Simplicity, symmetry, and syntely: Stimulus measures of binary pattern structure

A simple parameter free algorithm based solely on the sequential run and alternation structure of binary sequences is elaborated. The algorithm is designed to measure the sequence's syntely: the degree to which past consequences within a sequence converge on the continuation of that sequence's terminal run. This syntely algorithm is shown to predict subjects' expectancies in a sequential prediction task using short binary sequences. Other algorithms measuring the symmetry and simplicity of short binary patterns are demonstrated, and their measures shown to be correlated with each other, but not correlated with syntely. Goodness and strength of expectancy are unrelated. The syntely algorithm is shown to be successful in predicting the error profiles of subjects learning short recurrent patterns of binary sequences. The syntely algorithm is based on the straightforward principle of induction by enumeration: the composite of past events controls the expectancy of future events. The success of this algorithm, even though it may embody the principle of induction only imperfectly, provides good evidence that this principle is a useful normative grade for understanding the human processing of contingencies in binary sequences, making complicated schemes of rules and hypotheses unnecessary.