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Scale Convergence and Utility Measurement
, 1992
"... In order to investigate derived scales for the utility, or subjective value of money, subjects were instructed to perform four tasks: in two tasks, they judged “ratios” and “differences” of strengths of preference for monetary amounts; in two other tasks, they judged the values of gambles from buyer ..."
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In order to investigate derived scales for the utility, or subjective value of money, subjects were instructed to perform four tasks: in two tasks, they judged “ratios” and “differences” of strengths of preference for monetary amounts; in two other tasks, they judged the values of gambles from buyer’s or seller’s points of view. The two arrays of data for “ratios” and “differences” were consistent with the hypothesis that most subjects used only one operation to compare monetary amounts, although a few subjects appeared to use two operations. The buyer’s and seller’s prices would lead to two different utility functions for money under expected utility theory, subjective expected utility theory, or any theory that is additive across outcomes. However, configuralweight utility theory can predict these changes in rank order with an invariant utility function, by postulating that the configural weight of the smaller amount depends on point of view. The data also reveal systematic violations of dominance (monotonicity) that can be described by assuming that the configural weight of zero, when it is the lower value, has smaller weight at low probabilities than nonzero outcomes. Disregarding the minority of subjects who appeared to utilize two operations for judging “ratios ” and “differences” in utility, the majority of the data can be wellapproximated using a single scale of utility, the subtractive model for “ratio” and “difference” comparisons, and the configurai weight, rankdependent model for buyer’s and seller’s prices.
Falmagne’s Elements of Psychophysical Theory appeared
, 2006
"... Two forms of direct measurement are considered in the article: a strong form in which ratio productions named by number words are interpreted veridically as the numerical ratios they name; and a weak form in which the ratio productions named by number words may have interpretations as ratios that ar ..."
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Two forms of direct measurement are considered in the article: a strong form in which ratio productions named by number words are interpreted veridically as the numerical ratios they name; and a weak form in which the ratio productions named by number words may have interpretations as ratios that are different from numerical ratios they name. Both forms assume that the responses to instructions to produce ratios are represented numerically by ratios, and thus the word ‘‘ratio’’—and supposedly the participants concept associated with it—is being ‘‘directly’ ’ represented. The strong form additionally ‘‘directly represents’ ’ the number mentioned in the instruction by itself. The article provides an axiomatic theory for the numerical representations produced by both forms. This theory eliminates the need for assuming anything is being ‘‘directly represented,’ ’ allowing for a purely behavioral approach to ratio production data. It isolates two critical axioms for empirical testing. An measurementtheoretic explanation is provided for the puzzling empirical phenomenon that subjects do not distinguish between ratios and differences in a variety of direct measurement tasks.
PSYCHOLOGICAL SCIENCE Research Article MEASUREMENT OF STRESS: Scaling the Magnitudes of Life Changes
"... Abstract—This paper evaluates models and measurements of the stress induced by life changes to determine whether a single scale can explain several different phenomena, including Judgments of "ratios " and "differences " as well as "combinations." ..."
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Abstract—This paper evaluates models and measurements of the stress induced by life changes to determine whether a single scale can explain several different phenomena, including Judgments of &quot;ratios &quot; and &quot;differences &quot; as well as &quot;combinations.&quot; Judgments of &quot;ratios &quot; and &quot;differences &quot; were found to be approximately monotonically related, suggesting that these judgments should not be taken at face value, but instead that the same comparison operation governs both tasks. Judgments of &quot;combinations &quot; of stressful events were not simply the sums of their separate events; instead, they showed two systematic departures from additivity. First, the effect of a given event was less when it was the least stressful event in a combination than when it was the most, as if the most stressful event carries extra configural weight. Second, each additional stressor had diminishing marginal effect on the overall jtidgment. All three sets of data could be explained with a single scale using the theory that &quot;ratios &quot; and &quot;differences &quot; are both governed by subtraction and that &quot;combination &quot; judgments are a configurally weighted combination of the same scale values. This unified scale of stress seems preferable to the previous scale that was based on magnitude estimation.