From Algorithmic to Subjective Randomness

We explore the phenomena of subjective randomness as a case study in understanding how people discover structure embedded in noise. We present a rational account of randomness perception based on the statistical problemof model selection: given a stimulus, inferring whether the process that generated it was random or regular. Inspired by the mathematical definitionof randomness given by Kolmogorov complexity, we characterize regularity in terms of a hierarchy of automata that augment a finite controller with different forms of memory. We find that the regularities detectedin binary sequences depend upon presentation format, and that the kinds of automata that can identify these regularities are informative aboutthe cognitive processes engaged by different formats.