Are there jumps in evidence accumulation, and what, if anything, do they reflect psychologically? An analysis of Lévy Flights models of decision-making

Abstract

According to existing theories of simple decision-making, decisions are initiated by continuously sampling and accumulating perceptual evidence until a threshold value has been reached. Many models, such as the diffusion decision model, assume a noisy accumulation process, described mathematically as a stochastic Wiener process with Gaussian distributed noise. Recently, an alternative account of decision-making has been proposed in the Lévy Flights (LF) model, in which accumulation noise is characterized by a heavy-tailed power-law distribution, controlled by a parameter, $$\alpha $$ α . The LF model produces sudden large “jumps" in evidence accumulation that are not produced by the standard Wiener diffusion model, which some have argued provide better fits to data. It remains unclear, however, whether jumps in evidence accumulation have any real psychological meaning. Here, we investigate the conjecture by Voss et al. (Psychonomic Bulletin & Review,26(3), 813–832, 2019) that jumps might reflect sudden shifts in the source of evidence people rely on to make decisions. We reason that if jumps are psychologically real, we should observe systematic reductions in jumps as people become more practiced with a task (i.e., as people converge on a stable decision strategy with experience). We fitted five versions of the LF model to behavioral data from a study by Evans and Brown (Psychonomic Bulletin & Review, 24(2), 597–606, 2017), using a five-layer deep inference neural network for parameter estimation. The analysis revealed systematic reductions in jumps as a function of practice, such that the LF model more closely approximated the standard Wiener model over time. This trend could not be attributed to other sources of parameter variability, speaking against the possibility of trade-offs with other model parameters. Our analysis suggests that jumps in the LF model might be capturing strategy instability exhibited by relatively inexperienced observers early on in task performance. We conclude that further investigation of a potential psychological interpretation of jumps in evidence accumulation is warranted.

Lévy Flight Model of Gaze Trajectories to Assist in ADHD Diagnoses

“…These strategies are manifest in the movement of bacteria [10,11], the search for fish by albatrosses [12], or the foraging for food by sharks in the ocean [13]. This pattern is also present in several human tasks, such as the exploration of the Walt Disney Resort by children [14], the exploration of virtual environments [15], and was even proposed as a mathematical model for the way humans search for memories [16] or the response time in decision making based on the accumulation of evidence [17][18][19]. Using this framework, eye-tracking experiments found the characteristic Lévy exponent (α) to be approximately α = 0.9 (or α = 1.9 using a different convention than the one we are using here) [20], regardless of the level of difficulty of the visual task.…”