounts for the effect of the length of the first run on frequency estimates, given the total sequence length. We fitted data from Kusev et al. (Journal of Experimental Psychology: Human Perception and Performance 37:1874–1886, 2011) to the model parameters, so that with increasing values of w, subsequent items in the first run have less influence on judgments. We see the role of the model as essential for advancing knowledge in the psychology of judgments, as well as in other disciplines, such as computer science, cognitive neuroscience, artificial intelligence, and human–computer interaction.