Test of a response bias model of bisection

An algebraic model of bisection —a special case of Pfanzagl’s general measurement system-was tested for brightness. Nonparametric scalability, a condition derived from reflexivity, commutativity, and bisymmetry, was disconfirmed, leading to a rejection of the commutativity axiom, and necessitating the incorporation of a response bias parameter. The systematic bias in the data was substantially reduced by the introduction of the response bias parameter-interpreted as “position” bias, not hysteresis. The data are generally supportive of Pfanzagl’s bisection system, although the failure of commutativity requires the incorporation of a response bias parameter.