There are at least two kinds of probability matching: evidence from a secondary task

Probability matching is a suboptimal behavior that often plagues human decision-making in simple repeated choice tasks. Despite decades of research, recent studies cannot find agreement on what choice strategies lead to probability matching. We propose a solution, showing that two distinct local choice strategies—which make different demands on executive resources—both result in probability-matching behavior on a global level. By placing participants in a simple binary prediction task under dual- versus single-task conditions, we find that individuals with compromised executive resources are driven away from a one-trial-back strategy (utilized by participants with intact executive resources) and towards a strategy that integrates a longer window of past outcomes into the current prediction. Crucially, both groups of participants exhibited probability-matching behavior to the same extent at a global level of analysis. We suggest that these two forms of probability matching are byproducts of the operation of explicit versus implicit systems.     

The illusion of knowledge: When more information reduces accuracy and increases confidence

Intuition suggests that having more information can increase prediction accuracy of uncertain outcomes. In four experiments, we show that more knowledge can decrease accuracy and simultaneously increase prediction confidence. Participants were asked to predict basketball games sampled from a National Basketball Association season. All participants were provided with statistics (win record, halftime score), while half were additionally given the team names. Knowledge of names increased the confidence of basketball fans consistent with their belief that this knowledge improved their predictions. Contrary to this belief, it decreased the participants’ accuracy by reducing their reliance on statistical cues. One of the factors contributing to this underweighting of statistical cues was a bias to bet on more familiar teams against the statistical odds. Finally, in a real betting experiment, fans earned less money if they knew the team names while persisting in their belief that this knowledge improved their predictions.     

The role of causal models in multiple judgments under uncertainty

Two studies examined a novel prediction of the causal Bayes net approach to judgments under uncertainty, namely that causal knowledge affects the interpretation of statistical evidence obtained over multiple observations. Participants estimated the conditional probability of an uncertain event (breast cancer) given information about the base rate, hit rate (probability of a positive mammogram given cancer) and false positive rate (probability of a positive mammogram in the absence of cancer). Conditional probability estimates were made after observing one or two positive mammograms. Participants exhibited a causal stability effect: there was a smaller increase in estimates of the probability of cancer over multiple positive mammograms when a causal explanation of false positives was provided. This was the case when the judgments were made by different participants (Experiment 1) or by the same participants (Experiment 2). These results show that identical patterns of observed events can lead to different estimates of event probability depending on beliefs about the generative causes of the observations.     

The effects of statistical training on choice heuristics in choice under uncertainty

Kahneman and Tversky (1984) proposed that decision makers perceive choice uncertainty in two ways: (1) as a distribution of possible outcomes or (2) as a single uncertain outcome. Using statistical training as a factor that influences these perceptions, and thus the type of decision approach individuals use, we found that individuals with different levels of experience displayed differences in the decisions they made and in the choice heuristics used to make those decisions. Statistically naive individuals were more likely to prefer loss-minimizing alternatives, use a more non-compensatory heuristic, and spend more time on loss-related information than their statistically experienced counterparts. When a distributional cue, indicating the distributional nature of choice outcomes, was presented to both experience groups, the naive group was found to use a decision approach similar to the experienced group and to make similar decisions. The results are discussed in terms of the need to include factors that alter individuals' approaches to uncertainty in future behavioral models of uncertain choice.     

Between a rock and a hard place: Damned if you do, damned if you don’t

Individuals are frequently forced to make decisions from among undesirable choice-sets. Raise taxes or cut social services? Lay off workers or go bankrupt? Go deep in debt or forgo a college education? The research presented here suggests that in such situations, decision-makers are often evaluated negatively regardless of the choice they make. In Experiment 1, participants read about a judge deciding which of two seemingly unfit parents to award sole custody in a real-life divorce case. In Experiment 2, participants were led to believe that their partner in the experiment was forced to pick one of two unpleasant tasks for the participant to perform. In both cases, the decision and decision-maker were evaluated negatively regardless of the alternative chosen–and regardless of the fact that they were the only options in the choice-set. Discussion focuses on the source, scope, and consequences of this phenomenon.     

Developmental changes in children's understanding of future likelihood and uncertainty

Two measures assessed 4-10-year-olds’ and adults’ (N = 201) understanding of future likelihood and uncertainty. In one task, participants sequenced sets of event pictures varying by one physical dimension according to increasing future likelihood. In a separate task, participants rated characters’ thoughts about the likelihood of future events, their emotions, and their decisions in indeterminate social situations. Results showed significant development between ages 4 and 10 in seriating events according to future likelihood and in selecting thought and emotion ratings indicative of future uncertainty. Higher performance on the future likelihood ordering task correlated with greater understanding of future uncertainty in thought, emotion, and decision judgments. Females judged future events to be more uncertain than males.     

The rational side of egocentrism in social comparisons

Prior work has found that when people compare themselves with others they egocentrically focus on their own strengths and achievements more than on the (equally relevant) strengths and achievements of the comparison group. As a consequence, people tend to overestimate their comparative standing when absolute standing is high and underestimate their comparative standing when absolute standing is low. The present research investigated a rational discounting explanation of this bias—namely, that people weight the target of the comparison (the self) more than the referent of the comparison (others) because they typically have more knowledge about the former than the latter. In three studies, we found that the tendency to focus on the target in social comparisons—and the over and underestimation of relative standing that tendency engenders—was reduced (but not eliminated) as people’s knowledge about the comparison group increased. These results suggest that there may be a rational side to egocentrism in social comparisons.     

Social dilemmas as strong versus weak situations: Social value orientations and tacit coordination under resource size uncertainty

This study investigates how environmental uncertainty in resource dilemmas influences the decisions of participants differing in social value orientations. We argue that under resource size certainty people anchor their decisions on tacit coordination rules such as the equal division rule, whereas under resource size uncertainty people rely more on their own social value orientations to determine their choice behavior. The results corroborate our line of reasoning. When the size of the resource was certain, proselfs as well as prosocials anchored their decisions on the equal division rule. Under resource size uncertainty, the equal division rule appeared to lose its coordinating potential, inducing proselfs to harvest more than prosocials.     

Activating a mental simulation mind-set through generation of alternatives: Implications for debiasing in related and unrelated domains

Encouraging people to consider multiple alternatives appears to be a useful debiasing technique for reducing many biases (explanation, hindsight, and overconfidence), if the generation of alternatives is experienced as easy. The present research tests whether these alternative generation procedures induce a mental simulation mind-set (cf. Galinsky & Moskowitz, 2000), such that debiasing in one domain transfers to debias judgments in unrelated domains. The results indeed demonstrated that easy alternative generation tasks not only debiased judgments in the same domain but also generalized to debias judgments in unrelated domains, provided that participants were low in the need for structure. The alternative generation tasks (even when they were easy to perform) showed no evidence of activating a mental simulation mind-set in individuals high in need for structure, as these individuals displayed no transfer effects. Implications of the results for understanding the role of the need for structure, ease of generation, and mental simulation mind-set activation for debiasing are discussed.     

Probability judgment in hierarchical learning: a conflict between predictiveness and coherence

Why are people's judgments incoherent under probability formats? Research in an associative learning paradigm suggests that after structured learning participants give judgments based on predictiveness rather than normative probability. This is because people's learning mechanisms attune to statistical contingencies in the environment, and they use these learned associations as a basis for subsequent probability judgments. We introduced a hierarchical structure into a simulated medical diagnosis task, setting up a conflict between predictiveness and coherence. Thus, a target symptom was more predictive of a subordinate disease than of its superordinate category, even though the latter included the former. Under a probability format participants tended to violate coherence and make ratings in line with predictiveness; under a frequency format they were more normative. These results are difficult to explain within a unitary model of inference, whether associative or frequency-based. In the light of this, and other findings in the judgment and learning literature, a dual-component model is proposed.     

Developmental changes in probabilistic reasoning: The role of cognitive capacity,instructions, thinking styles,and relevant knowledge

In three experiments we explored developmental changes in probabilistic reasoning, taking into account the effects of cognitive capacity, thinking styles, and instructions. Normative responding increased with grade levels and cognitive capacity in all experiments, and it showed a negative relationship with superstitious thinking. The effect of instructions (in Experiments 2 and 3) was moderated by level of education and cognitive capacity. Specifically, only higher-grade students with higher cognitive capacity benefited from instructions to reason on the basis of logic. The implications of these findings for research on the development of probabilistic reasoning are also discussed.     

The generalized matching law in elite sport competition: football play calling as operant choice

A mathematical model of operant choice, the generalized matching law was used to analyze play-calling data from the 2004 National Football League season. In all analyses, the relative ratio of passing to rushing plays was examined as a function of the relative ratio of reinforcement, defined as yards gained, from passing versus rushing. Different analyses focused on season-aggregate data for the league as a whole, game-by-game data for the league as a whole, and game-by-game data for individual teams. In all analyses except those for a few individual teams, the generalized matching law accounted for a majority of variance in play calling. The typical play-calling pattern reflected undermatching (suggesting imperfect sensitivity of play calling to yardage-gained reinforcers) and a bias for calling rushing plays. Bias was found to be a function of both the relative risk of turnovers and the relative variability in yards gained associated with passing versus rushing plays. The external validity of the matching analyses was supported by significant correlations between parameters of the generalized matching law and team success on offense and season winning percentage. These results illustrate the broad applicability of the generalized matching law to problems outside of the laboratory.     

Choice-induced preferences in the absence of choice: Evidence from a blind two choice paradigm with young children and capuchin monkeys

In two studies, we provide a test of the revealed-preferences account of choice-induced preferences. To do so, we introduce a blind two-choice task in which preferences cannot guide choices. Children chose between two similar objects while ignorant of the objects’ identities, and then chose between the rejected alternative and a third similar object. Monkeys were given an illusion of choice between two similar objects, and then chose between the rejected object and a third similar object. Both children and monkeys preferred the third object, indicating that they devalued the rejected object. This response pattern did not occur when the children and monkeys were not given the opportunity to choose between the two initial items. These results provide evidence against a revealed-preferences account of choice-induced preferences and demonstrate that the process of making a choice itself induces preferences.     

Base rates versus sample accuracy: competition for control in human matching to sample

People often place undue weight on specific sources of information (case cues) and insufficient weight on more global sources (base rates) even when the latter are highly predictive, a phenomenon termed base-rate neglect. This phenomenon was first demonstrated with paper-and-pencil tasks, and also occurs in a matching-to-sample procedure in which subjects directly experience case sample (cue) accuracy and base rates, and in which discrete, nonverbal choices are made. In two nonverbal experiments, subjects were exposed to hundreds of trials in which they chose between two response options that were both probabilistically reinforced. In Experiment 1, following one of two possible samples (the unpredictive sample), either response was reinforced with a .5 probability. The other sample (predictive) provided reinforcement for matching on 80% of the trials in one condition but in only 20% of the trials in another condition. Subjects' choices following the unpredictive sample were determined primarily by the contingencies in effect for the predictive sample: If matching was reinforced following the predictive sample, subjects tended to match the unpredictive sample as well; if countermatching the predictive sample was generally reinforced, subjects tended to countermatch the unpredictive sample. These results demonstrate only weak control by base rates. In Experiment 2, base rates and sample accuracy were simultaneously varied in opposite directions to keep one set of conditional probabilities constant. Subjects' choices were determined primarily by the overall accuracy of the sample, again demonstrating only weak control by base rates. The same pattern of choice occurred whether this pattern increased or decreased rate of reinforcement. Together, the results of the two experiments provide a clear empirical demonstration of base-rate neglect.     

Decision by sampling: The role of the decision environment in risky choice

Decision by sampling (DbS) is a theory about how our environment shapes the decisions that we make. Here, I review the application of DbS to risky decision making. According to classical theories of risky decision making, people make stable transformations between outcomes and probabilities and their subjective counterparts using fixed psychoeconomic functions. DbS offers a quite different account. In DbS, the subjective value of an outcome or probability is derived from a series of binary, ordinal comparisons with a sample of other outcomes or probabilities from the decision environment. In this way, the distribution of attribute values in the environment determines the subjective valuations of outcomes and probabilities. I show how DbS interacts with the real-world distributions of gains, losses, and probabilities to produce the classical psychoeconomic functions. I extend DbS to account for preferences in benchmark data sets. Finally, in a challenge to the classical notion of stable subjective valuations, I review evidence that manipulating the distribution of attribute values in the environment changes our subjective valuations just as DbS predicts.     

Probability: A new logico-semantical approach

This approach does not define a probability measure by syntactical structures. It reveals a link between modal logic and mathematical probability theory. This is shown (1) by adding an operator (and two further connectives and constants) to a system of lower predicate calculus and (2) regarding the models of that extended system. These models are models of the modal systemS ₅ (without the Barcan formula), where a usual probability measure is defined on their set of possible worlds. Mathematical probability models can be seen as models ofS ₅.