Among the most popular models for decision under risk and uncertainty are the rank-dependent models, introduced by Quiggin and Schmeidler. Central concepts in these models are rank-dependence and comonotonicity. It has been suggested in the literature that these concepts are technical tools that have no intuitive or empirical content. This paper describes such contents. As

This review article attempts to highlight from my personal perspective some of the major developments in the representational theory of measurement during the past 50 years. Emphasis is placed on the ongoing interplay between the development of abstract theory and the attempts to apply it to empirically testable phenomena. The article has four major sections. The first concerns classical representational measurement, which was the successful attempt to formulate the major measurement methods of classical physics: extensive and additive conjoint structures, their distributive interlock in dimensional analysis, and intensive (averaging) structures. The second illustrates a nontrivial behavioral example using both extensive and conjoint measurement plus functional equations to arrive at rank- and sign-dependent utility (also called cumulative prospect) representations for decision making under risk. The third section, contemporary representational measurement, somewhat overlaps the classical one but includes new findings and approaches: representations of nonadditive concatenation and conjoint structures; a general theory of scale types; results for general, finitely unique, homogeneous structures; structures that are homogeneous between singular points; generalized distributive triples; and a generalization of dimensional analysis to include any ratio scalable attribute; and the concept of meaningfulness. The final section concerns applications of the latter ideas to psychophysical scaling and merging functions.] 1996 Academic Press, Inc. 1.

The paper reports the results of an experiment on individual investors’ risk perception in a stock market context under two different modes of information presentation (framings). While the concentration on two moments of a return distribution has been a cornerstone of neo-classic finance theory from the start (Markowitz 1952) an alternative’s mean and variance have been selected more by convenience and ease of computation than by theoretical or empirical justification. Even though the most influential models are based on variance as risk measure there has always been much discontent with this proposal. The symmetrical nature of variance does not capture the common notion of risk as something undesired, e. g. negative deviations from a reference point. Instead, lower partial moments (LPM) seem to be more appropriate for measuring risk. The purpose of this paper is to examine experimentally private investors’ risk perception in a financial context. The focus is on the correspondence of people’s risk perceptions with specific LPMs. The main findings can be summarized as follows. First, symmetrical risk measures like variance can be clearly dismissed in favor of shortfall measures like LPMs. Second, the reference point (target) of individuals for defining losses is not a distribution’s mean but the initial price in a time series of stock prices. Third, the LPM which explains risk perception best is the LPM0, i. e. the probability of loss. Fourth,

The dominance principle states that one should prefer the option with consequences that are at least as good as those of other options for any state of the world. When applied to judged prices of gambles, the dominance principle requires that increasing one or more outcomes of a gamble should increase the judged price of the gamble, with everything else held constant. Previous research has uncovered systematic violations of the dominance principle: people assign higher prices to a gamble with a large probability of winning an amount, Y, otherwise zero, than they do to a superior gamble with the same chance of winning Y, otherwise winning a small amount, X! These violations can be explained by a configural-weight theory in which two-outcome gambles are represented with two sets of decision weights; one set for outcomes having values of zero and another set for lower-valued outcomes that have nonzero values. The present paper investigates whether dominance violations are limited to two-outcome gambles. Results show that people violate the dominance principle with three-outcome gambles even with financial incentives. Furthermore, results could be predicted from the configural-weight theory. The data do not support the view that configural weighting is caused by a shift in strategy that would apply only to two-outcome gambles. KEY WORDS dominance principle; two-outcome gambles; three-outcome gambles; configural-weight theory

Correspondence concerning this article should be addressed to X.T. Wang, Psychology Department,

People judged both the attractiveness and risk of lotteries to win or lose money. The lotteries were designed to test whether risk and attractiveness judgments show systematic deviations from the simple sum of probability-byutility-products analogous to (S)EU theory. Our results led to an alternative combination rule for probability and outcome information, with a relative weight averaging component and a configural (i.e., sign- or rank-dependent) probability weighting component. Ratings of risk and attractiveness were negatively correlated, but the two tasks showed systematic differences in the rank order of judgments. Both judgments could be tit by the same configural relative weight averaging model, but with different parameters (especially the sign-dependent probability weighting functions). Risk judgments were more sensitive to the probability of losses and zero outcomes compared to attractiveness judgments, which were more sensitive to the probability of gains. There were individual differences on the extent of this difference in probability weights between risk and attractiveness judgments.