You say "probable" and I say "likely": improving interpersonal communication with verbal probability phrases

When forecasters and decision makers describe uncertain events using verbal probability terms, there is a risk of miscommunication because people use different probability phrases and interpret them in different ways. In an effort to facilitate the communication process, the authors investigated various ways of converting the forecasters' verbal probabilities to the decision maker's terms. The authors present 3 studies in which participants judged the probabilities of distinct events using both numerical and verbal probabilities. They define several indexes of interindividual coassignment of phrases to the same events and evaluate the conversion methods by comparing the values of these indexes for the converted and the unconverted judgments. In all the cases studied, the conversion methods significantly reduced the error rates in communicating uncertainties.     

Decision making under internal uncertainty: the case of multiple-choice tests with different scoring rules

This paper assesses framing effects on decision making with internal uncertainty, i.e., partial knowledge, by focusing on examinees' behavior in multiple-choice (MC) tests with different scoring rules. In two experiments participants answered a general-knowledge MC test that consisted of 34 solvable and 6 unsolvable items. Experiment 1 studied two scoring rules involving Positive (only gains) and Negative (only losses) scores. Although answering all items was the dominating strategy for both rules, the results revealed a greater tendency to answer under the Negative scoring rule. These results are in line with the predictions derived from Prospect Theory (PT) [Econometrica 47 (1979) 263]. The second experiment studied two scoring rules, which allowed respondents to exhibit partial knowledge. Under the Inclusion-scoring rule the respondents mark all answers that could be correct, and under the Exclusion-scoring rule they exclude all answers that might be incorrect. As predicted by PT, respondents took more risks under the Inclusion rule than under the Exclusion rule. The results illustrate that the basic process that underlies choice behavior under internal uncertainty and especially the effect of framing is similar to the process of choice under external uncertainty and can be described quite accurately by PT.     

The Relative Importance of Probabilities, Outcomes, and Vagueness in Hazard Risk Decisions

This study investigated the joint effects of vagueness on both the probability and the outcome dimensions of hazard risk, using both pairwise choice and rating response tasks. Seventy-two subjects evaluated risk stimuli (concerning either environmental or health hazards), which varied in the level of probability of loss, the amount of loss, and the precision with which each dimension was specified. We found strong evidence of a consistent individual attitude toward vagueness on both risk dimensions and an almost equal number of vagueness-seeking and precision-seeking subjects. Choices were consistent with a decision rule based on dimension preference, but attitude toward vagueness significantly predicted choice in cases where a dimension preference rule was not appropriate. An asymmetric preference reversal pattern was also demonstrated, with many subjects choosing an option in a pair that they rated as more risky.     

The same but different: an empirical investigation of the reducibility principle

According to classical utility theory the valuation of any lottery should depend only on its outcomes and their respective probabilities, and should not be affected by the nature, complexity and structure of the chance mechanism. Previous research has documented systematic violations of this principle. For example, most subjects prefer lotteries in which the payoffs are contingent on the joint occurrence of multiple (high probability) events to simple lotteries, and lotteries in which the earlier stages offer higher probabilities than the later stages. We review the various violations of this principle and suggest a classification into two major types associated with misunderstanding of chance mechanisms and attitude towards the chance mechanism and process. In the present study 40 subjects were presented with 30 pairs of binary gambles. In any given pair the lotteries had identical outcomes and equal ‘reduced’ probabilities (and thus equal expected values). However, the chance mechanisms varied along a variety of factors such as the size of the sample space, the number of stages, temporal ordering, order of probabilities, their transparency and time constraints. Half the subjects saw lotteries involving gains and the other half considered only losses. After choosing one lottery in each pair, the subjects were asked to explain and justify their choices. The findings revealed systematic violations of the reducibility principle: subjects displayed a preference for lotteries with larger sample spaces, and for lotteries that allow quicker resolutions in the earlier stages. A clear distinction between some patterns of preferences in the gains and loss domains was revealed. In gambles involving gains subjects preferred to have the highest probability on the first stage (and the lowest probability on the last stage), but displayed the opposite preferences for losses. A content analysis of the subjects' stated reasons for their choices identified eight major categories. The most frequently invoked were hope, fun, simplicity, stress and time. Copyright © 2001 John Wiley & Sons, Ltd.     

How to measure diversity when you must

Racial/ethnic diversity has become an increasingly important variable in the social sciences. Research from multiple disciplines consistently demonstrates the tremendous impact of ethnic diversity on individuals and organizations. Investigators use a variety of measures, and their choices can affect the conclusions that can be drawn and limit the ability to compare and generalize results across studies effectively. The current article reviews 3 popular approaches to the measurement of diversity: the simplistic majority-minority approach and 2 multiple categories variants, the generalized variance and the lesser used entropy statistic. We discuss the properties of each approach and reject the majority-minority approach. We provide 5 examples using the generalized variance and entropy statistics and illustrate their versatility and flexibility. We urge investigators to adopt these multicategory measures and to use our discussion to determine which measure of diversity is most appropriate given the nature of one's data set and research question.     

An Extension of Dominance Analysis to Canonical Correlation Analysis

Dominance analysis (Budescu, 1993 Budescu, D. V. 1993. Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression.. Psychological Bulletin, 114: 542–551. [Crossref], [Web of Science ®] , [Google Scholar]) offers a general framework for determination of relative importance of predictors in univariate and multivariate multiple regression models. This approach relies on pairwise comparisons of the contribution of predictors in all relevant subset models. In this article we extend dominance analysis to canonical correlation analysis to explore the relative importance of the variables in both sets. The proposed extension provides (a) a decomposition of the models' fit into components associated with the individual variables; (b) the ability to compare the relative importance of variables from the two sets; (c) the ability to perform multistage analyses, involving all canonical variates; and (d) a bootstrapping inference procedure. The approach is illustrated with an empirical data example involving parenting styles and youth outcomes and its unique features are highlighted and discussed.     

Predicting World Cup results: Do goals seem more likely when they pay off?

Bar-Hillel and Budescu (1995) failed to find a desirability bias in probability estimation. The World Cup soccer tournament provided an opportunity to revisit the phenomenon in a context in which desirability biases are notoriously rampant. Participants estimated the probabilities of various teams’ winning their upcoming games. They were promised money if one team—randomly designated by the experimenter—won its upcoming game. Participants assigned a higher probability to a victory by their target team than did other participants, whose promised monetary reward was contingent on the victory of its opponent. Prima facie, this seems to be a desirability bias. However, in a follow-up study that made one team salient, without promising monetary rewards, participants also judged their target team to be more likely to win. On grounds of parsimony, we conclude that what appears to be a desirability bias may just be a salience/marking effect, and—although optimism is a robust and ubiquitous human phenomenon—that wishful thinking still remains elusive.     

Resource dilemmas with environmental uncertainty and asymmetric players

Groups of subjects participated in a series of 30 noncooperative independent single-trial resource dilemmas. On each trial the subjects in each group requested privately a number of points from a common pool. Individual requests were granted if and only if the total group request was equal to or smaller than the pool size. The pool size on each trial was sampled randomly from a uniform distribution that was common knowledge. Asymmetry in payoff was induced by assigning to each group member a different points-to-money exchange rate. The results show that as the uncertainty about the pool size increases subjects (1) overestimate the pool size, (2) increase their requests, and (3) expect others to increase their requests. In addition (4) individual requests and expectations regarding others' requests are inversely related to the exchange rates, reflecting attempts to equate payoffs across group members.     

Parenting Practices and Adolescent Internalizing and Externalizing Problems: Moderating Effects of Socially Demanding Kin Relations

Association of socially demanding kin relations, mother’s emotional support, behavioral control/monitoring, family organization and psychological control with adolescent’s internalizing and externalizing problems were assessed in 200 economically disadvantaged, African American mothers and adolescents. Demanding kin relations and mother’s psychological control were positively associated with adolescent’s internalizing problems. Demanding kin relations also moderated the association of control/monitoring, family organization, and psychological control, with internalizing. For mothers with more demanding kin relations, increased control/monitoring was associated with increased adolescent internalizing. In comparison, increased control/monitoring was associated with decreased adolescent internalizing for mothers with less demanding kin relations. Negative association of family organization with internalizing was more apparent for mothers with more compared to less demanding kin relations. Positive association of mother’s psychological control with internalizing was more apparent for mothers with more compared to less socially demanding kin relations. Demanding kin relations and mother’s psychological control were positively associated with adolescent’s externalizing problems. Mother’s emotional support and family organization were negatively associated with externalizing. Also, negative association of family organization with externalizing was more apparent for families with more compared to less demanding kin relations. The need for research on the factors associated with negative relation with kin was discussed.