Michael H. Birnbaum

Using contextual effects to derive psychophysical scales

This paper presents a functional measurement analysis of Parducci’s range-frequency theory. The theory provides a basis for (1)finding context-invariant psychophysical scales, (2)establishing the validity of rating scales, and (3) explaining contextual effects in judgment. In an experimental illustration, Ss judged the magnitude of numerals in nine different distributions. All data were used to obtain the psychophysical function for numerals and also to test the model. The large contextual effects were consistent with the model. Quantitative tests of fit supported the equal-interval assumption of the category scale. The psychophysical function appeared nearly linear but with a significant negative acceleration. The data were shown to be qualitatively inconsistent with generalizations of Helson’s theory of adaptation level and Johnson’s correlation-regression theory. They supported Parducci’s range-frequency theory and illustrated how it could be used to factor out contextual effects from effects of stimulus magnitude. Extensions of the range-frequency approach are also discussed.

Scale convergence as a criterion for rescaling: Information integration with difference, ratio, and averaging tasks

Ss lifted pairs of weights simultaneously, one in each hand, and judged either the difference, ratio, or average heaviness of the two weights. Data for the difference and ratio tasks were in general agreement with subtractive and ratio models, but the averaging data showed discrepancies from the constant-weight averaging model similar to those reported in previous psychophysical research. Rescaling was ruled out for the averaging data, because responses to pairs of equal weight were a linear function of subtractive model scale values derived from the difference task data. Scale values for the ratio and difference task data were related exponentially, as were the responses to the pairs, consistent with Torgerson’s conjecture that Ss do not distinguish “differences” from “ratios.” They appear to use the same composition rule but different output functions, depending on the procedures for responding. The scale convergence criterion can thus prevent inappropriate rescaling when a model fails and can dictate rescaling even when a model fits.

Testing Critical Properties of Decision Making on the Internet

This article reviews recent findings that violate a broad class of descriptive theories of decision making. A new study compared 1,224 participants tested via the Internet and 124 undergraduates tested in the laboratory. Both samples confirmed systematic violations of stochastic dominance and cumulative independence; new tests also found violations of coalescing. The Internet sample was older, more highly educated, more likely male, and also more demographically diverse than the lab sample. Internet participants were more likely than undergraduates to choose the gamble with higher expected value, but no one conformed exactly to expected value. Violations of stochastic dominance decreased as education increased, but violations of stochastic dominance and coalescing were still substantial in persons with doctoral degrees who had read a scientific work on decision making. In their implications, Internet research and lab findings agree: Descriptive decision theories cannot assume that identical consequences can be coalesced.

Loudness “ratios” and “differences” involve the same psychophysical operation

Subjects judged both “atios” of loudness and “differences” in loudness between pairs of tones that varied in intensity. The pairs were constructed from factorial designs, permitting separation of stimulus and response scaling for each subject. Ratings of “differences” and estimations of “ratios” were monotonically related, inconsistent with the hypothesis that subjects perform both subtractive and ratio operations on a common scale. Instead, the data suggest that both tasks involve the same psychophysical comparison operation with different response transformations. If the operation can be represented by the subtractive model, then category ratings involve a nearly linear transformation and magnitude estimations involve a nearly exponential transformation.

A change-of-process theory for contextual effects and preference reversals in risky decision making

Abstract Three experiments were conducted to investigate contextual effects and response mode effects (e.g., preference reversals) in risky decision making. Judgments of the worth of binary gambles were examined using two different contexts (positively and negatively skewed distributions of expected values) and two different response modes (attractiveness ratings and buying prices). Changes in the response mode affected the preference order of gambles, and changes in the context due to variations in skewing influenced the metric properties of the judgments but had a minimal effect on preference orders. Data were inconsistent with contingent weighting theory (Tversky, Sattath, & Slovic, 1988) and expression theory (Goldstein & Einhorn, 1987) . Results could be described by a change-of-process theory which assumes that the method of elicitation influences the manner in which people combine information and arrive at judgments. Under certain conditions, attractiveness ratings could be described by an additive combination of subjective probability and utility ( s and u ), whereas pricing judgments were accounted for by a multiplicative function, with the same scales of s and u in both tasks. When the range of outcomes included zero and negative values, preference orders for attractiveness ratings of gambles changed. This change in rank order was consistent with the hypothesis that inclusion of these levels caused more subjects to use a multiplicative rule for combining u and s when rating the attractiveness of gambles. Thus, preference reversals can be explained by the theory that the combination rule changes, while utilities and subjective probabilities remain constant.

Preferences, prices, and ratings in risky decision making

Systematically different preference orders are obtained when different procedures are used to elicit preferences for gambles. Three new experiments found different preference orders with attrativeness ratings, risk ratings, buying prices, selloing prices, avoidance prices, and strength-of-preference judgments. Preference reversals persisted event when Ss were given financial incentives to motivate them to rank the gambles identically. Results were consistent with a change-of process theory in which Ss are assumed to use different strategies in different tasks with the same scales. Attractiveness and risk ratings could be described by an additive combination of probability and amount, and prices could be predicted by a multiplicative combination of the same scales. Strength-of-preference judgments were consistent with contrast-weighting model in which the weight of a dimension (either probability or amount) depends on the contrast between the 2 gambles along that dimension

Combining information from sources that vary in credibility.

Models describing the role of source credibility in information integration were tested in two experiments. In the first experiment, subjects estimated the value of used cars based on two cues: blue book value and an estimate provided by one of three friends who examined the car. The three sources were described as differing in mechanical expertise. In the second experiment, subjects rated the likeableness of persons described by either one or two adjectives, each adjective contributed by a different source. The sources differed with respect to the length of their acquaintance with the person to be rated. In both experiments, credibility of the source magnified the impact of the information he provided. Further, this multiplicative effect of a source was inversely related to the credibility of the other source, in violation of additive or constant-weight averaging models, but consistent with a relative-weight averaging model.

Intuitive Numerical Prediction

Subjects were trained, with feedback, to predict a numerical criterion from each of two separate cues and then asked, without feedback, to predict it from a pair of independent cues or a single cue. Their intuitive predictions were qualitatively inconsistent with an additive model, since the effect of one cue varied inversely with the number of cues available, and with a constant-weight averaging model, since the effect of one cue varied inversely with the validity of the other cue. The data were consistent with a relative-weight averaging model, which assumes that subjective cue values are averaged using weights that depend on cue validities. Normative and descriptive theories of intuitive prediction are compared.

Violations of Monotonicity and Contextual Effects in Choice-Based Certainty Equivalents

This article investigates choices between gambles and amounts of money to explore two issues in decision making First, in recent studies, judgments of the values of gambles violated monotonicity (dominance), yet choices between the same gambles satisfied monotonicity, producing reversals of preference This experiment tested whether certainty equivalents based on choices between gambles and money would violate monotonicity Results indicated that these choices violated monotonicity in the same way as had Judgments Second, this experiment investigated whether the certainty equivalent of a gamble would depend on the distribution of amounts offered for comparison It was found that certainty equivalents based on choices depended on the context in the same fashion as psychophysical comparisons Apparently, paradoxes of behavioral decision making are not eliminated by using choices instead of judgments to investigate human preferences

Scale Convergence and Utility Measurement

Abstract 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 buyers or sellers 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 buyers and sellers 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 configurai 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 configurai 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 configurai weight, rank-dependent model for buyers and sellers prices.