The Race Levy Flight Model: Jumping in multi-alternative decisions

Sequential sampling models have become the dominant explanation for how information processing operates in decision making. One recent variant of these models, the Levy Flight model (Voss et al. 2019), proposes non-Gaussian noise for the evidence accumulation process, which theoretically implies that evidence accumulation may involve noisier “jumps” than those contained in models with Gaussian noise. While the Levy Flight model proposed by Voss et al. (2019) was shown to provide a better account of their data than the standard diffusion model, this formulation has two key weaknesses: (1) it does not have an exact likelihood function, and (2) it is only applicable to 2-alternative tasks. Here, we develop the Race Levy Flight Model (RLFM): a Levy Flight model that utilizes a racing accumulator framework with non-Gaussian noise. Importantly, the independent accumulator framework allows for an easy extension to multi-alternative decisions and the calculation of the first passage time for each accumulator using a fractional partial differential equation, providing a Levy Flight model that has an exact likelihood function for any number of decision alternatives. To assess the performance of our proposed RLFM, we fit the model to the speed-accuracy emphasis data-set of Forstmann et al. (2008). Our results show that the RLFM greatly outperforms the racing diffusion model, showing an advantage for the Levy Flight process consistent with the findings of Voss et al. (2019), and produces a theoretically sensible ordering of parameter estimates across speed-accuracy conditions.