Predicting Outcomes in a Sequence of Binary Events: Belief Updating and Gambler's Fallacy Reasoning.

Beliefs like the Gambler's Fallacy and the Hot Hand have interested cognitive scientists, economists, and philosophers for centuries. We propose that these judgment patterns arise from the observer's mental models of the sequence-generating mechanism, moderated by the strength of belief in an a priori base rate. In six behavioral experiments, participants observed one of three mechanisms generating sequences of eight binary events: a random mechanical device, an intentional goal-directed actor, and a financial market. We systematically manipulated participants' beliefs about the base rate probabilities at which different outcomes were generated by each mechanism. Participants judged 18 sequences of outcomes produced by a mechanism with either an unknown base rate, a specified distribution of three equiprobable base rates, or a precise, fixed base rate. Six target sequences ended in streaks of between two and seven identical outcomes. The most common predictions for subsequent events were best described as pragmatic belief updating, expressed as an increasingly strong expectation that a streak of identical signals would repeat as the length of that streak increased. The exception to this pattern was for sequences generated by a random mechanical device with a fixed base rate of .50. Under this specific condition, participants exhibited a bias toward reversal of streaks, and this bias was larger when participants were asked to make a dichotomous choice versus a numerical probability rating. We review alternate accounts for the anomalous judgments of sequences and conclude with our favored interpretation that is based on Rabin's version of Tversky & Kahneman's Law of Small Numbers.

Do people reason rationally about causally related events? Markov violations, weak inferences, and failures of explaining away.

Making judgments by relying on beliefs about the causal relationships between events is a fundamental capacity of everyday cognition. In the last decade, Causal Bayesian Networks have been proposed as a framework for modeling causal reasoning. Two experiments were conducted to provide comprehensive data sets with which to evaluate a variety of different types of judgments in comparison to the standard Bayesian networks calculations. Participants were introduced to a fictional system of three events and observed a set of learning trials that instantiated the multivariate distribution relating the three variables. We tested inferences on chains X1→Y→X2, common cause structures X1←Y→X2, and common effect structures X1→Y←X2, on binary and numerical variables, and with high and intermediate causal strengths. We tested transitive inferences, inferences when one variable is irrelevant because it is blocked by an intervening variable (Markov Assumption), inferences from two variables to a middle variable, and inferences about the presence of one cause when the alternative cause was known to have occurred (the normative "explaining away" pattern). Compared to the normative account, in general, when the judgments should change, they change in the normative direction. However, we also discuss a few persistent violations of the standard normative model. In addition, we evaluate the relative success of 12 theoretical explanations for these deviations.

Reasoning about causal relationships: Inferences on causal networks.

Over the last decade, a normative framework for making causal inferences, Bayesian Probabilistic Causal Networks, has come to dominate psychological studies of inference based on causal relationships. The following causal networks-[X→Y→Z, X←Y→Z, X→Y←Z]-supply answers for questions like, "Suppose both X and Y occur, what is the probability Z occurs?" or "Suppose you intervene and make Y occur, what is the probability Z occurs?" In this review, we provide a tutorial for how normatively to calculate these inferences. Then, we systematically detail the results of behavioral studies comparing human qualitative and quantitative judgments to the normative calculations for many network structures and for several types of inferences on those networks. Overall, when the normative calculations imply that an inference should increase, judgments usually go up; when calculations imply a decrease, judgments usually go down. However, 2 systematic deviations appear. First, people's inferences violate the Markov assumption. For example, when inferring Z from the structure X→Y→Z, people think that X is relevant even when Y completely mediates the relationship between X and Z. Second, even when people's inferences are directionally consistent with the normative calculations, they are often not as sensitive to the parameters and the structure of the network as they should be. We conclude with a discussion of productive directions for future research.

The influence of perceived causation on judgments of time: an integrative review and implications for decision-making.

RECENT RESEARCH HAS SHOWN THAT THE PERCEPTION OF CAUSALITY AFFECTS THE JUDGMENT OF ELAPSED TIME: an interval between an action and a subsequent event seems to be shorter when people believe that action has caused the event. This article reviews past work on the phenomenon and integrates the findings from the different settings in which it has been observed. The effect is found for actions people have personally taken, as well as for those they have simply read or heard about. It occurs for very short intervals (e.g., milliseconds) as well as longer periods (e.g., months or years). Beliefs and expectations about different types of causal forces and their trajectories over time can affect the degree of time compression in some settings. But the tendency toward compression of time is the default and dominant response: It persists when people think of generic causal relations and is enhanced when people opt for the quickest interpretation of causal relations. This robust influence of causality on time judgment appears to be linked to the basic tendency to rely on temporal proximity in processing causal relations and to people's early experience with the physical-mechanical world. Past work has focused primarily on the implications of time compression for the sense of agency, but this phenomenon has implications also for decisions that depend on time judgment. The compression of subjective time elapsed between actions and outcomes makes people more optimistically plan the timing of a focal action in the future, experience its effect earlier in the future, and be less likely to switch to an alternative course of action. The tendency toward compression can thus endow an action with a sort of privileged status or advantage.

Democracy under uncertainty: the wisdom of crowds and the free-rider problem in group decision making.

We introduce a game theory model of individual decisions to cooperate by contributing personal resources to group decisions versus by free riding on the contributions of other members. In contrast to most public-goods games that assume group returns are linear in individual contributions, the present model assumes decreasing marginal group production as a function of aggregate individual contributions. This diminishing marginal returns assumption is more realistic and generates starkly different predictions compared to the linear model. One important implication is that, under most conditions, there exist equilibria where some, but not all, members of a group contribute, even with completely self-interested motives. An agent-based simulation confirmed the individual and group advantages of the equilibria in which behavioral asymmetry emerges from a game structure that is a priori perfectly symmetric for all agents (all agents have the same payoff function and action space but take different actions in equilibria). A behavioral experiment demonstrated that cooperators and free riders coexist in a stable manner in groups performing with the nonlinear production function. A collateral result demonstrated that, compared to a dictatorial decision scheme guided by the best member in a group, the majority/plurality decision rules can pool information effectively and produce greater individual net welfare at equilibrium, even if free riding is not sanctioned. This is an original proof that cooperation in ad hoc decision-making groups can be understood in terms of self-interested motivations and that, despite the free-rider problem, majority/plurality decision rules can function robustly as simple, efficient social decision heuristics.

Naïve theories of causal force and compression of elapsed time judgments.

Recent research has shown that when people perceive a causal relation between 2 events, they "compress" the intervening elapsed time. The present work shows that a naïve mechanical-physical conception of causality, in which causal forces are believed to dissipate over time, underlies the estimates of shorter elapsed time. Being primed with alternative, nondissipative causal mechanisms and having the cognitive capacity to consider such mechanisms moderates the compression effect. The studies rule out similarity, mnemonic association, and anchoring as alternative accounts for the effect. Taken together, the findings support the hypothesis that causal cognition plays a major role in judgments of elapsed time. The implications of the compression effect on the timing of future actions, persistence, and causal learning are discussed.

Order in choice: effects of serial position on preferences.

When several choice options are sampled one at a time in a sequence and a single choice of the best option is made at the end of the sequence, which location in the sequence is chosen most often? We report a large-scale experiment that assessed tasting preferences in choice sets of two, three, four, or five wines. We found a large primacy effect-the first wine had a large advantage in the end-of-sequence choice. We also found that participants who were knowledgeable about wines showed a recency effect in the longer sequences. We conclude with a process model that explains our findings.

What's next? Judging sequences of binary events.

The authors review research on judgments of random and nonrandom sequences involving binary events with a focus on studies documenting gambler's fallacy and hot hand beliefs. The domains of judgment include random devices, births, lotteries, sports performances, stock prices, and others. After discussing existing theories of sequence judgments, the authors conclude that in many everyday settings people have naive complex models of the mechanisms they believe generate observed events, and they rely on these models for explanations, predictions, and other inferences about event sequences. The authors next introduce an explanation-based, mental models framework for describing people's beliefs about binary sequences, based on 4 perceived characteristics of the sequence generator: randomness, intentionality, control, and goal complexity. Furthermore, they propose a Markov process framework as a useful theoretical notation for the description of mental models and for the analysis of actual event sequences.

Hedonomics: Bridging Decision Research With Happiness Research.

One way to increase happiness is to increase the objective levels of external outcomes; another is to improve the presentation and choices among external outcomes without increasing their objective levels. Economists focus on the first method. We advocate the second, which we call hedonomics. Hedonomics studies (a) relationships between presentations (how a given set of out-comes are arranged among themselves or relative to other outcomes) and happiness and (b) relationships between choice (which option among alternative options one chooses) and happiness.

We want the same thing: projection in judgments of sexual intent.

This article details two studies investigating the proximal role of social projection (i.e., assumed similarity) in judgments of sexual intent. Study 1 demonstrates that men and women who have a greater desire for casual sex are more likely to perceive sexual intent in others. Study 2 replicates this finding in a more realistic context and, further, situates judgments of sexual intent squarely into the cognitive domain, as results show that projection of casual sexual motivation is more likely when the target is similar to the perceiver and when the target's motivation is relatively ambiguous to begin with.

Calibration trumps confidence as a basis for witness credibility.

Confident witnesses are deemed more credible than unconfident ones, and accurate witnesses are deemed more credible than inaccurate ones. But are those effects independent? Two experiments show that errors in testimony damage the overall credibility of witnesses who were confident about the erroneous testimony more than that of witnesses who were not confident about it. Furthermore, after making an error, less confident witnesses may appear more credible than more confident ones. Our interpretation of these results is that people make inferences about source calibration when evaluating testimony and other social communication.

Decision and experience: why don't we choose what makes us happy?

Recent years have witnessed a growing interest among psychologists and other social scientists in subjective well-being and happiness. Here we review selected contributions to this development from the literature on behavioral-decision theory. In particular, we examine many, somewhat surprising, findings that show people systematically fail to predict or choose what maximizes their happiness, and we look at reasons why they fail to do so. These findings challenge a fundamental assumption that underlies popular support for consumer sovereignty and other forms of autonomy in decision-making (e.g. marriage choice), namely, the assumption that people are able to make choices in their own best interests.

Perceived causality as a cue to temporal distance.

The three experiments reported show that judgments of elapsed time between events depend on perceived causal relations between the events. Participants judged pairs of causally related events to occur closer together in time than pairs of causally unrelated events that were separated by the same actual time interval. The causality-time relationship was first demonstrated for time judgments about historical events. Causally related events were judged to be significantly closer together in time than causally unrelated events. In two subsequent experiments, perceived causality was manipulated by providing expert information and by asking the participants themselves to imagine causal relationships between the to-be-judged events. Again, substantial and reliable effects of perceived causality were obtained. Our results suggest that people use strength of perceived causality as a cue to infer temporal distance.

The robust beauty of majority rules in group decisions.

How should groups make decisions? The authors provide an original evaluation of 9 group decision rules based on their adaptive success in a simulated test bed environment. When the adaptive success standard is applied, the majority and plurality rules fare quite well, performing at levels comparable to much more resource-demanding rules such as an individual judgment averaging rule. The plurality rule matches the computationally demanding Condorcet majority winner that is standard in evaluations of preferential choice. The authors also test the results from their theoretical analysis in a behavioral study of nominal human group decisions, and the essential findings are confirmed empirically. The conclusions of the present analysis support the popularity of majority and plurality rules in truth-seeking group decisions.

Category coherence and category-based property induction.

One important property of human object categories is that they define the sets of exemplars to which newly observed properties are generalized. We manipulated the causal knowledge associated with novel categories and assessed the resulting strength of property inductions. We found that the theoretical coherence afforded to a category by inter-feature causal relationships strengthened inductive projections. However, this effect depended on the degree to which the exemplar with the to-be-projected predicate manifested or satisfied its category's causal laws. That is, the coherence that supports inductive generalizations is a property of individual category members rather than categories. Moreover, we found that an exemplar's coherence was mediated by its degree of category membership. These results were obtained across a variety of causal network topologies and kinds of categories, including biological kinds, non-living natural kinds, and artifacts.

Phineas gauged: decision-making and the human prefrontal cortex.

Poor social judgment and decision-making abilities have often been attributed to people who have suffered injury to the ventromedial prefrontal cortex (VMPFC). However, few laboratory tests of decision-making have been conducted on these patients. The exception to this is the Iowa Gambling Task which has often, but not always, demonstrated differential performance between patients and controls. Results from patients with prefrontal cortex lesions on a novel test of decision-making are presented. Participants explored and chose from pairs of gambles that differed in their underlying distributions, primarily in the variance of their respective outcomes. In accordance with many findings from the behavioral decision-making literature, both young normal participants and older patient controls demonstrated a marked avoidance of risk and selected largely from secure, low variance gambles. In contrast, patients with ventromedial lesions were divided into two clear sub-groups. One group behaved similarly to normals, showing a risk-averse strategy. The other group displayed a distinctive risk-seeking behavior pattern, choosing predominantly from the high-variance, high-risk decks. This research demonstrates some of the advantages of using methods and theories from traditional decision-making research to study the behavior of patients, as well as the benefits of examining individual participants, and provides new insights into the nature of the decision-making deficit in patients with ventromedial prefrontal cortex lesions.

The logic of social sharing: an evolutionary game analysis of adaptive norm development.

Although norms can potentially serve useful constructs to understand human minds, being fundamentally social in evolutionary as well as cultural senses, there are as yet no useful psychological theories of adaptive norm development. This article provides an illustrative model about how a norm emerges in a society. We focus on the "communal-sharing norm" in primordial societies, a norm designating uncertain resources as common properties to be shared with other members. Based on anthropological findings, we develop a theory about how the communal-sharing norm emerges and is maintained. Then, using evolutionary computer simulations, we test several hypotheses about the conditions under which the norm will dominate social resource sharing. We further test behavioral implications of the norm, demonstrating that uncertainty involved in resource acquisition is a key factor that triggers the psychology of sharing even in highly industrialized societies. Finally, we discuss the importance of norm construct for analyzing the dynamic relation between minds and society.

The reliability of the DRM paradigm as a measure of individual differences in false memories.

Despite considerable research on the Deese-Roediger-McDermott (DRM) false memory paradigm, little attention has been paid to the reliability of the paradigm as a measure of individual differences. In the present research, we examined the reliability of the DRM paradigm in a 2-week test-retest design. This analysis showed that the false memories produced in the paradigm were quite stable across the 2-week period and that this stability had both global (cross-list) and list-specific components. In contrast, correct memories showed only global stability across the testing period.

Interevent relationships and judgment under uncertainty: structure determines strategy.

A fundamental empirical question regarding judgments about events is whether experienced absolute frequencies or relative frequencies are relied on when the likelihood of a particular occurrence is judged. The present research explicates the conditions under which people rely on remembered raw absolute frequencies versus on inferred relative frequencies or proportions when making predictions. Participants saw opinion poll results for candidates prior to an election and, on the basis of these, made judgments concerning the likelihood of each candidate's winning this election. Certain candidates demonstrated a high absolute frequency of winning in the polls, whereas other candidates had high relative win frequencies. The results indicated that adults are cognitively flexible with regard to the inputs used in this judgment. Certain stimulus event configurations induced reasoning by way of absolute frequencies, whereas other configurations elicited judgments based on relative frequencies. More specifically, as the relational complexity of the event structure increased and more inferences were required to make predictions, the tendency to rely on absolute, as opposed to relative, frequencies also increased.

Content Effects on Decision Making.

How does the domain or subject matter of a decision problem affect the outcome of the decision? Although decision-making research typically dismisses content as merely a cover story, the present research shows that it plays a fundamental role in the decision process by influencing the information processing that underlies it. An experiment is reported in which the same basic decision problem was presented in several content domains (legal traffic tickets, academic course grades, stock investments, and casino gambling). The changes in content led to changes in both strategies and mental representations, which in turn led to changes in decision outcomes, even though measures of the subjective utilities of the options remained unchanged. Copyright 2001 Academic Press.