Refuting data aggregation arguments and how the IBL model stands criticism: A reply to Hills and Hertwig (2012)

Hills and Hertwig (2012) challenge the proposed similarity of the exploration-exploitation transitions found in Gonzalez and Dutt (2011) between the two experimental paradigms of decisions from experience (sampling and repeated-choice), which was predicted by an Instance-Based Learning (IBL) model. The heart of their argument is that in the sampling paradigm, an impression of reduced exploration over time (alternation rate, A-rate) is produced by an inverse relationship between the sample size and the A-rate, and the aggregation of participants with different sample sizes. They suggest a normalization of the A-rate, which produces constant A-rate curves during sampling, and conclude with certain “ensuing problems for the IBL model.” We show that: the reduction of A-rate during sampling occurs even when sample length is controlled for; that regardless of the sampling length, the maximization behavior during sampling predicts the final choice; and that the IBL model accounts for a negative correlation between sample size and the predicted A-rate. Furthermore, when the IBL model's data is normalized following the procedure specified by Hills and Hertwig (2012), it results in similar flattened exploration curves as those found in human data. These results indicate that the transition from exploration to exploitation in the sampling paradigm (which has also been found in the repeated-choice paradigm) is not an illusion resulting from data aggregation: The same data with or without normalization may be interpreted differently, but such interpretations do not invalidate the mechanisms of the IBL model.