Violations of the betweenness axiom and nonlinearity in probability

Betweenness is a weakened form of the independence axiom, stating that a probability mixture of two gambles should lie between them in preference. Betweenness is used in many generalizations of expected utility and in applications to game theory and macroeconomics. Experimental violations of betweenness are widespread. We rule out intransitivity as a source of violations and find that violations are less systematic when mixtures are presented in compound form (because the compound lottery reduction axiom fails empirically). We also fit data from nine studies using Gul's disappointment-aversion theory and two variants of EU, which weight separate or cumulative probabilities nonlinearly. The three theories add only one parameter to EU and fit much better.     

CANONICAL VARIATE ANALYSIS—A GENERAL MODEL FORMULATION

A general model, specifying the population means as a function of the population canonical vectors, provides a natural basis for considering many aspects of canonical variate analysis. These aspects include: estimation for elliptical densities, and robust estimation; estimation of missing values; adequacy of hypothetical variables; regression in dummy variable space; and comparison of solutions.     

Testing equality of proportions with incomplete correlated data

Let (ψ_i,φ_i) be independent, identically distributed pairs of zero-one random variables with (possible) dependence of ψ_i and φ_i within the pair. For n pairs, both variables are observed, but for m₁ additional pairs only ψ_i is observed and for m₂ others φ_i is observed. If π_1· = P{ψ_i = 1} and π_·1=P{φ_i, the problem is to test π_1·=π_·1. Maximum likelihood estimates of π_1· and π_·1 are obtained via the EM algorithm. A test statistic is developed whose null distribution is asymptotically chi-square with one degree of freedom (as n and either m₁ or m₂ tend to infinity). If m₁ = m₂ = 0 the statistic reduces to that of McNemar's test; if n = 0, it is equivalent to the statistic for testing equality of two independent proportions. This test is compared with other tests by means of Pitman efficiency. Examples are presented.     

Physicians and clergy as facilitators of formal services for older adults

Researchers have sought to understand the determinants of the use of in-home and community-based services in order to better serve the needs of older adults. One component frequently included in formal service utilization models is the role of individuals who exert an influence on the service use process. An analysis of in-depth interviews conducted with 115 older adults revealed the important facilitating role that physicians and religious leaders play in encouraging the use of these services. The sample, which included African-American and white adults age 65+ from rural and urban environments, described various ways in which these "facilitators" influence the use of formal services. These ways include: (1) supplying instrumental support either by "ordering" a particular program for or linking the elder with the program and (2) providing informational and affective support, including advising or recommending the use of a program, conveying necessary background on formal services, and legitimizing the use of formal services. Regardless of personal characteristics (such as ethnicity and residence), a majority of elders in the sample recognized the important role played by physicians, and clergy. The acknowledgement of the role played by these facilitators should be viewed as an opportunity for physicians and clergy to enhance the knowledge and appropriate use of needed formal services for elders. In addition, these findings have policy implications for the current provision of aging services.     

Recent developments in modeling preferences: Uncertainty and ambiguity

In subjective expected utility (SEU), the decision weights people attach to events are their beliefs about the likelihood of events. Much empirical evidence, inspired by Ellsberg (1961) and others, shows that people prefer to bet on events they know more about, even when their beliefs are held constant. (They are averse to ambiguity, or uncertainty about probability.) We review evidence, recent theoretical explanations, and applications of research on ambiguity and SEU.Thanks to Jonathan Baron, James Dow, Peter Fishburn, Itzhak Gilboa, Gordon Hazen, Howard Kunreuther, Tomas Phillipson, David Schmeidler, Amos Tversky, the editor, and several anonymous referees for corrections and helpful comments. Camerer's contribution to this work was supported by the National Science Foundation, grant no. SES 88-09299. Weber's contribution was supported by the Deutsche Forschungsge-meinschaft, grant no. WE 993/5-1.