How symmetry restricts symmetric choice

Abstract

In a symmetric choice experiment, the share of response found on the ith alternative, or state, S i , is proportional to f( S i ), a weight function that describes the results. The form of f is restricted by the symmetries of the experimental situation through a functional equation. The response distribution must obey that equation and the extraction of a satisfactory theoretical expression for it is analogous to the standard procedures used with differential equations to analyze mechanical systems. It is shown that every symmetric choice function, f, is equivalent to a simpler, normal function, the product of whose separate values is unity. This can simplify the discovery of simple formulas underlying otherwise obscure numerical results. Applications are given to behavioral problems. Applicability to symmetric neural channels (such as paired optic or auditory nerves) is noted.