We propose and evaluate a memory-based model of Hick's law, the approximately linear increase in choice reaction time with the logarithm of set size (the number of stimulus-response alternatives). According to the model, Hick's law reflects a combination of associative interference during retrieval from declarative memory and occasional savings for stimulus-response repetitions due to non-retrieval. Fits to existing data sets show that the model accounts for the basic set-size effect, changes in the set-size effect with practice, and stimulus-response repetition effects that challenge the information-theoretic view of Hick's law. We derive the model's prediction of an interaction between set size, stimulus fan (the number of responses associated with a particular stimulus), and stimulus-response transition, which is subsequently tested and confirmed in two experiments. Collectively, the results support the core structure of the model and its explanation of Hick's law in terms of basic memory effects.
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Being able to correctly identify a target when presented with multiple possible alternatives, or increasing uncertainty, is highly beneficial in a wide variety of situations. This has been intensely investigated with human participants and results consistently demonstrated that participant reaction time (RT) increases linearly with the number of response alternatives, described as Hick's Law. Yet, the strength of this relationship is impacted by a variety of parameters, including stimulus-response compatibility, stimulus intensity, and practice.
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