A theory of bidirectional judgments

Abstract

This paper is concerned with a scaling theory for "bidirectional" judgments, for which the order of judgment is reversible, as in fractional and multiple ratio estimation judgments. With the assumption that judgments are mediated by perceived relations of pairs of stimuli, the theory is developed for judgments of comparison stimuli in relation to standards, taking explicit account of the location of the comparison stimulus relative to the standard. The theory of bidirectional judgments, based on a theory of relative judgment by Fagot (1978Fagot ( ,1979,entails a partial nesting of models characterized by a progressive weakening of the constraints placed on the structure of the data. The weakest model, the relative bias/directional standard (RBDS) model, allows each standard to have two biasing effects, depending on the location of the standard above or below the comparison stimulus. Tests of the theory were carried out on the ratio estimation of brightness and weight data of Engen and Levy (l955),and the part-sum estimation data of Goude (1962). Only the RBDS model was found acceptable for all three data sets. THEORY

Bias effects on magnitude and ratio estimation power function exponents

“…The RBDS model allows each standard to have two biasing effects, depending on the location of the standard relative to the comparison stimulus (see Fagot, 1981, p. 183, for details). Considerable evidence (Fagot, 1981) indicates that the RBDS model provides a good account of the biasing effects of standards. The RBDS power function is then:…”

“…The axiom for the ratio estimation RBDS model is the following ratio of ratios condition (Fagot, 1981): where the ratios M./M b are formed from two independent…”

“…R. Teghtsoonian (1973) and R. Teghtsoonian and M. Teghtsoonian (1978) propose a model utilizing stimulus and response ratios that gives a good description of the effects of intramodal stimulus-range variation, making it possible in theory to isolate the exponent as an invariant, relative to the effects of range v a r i a t i o n . , It is in this spirit that we propose in the present study to use a model of relative judgment (Fagot, 1981), with which we will attempt to account for the biasing effects of standards, and from which a power function will be derived. To the extent that the theory is correct, the exponents of the derived power function should be relatively free of the effects of standards.…”

“…It is in this spirit that we propose in the present study to use a model of relative judgment (Fagot, 1981), with which we will attempt to account for the biasing effects of standards, and from which a power function will be derived. To the extent that the theory is correct, the exponents of the derived power function should be relatively free of the effects of standards.…”

“…Note that the multiplicative constant, c, cancels, and Equation 3 contains only one unknown, the exponent r. We shall refer to Equation 3 as the RE(C) power function. Fagot (1981) proposed the following judgment function in an attempt to deal with the biasing effects of standards: L(if;b!if;. ) where the first subscript on R denotes the comparison stimulus and the second the standard.…”