Human Inferences about Sequences: A Minimal Transition Probability Model
Fig 5
Asymmetric perception of randomness.
(A) Data redrawn from Falk (1975) and reported in [25]. Subjects were presented with various binary sequences of 21 stimuli. They were asked to rate the apparent randomness of each sequence. The range of perceived randomness was normalized between 0 and 1. Ratings were sorted based on the alternation frequency in the sequences. (B-D) Theoretical levels of entropy estimated by distinct local models. The entropy characterizes the unpredictability of a sequence. For each model, we generated random sequences differing in their alternation frequencies. For each sequence and model, we computed the estimated probability of the next stimulus of the sequence, given the preceding stimuli. We then converted these predictions into entropy levels and plotted the average for different values of the leak parameter of the model. Note that only a learning of transition probabilities predicts a slight asymmetry of perceived randomness.