Theory of Behavioral Power Functions

Data in operant conditioning and psychophysics are often well fitted by functions of the form y — qx'. A simple theory derives these power functions from the simultaneous equations dx/x = aif(z)dz and dy/y = a j ( z ) d z , where z is a comparison variable that is equated for the effects of x and y, and Oj and a2 are sensitivity parameters. In operant conditioning, * and y are identified with response rates; in psychophysics, with measures of stimulus and response. The theory can explain converging sets of power functions, solves the dimensional problems with the standard power function, and can account for the relation between Type I and Type II psychophysical scales.