Human subjects indicated their preference between a hypothetical $1,000 reward available with various probabilities or delays and a certain reward of variable amount available immediately. The function relating the amount of the certain-immediate reward subjectively equivalent to the delayed $1,000 reward had the same general shape (hyperbolic) as the function found by Mazur (1987) to describe pigeons' delay discounting. The function relating the certain-immediate amount of money subjectively equivalent to the probabilistic $1,000 reward was also hyperbolic, provided that the stated probability was transformed to odds against winning. In a second experiment, when human subjects chose between a delayed $1,000 reward and a probabilistic $1,000 reward, delay was proportional to the same odds-against transformation of the probability to which it was subjectively equivalent.

Research on sequential effects in magnitude scaling is reviewed, and its implications about the adequacy of current time series regression models is discussed. A regression model that unifies what at first appear to be contradictory results is proposed. Theoretical models of judgment and perception are introduced, and their relation to alternative regression models is clarified. A theoretical model of relative judgment that clarifies the role of judgmental error and frames of reference in magnitude scaling is examined in detail. Four experiments that test the model are presented. The results, along with recent results presented by Ward (1987), provide support for the model. The importance of being explicit about the relation of theoretical models to regression models and about the role of error in these models is discussed.

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A formula for the size-weight illusion was derived from the Stevens and Rubin (1970) finding that heaviness functions form a family of power functions that converge at a common point in the vicinity of the heaviest weight that can be lifted. Magnitude estimations of the apparent heaviness of 42 plastic cylinders varying in size and weight were obtained from 20 subjects, who were allowed to use both hands to lift the weights. It was predicted that this would increase the maximum weight that could be lifted, which would, in turn, enhance the magnitude of the illusion (the dependence of heaviness on size). The results supported this and other predictions of the model concerning the dependence of the illusion on weight as well as volume.object's volume , V, as expressed in the following equation:From what has been given. it is easy to show that relative heaviness is a simple power function of relative weight as represented by the equation (2) (3)where