A harmonious note on pitch: Scales of pitch derived from subtractive model of comparison agree with the musical scale

Elmasian, R.; Birnbaum, Michael H.

doi:10.3758/bf03207513

Cited by 43 publications

(3 citation statements)

References 36 publications

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“…For many continua, when people are asked to judge “ratios” and “differences” of stimuli, they appear to use a subtractive operation regardless of the instructions. Judgments of “ratios” and “differences” are monotonically related for continua such as loudness and pitch of tones (Birnbaum & Elmasian, 1977; Elmasian & Birnbaum, 1984), heaviness of weights (Mellers, Davis, & Birnbaum, 1984), likableness of persons described by trait adjectives, darkness of dot patterns, and many others. However, when subjects are asked to judge “ratios” and “differences” of distances between stimuli, they appear to use both ratio and subtractive operations as instructed (Birnbaum, 1978, 1982; Birnbaum, Anderson, & Hynan, 1989; Veit, 1978).…”

Section: Methodsmentioning

confidence: 99%

Judgments of proportions.

Varey¹,

Mellers²,

Birnbaum³

1990

Journal of Experimental Psychology: Human Perception and Perfor

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This study investigated the processes that underlie estimates of relative frequency. Ss performed 4 tasks using the same stimuli (squares containing black and white dots); they judged "percentages" of white dots, "percentages" of black dots, "ratios" of black dots to white dots, and "differences" between the number of black and white dots. Results were consistent with the theory that Ss used the instructed operations with the same scale values in all tasks. Despite the use of the correct operation, Ss consistently overestimated small proportions and underestimated large proportions. Variations in the distributions of actual proportions affected the extent to which Ss overestimated small proportions and underestimated large proportions in the direction predicted by range-frequency theory. Results suggest that proportion judgments, and by analogy probability judgments, should not be taken at face value.

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Section: Methodsmentioning

confidence: 99%

Judgments of proportions.

Varey¹,

Mellers²,

Birnbaum³

1990

Journal of Experimental Psychology: Human Perception and Perfor

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“…3, but instead can be represented by the theory that the subject evaluates differences in both cases, but there are different judgment functions in the two tasks (Bimbaum, 1978(Bimbaum, , 1980(Bimbaum, , 1982Bimbaum & Elmasian, 1977;Bimbaum & Mellers, 1978;Bimbaum & Veit, 1974;Elmasian & Bimbaum, 1984;Hardin & Bimbaum, 1990;Mellers, Davis, & Birnbaum, 1984;Veit, 1978). Subtractive theory replaces Eq.…”

Section: R = Jrmx)my)imentioning

confidence: 99%

Scale convergence and utility measurement

Birnbaum

Sutton

1992

Organizational Behavior and Human Decision Processes

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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 "diierences" 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, configural-weight 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 well-approximated using a single scale of utility, the subtractive model for "ratio" and "difference" comparisons, and the confiiurai weight, rank-dependent model for buyer's and seller's prices.

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“…For a variety of continua, judgments of “ratios” and “differences” of subjective magnitudes appear to be monotonically related (Birnbaum, 1978, 1980, 1982; Birnbaum & Elmasian, 1977; Birnbaum & Veit, 1974; De Graaf & Frijters, 1988; Elmasian & Birnbaum, 1984; Hardin & Birnbaum, in press; Schneider, 1982; Schneider, Parker, & Upenieks, 1982; Veit, 1978, 1980). Because actual ratios and differences would not be expected to be monotonically related in the factorial designs used in this research (Krantz, Luce, Suppes, & Tversky, 1971; Miyamoto, 1983), such experiments provide nontrivial tests of Torgerson's (1961) hypothesis that subjects perceive or appreciate but a single relation between a pair of stimuli, despite instructions to judge “ratios” or “differences.” 1…”

mentioning

confidence: 99%

Two operations for "ratios" and "differences" of distances on the mental map.

Birnbaum¹,

Anderson²,

Hynan³

1989

Journal of Experimental Psychology: Human Perception and Perfor

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Ss judged "ratios of distances" and "differences of distances" between pairs of U.S. cities. Results fit the theory that Ss used two comparison processes as instructed. A ratio scale of distances between cities was constructed from the 2 rank orders. From this scale, an interval scale of the city locations on an east-west continuum was derived. This scale agrees with the subtractive model fit to "ratios" and "differences" of easterliness and westerliness, and it also agrees with multidimensional scaling of judged distances between cities. These findings are consistent with the theory that Ss use subtraction when instructed to judge either "ratios" or "differences," but that they can use both ratio and difference operations when the stimuli (in this case, distances) constitute a ratio scale on the subjective continuum. We thank Barbara A. Mellers, Allen Parducci, and anonymous reviewers for helpful suggestions.

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A harmonious note on pitch: Scales of pitch derived from subtractive model of comparison agree with the musical scale

Cited by 43 publications

References 36 publications

Judgments of proportions.

Judgments of proportions.

Scale convergence and utility measurement

Two operations for "ratios" and "differences" of distances on the mental map.

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