Risk Attitudes and Decision Weights

To accommodate the observed pattern of risk-aversion and risk-seeking, as well as common violations of expected utility (e.g., the certainty effect), we introduce and characterize a weighting function according to which an event has greater impact when it turns impossibility into possibility, or possibility into certainty, that when it merely makes a possibility more or less likely. We show how to compare such weighting functions (of different individuals) with respect to the degree of departure from expected utility, and we present a method for comparing an individual's weighting functions for risk and for uncertainty

On the optimal number of alternatives at a choice point

Given a fixed total number of alternatives for a multiple-choice type test, the use of three alternatives at each choice point will maximize discriminability, power and information of a test. A proof is presented and applications to test construction, task design, and information processing are briefly discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32117/1/0000167.pd

Additivity, utility, and subjective probability

The additive conjoint measurement model is applied to the study of decision making under certainty and risk. A data matrix is called additive if it is possible to rescale its cell entries such that their order is preserved and that every rescaled entry can be expressed as a sum of its row and column components. It is shown that the SEU model, according to which individuals attempt to maximize their subjectively expected utility, is equivalent to additivity for a specified class of risky choices.In the experimental study eleven prisoners bid for both risky and riskless offers. Additivity is confirmed by the data supporting the independence between utility and subjective probability. Two alternative variants of the SEU model are used to derive subjective probability and utility functions for each subject. In order to account for the data, one needs either (a) a positive utility for gambling or (b) subjective probability functions where complementary events do not sum to unity. Neither variant is compatible with classical utility theory but both are successful in predicting an independent set of data. Relationships to existing data and implications for future research are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33321/1/0000717.pd

A general theory of polynomial conjoint measurement,

The present theory generalizes conjoint measurement in five major respects. (a) It is formulated in terms of partially rather than fully ordered data. (b) It applies to both ordinal and numerical data. (c) It is applicable to finite as well as infinite data structures. (d) It provides a necessary and sufficient condition for measurement. (e) This condition applies to any polynomial measurement model; that is, any model where each data element is expressed as a specified real-valued, order-preserving polynomial function of its components.Examples of polynomial measurement models include Savage's subjective expected utility model, Hull's and Spence's performance models, Luce's choice model, and multidimensional scaling models.It is shown that a data structure D satisfies a given polynomial measurement M if and only if D satisfies an abstract irreflexivity axiom with respect to M. The interpretation of the result and its implications to measurement theory are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33362/1/0000760.pd

Probabilistic Insurance

Probabilistic insurance is an insurance policy involving a small probability that the consumer will not be reimbursed. Survey data suggest that people dislike probabilistic insurance and demand more than a 20% reduction in the premium to compensate for a 1% default risk. While these preferences are intuitively appealing they are difficult to reconcile with expected utility theory. Under highly plausible assumptions about the utility function, willingness to pay for probabilistic insurance should be very close to willingness to pay for standard insurance less the default risk. However, the reluctance to buy probabilistic insurance is predicted by the weighting function of prospect theory. This finding highlights the potential role of the weighting function to explain insurance

A theory of risk

A psychological theory of perceived risk is developed. The theory is formulated in terms of an ordering of options, conceived of as probability distributions with respect to risk. It is shown that, under the assumptions of the theory, the risk of an option is expressible as a linear combination of its mean and variance. The relationships to other theories of risk and preference are explored.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32689/1/0000056.pd

The dimensional representation and the metric structure of similarity data

A set of ordinal assumptions, formulated in terms of a given multidimensional stimulus set, is shown to yield essentially unique additive difference measurement of dissimilarity, or psychological distance. According to this model, dissimilarity judgments between multidimensional objects are regarded as composed of two independent processes: an intradimensional subtractive process, and an interdimensional additive process. Although the additive difference measurement model generalizes traditional metric models, the conditions under which it satisfies the metric axims impose severe restrictions on the measurement scales. The implications of the results for the representation of similarity data by metric and/or dimensional models are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32692/1/0000059.pd