The Testing Principle: Inductive Reasoning and the Ellsberg Paradox

We postulate the Testing Principle : that individuals ''act like statisticians'' when they face uncertainty in a decision problem, ranking alternatives to the extent that available evidence allows. The Testing Principle implies that completeness of preferences, rather than the sure-thing principle, is violated in the Ellsberg Paradox. In the experiment, subjects chose between risky and uncertain acts in modified Ellsberg-type urn problems, with sample information about the uncertain urn. Our results show, consistent with the Testing Principle, that the uncertain urn is chosen more often when the sample size is larger, holding constant a measure of ambiguity (proportion of balls of unknown colour in the urn). The Testing Principle rationalises the Ellsberg Paradox. Behaviour consistent with the principle leads to a reduction in Ellsberg-type violations as the statistical quality of sample information is improved, holding ambiguity constant. The Testing Principle also provides a normative rationale for the Ellsberg paradox that is consistent with procedural rationality.     

模糊决策的情境依赖性

实验1采用艾尔斯伯格悖论的研究范式,探究被试对模糊的厌恶倾向以及在决策过程中所采用的决策策略。结果发现：被试对确定选项和模糊选项的选择存在差异;在肯定形式下倾向于确定选项,而在否定形式下则倾向于模糊选项,采用了利益最大化策略。实验2采用艾尔斯伯格悖论的变式,通过操纵概率和任务类型,发现：模糊决策具有情境依赖性,并非任何情况下个体都厌恶模糊。当风险选项不能满足自己的需要,即获胜机率比较小时,人们会偏向模糊选项。     

Bayesian techniques for analyzing group differences in the Iowa Gambling Task: A case study of intuitive and deliberate decision-makers

The Iowa Gambling Task (IGT) is one of the most popular experimental paradigms for comparing complex decision-making across groups. Most commonly, IGT behavior is analyzed using frequentist tests to compare performance across groups, and to compare inferred parameters of cognitive models developed for the IGT. Here, we present a Bayesian alternative based on Bayesian repeated-measures ANOVA for comparing performance, and a suite of three complementary model-based methods for assessing the cognitive processes underlying IGT performance. The three model-based methods involve Bayesian hierarchical parameter estimation, Bayes factor model comparison, and Bayesian latent-mixture modeling. We illustrate these Bayesian methods by applying them to test the extent to which differences in intuitive versus deliberate decision style are associated with differences in IGT performance. The results show that intuitive and deliberate decision-makers behave similarly on the IGT, and the modeling analyses consistently suggest that both groups of decision-makers rely on similar cognitive processes. Our results challenge the notion that individual differences in intuitive and deliberate decision styles have a broad impact on decision-making. They also highlight the advantages of Bayesian methods, especially their ability to quantify evidence in favor of the null hypothesis, and that they allow model-based analyses to incorporate hierarchical and latent-mixture structures.     

Probabilistic models in human sensorimotor control

Sensory and motor uncertainty form a fundamental constraint on human sensorimotor control. Bayesian decision theory (BDT) has emerged as a unifying framework to understand how the central nervous system performs optimal estimation and control in the face of such uncertainty. BDT has two components: Bayesian statistics and decision theory. Here we review Bayesian statistics and show how it applies to estimating the state of the world and our own body. Recent results suggest that when learning novel tasks we are able to learn the statistical properties of both the world and our own sensory apparatus so as to perform estimation using Bayesian statistics. We review studies which suggest that humans can combine multiple sources of information to form maximum likelihood estimates, can incorporate prior beliefs about possible states of the world so as to generate maximum a posteriori estimates and can use Kalman filter-based processes to estimate time-varying states. Finally, we review Bayesian decision theory in motor control and how the central nervous system processes errors to determine loss functions and select optimal actions. We review results that suggest we plan movements based on statistics of our actions that result from signal-dependent noise on our motor outputs. Taken together these studies provide a statistical framework for how the motor system performs in the presence of uncertainty.     

不同模糊程度下模糊决策的决策偏好

该研究采用艾尔斯伯格悖论的变式,选取二择一的迫选任务,旨在探讨不同球数和不同模糊程度下模糊决策的决策偏好。结果发现,球数的不同对决策的偏好基本上没有影响;而模糊程度的不同,对决策的偏好有影响。具体表现为：模糊程度较高时,被试倾向于模糊厌恶,模糊程度较低时倾向于模糊寻求。     

The psychophysics of uneconomical choice: non-linear reward evaluation by a nectar feeder

Uneconomical choices by humans or animals that evaluate reward options challenge the expectation that decision-makers always maximize the return currency. One possible explanation for such deviations from optimality is that the ability to sense differences in physical value between available alternatives is constrained by the sensory and cognitive processes for encoding profitability. In this study, we investigated the capacity of a nectarivorous bat species (Glossophaga commissarisi) to discriminate between sugar solutions with different concentrations. We conducted a two-alternative free-choice experiment on a population of wild electronically tagged bats foraging at an array of computer-automated artificial flowers that recorded individual choices. We used a Bayesian approach to fit individual psychometric functions, relating the strength of preferring the higher concentration option to the intensity of the presented stimulus. Psychometric analysis revealed that discrimination ability increases non-linearly with respect to intensity. We combined this result with a previous psychometric analysis of volume perception. Our theoretical analysis of choice for rewards that vary in two quality dimensions revealed regions of parameter combinations where uneconomic choice is expected. Discrimination ability may be constrained by non-linear perceptual and cognitive encoding processes that result in uneconomical choice.     

Navigating through abstract decision spaces: Evaluating the role of state generalization in a dynamic decision-making task

Research on dynamic decision-making tasks, in which the payoffs associated with each choice vary with participants’ recent choice history, shows that humans have difficulty making long-term optimal choices in the presence of attractive immediate rewards. However, a number of recent studies have shown that simple cues providing information about the underlying state of the task environment may facilitate optimal responding. In this study, we examined the mechanism by which this state knowledge influences choice behavior. We examined the possibility that participants use state information in conjunction with changing payoffs to extrapolate payoffs in future states. We found support for this hypothesis in an experiment in which generalizations based on this state information worked to the benefit or detriment of task performance, depending on the task’s payoff structure.     

Relating individual differences in Attitude toward Ambiguity to risky choices

Subjects (76 adult Italians of varying ages) completed a two‐part procedure. One part used an Ellsberg‐type task which allowed for both aggregate and individual level analysis of Attitude toward Ambiguity. The other part used an expanded risky choice task to assess the same subjects' Attitude toward Risk. While there was an overall tendency for subjects to be slightly ambiguity‐averse, there was a positive correlation between Attitude toward Ambiguity and Attitude toward Risk. This relation was particularly strong when the risky choice was to avoid a loss rather than to achieve a gain. Copyright © 2001 John Wiley & Sons, Ltd.     

The dynamics of bidirectional thought

High-level judgement and decision-making tasks display dynamic bidirectional relationships in which salient cues determine how responses are evaluated by decision-makers, and these responses in turn determine the cues that are considered. In this paper, we propose Kosko's bidirectional associative memory (BAM) network, a minimal two-layer recurrent neural network, as a mathematically tractable toy model with which the properties of existing bidirectional models, and the behavioural implications of these properties, can be studied. We first derive results regarding the dynamics of the BAM network, and then show how these results can be used to provide an analytically sound explanation for a number of important findings, including coherence shifts in judgement and choice, anchoring effects, and reference point effects.     

Historical Analogies and the Cognitive Dimension of Domestic Policymaking

Established models of the domestic policymaking process accord some role to the individual decision-maker, but they usually fail to show how policy decisions are ultimately influenced by the character of the information available to the policymakers concerned. Drawing on one prominent model of decision-making developed by analysts of foreign policy—the analogical reasoning approach—this article proposes that individual-level approaches are most useful in domestic policy analysis where decision-makers must confront a discrete policy "episode" in which perceived levels of cognitive uncertainty and ambiguity are high. An analysis of decision-making by political leaders during the 1967 Detroit riots reveals that these leaders made widespread use of historical analogies at various stages of the policymaking process. Policymakers can probably be expected to rely on analogizing under circumstances and contexts that make cognitive demands similar to those observed in the Detroit case.     

Generalizability of evidence-based assessment recommendations for pediatric bipolar disorder

Bipolar disorder is frequently clinically diagnosed in youths who do not actually satisfy Diagnostic and Statistical Manual of Mental Disorders (4th ed., text revision; DSM-IV-TR; American Psychiatric Association, 1994) criteria, yet cases that would satisfy full DSM-IV-TR criteria are often undetected clinically. Evidence-based assessment methods that incorporate Bayesian reasoning have demonstrated improved diagnostic accuracy and consistency; however, their clinical utility is largely unexplored. The present study examines the effectiveness of promising evidence-based decision-making strategies compared with the clinical gold standard. Participants were 562 youths, ages 5 to 17 and predominantly African American, drawn from a community mental health clinic. Research diagnoses combined a semistructured interview with youths' psychiatric, developmental, and family mental health histories. Independent Bayesian estimates that relied on published risk estimates from other samples discriminated bipolar diagnoses (area under curve = .75, p < .00005). The Bayes and confidence ratings correlated at rs = .30. Agreement about an evidence-based assessment intervention threshold model (wait/assess/treat) was κ = .24, p < .05. No potential moderators of agreement between the Bayesian estimates and confidence ratings, including type of bipolar illness, were significant. Bayesian risk estimates were highly correlated with logistic regression estimates using optimal sample weights (r = .81, p < .0005). Clinical and Bayesian approaches agree in terms of overall concordance and deciding next clinical action, even when Bayesian predictions are based on published estimates from clinically and demographically different samples. Evidence-based assessment methods may be useful in settings in which gold standard assessments cannot be routinely used, and they may help decrease rates of overdiagnosis while promoting earlier identification of true cases.     

A Bayesian analysis of human decision-making on bandit problems

The bandit problem is a dynamic decision-making task that is simply described, well-suited to controlled laboratory study, and representative of a broad class of real-world problems. In bandit problems, people must choose between a set of alternatives, each with different unknown reward rates, to maximize the total reward they receive over a fixed number of trials. A key feature of the task is that it challenges people to balance the exploration of unfamiliar choices with the exploitation of familiar ones. We use a Bayesian model of optimal decision-making on the task, in which how people balance exploration with exploitation depends on their assumptions about the distribution of reward rates. We also use Bayesian model selection measures that assess how well people adhere to an optimal decision process, compared to simpler heuristic decision strategies. Using these models, we make inferences about the decision-making of 451 participants who completed a set of bandit problems, and relate various measures of their performance to other psychological variables, including psychometric assessments of cognitive abilities and personality traits. We find clear evidence of individual differences in the way the participants made decisions on the bandit problems, and some interesting correlations with measures of general intelligence.     

A computational-level explanation of the speed of goal inference

The ability to understand the goals that drive another person’s actions is an important social and cognitive skill. This is no trivial task, because any given action may in principle be explained by different possible goals (e.g., one may wave ones arm to hail a cab or to swat a mosquito). To select which goal best explains an observed action is a form of abduction. To explain how people perform such abductive inferences, Baker, Tenenbaum, and Saxe (2007) proposed a computational-level theory that formalizes goal inference as Bayesian inverse planning (BIP). It is known that general Bayesian inference–be it exact or approximate–is computationally intractable (NP-hard). As the time required for computationally intractable computations grows excessively fast when scaled from toy domains to the real world, it seems that such models cannot explain how humans can perform Bayesian inferences quickly in real world situations. In this paper we investigate how the BIP model can nevertheless explain how people are able to make goal inferences quickly. The approach that we propose builds on taking situational constraints explicitly into account in the computational-level model. We present a methodology for identifying situational constraints that render the model tractable. We discuss the implications of our findings and reflect on how the methodology can be applied to alternative models of goal inference and Bayesian models in general.     

Do the right thing: The assumption of optimality in lay decision theory and causal judgment

Human decision-making is often characterized as irrational and suboptimal. Here we ask whether people nonetheless assume optimal choices from other decision-makers: Are people intuitive classical economists? In seven experiments, we show that an agent’s perceived optimality in choice affects attributions of responsibility and causation for the outcomes of their actions. We use this paradigm to examine several issues in lay decision theory, including how responsibility judgments depend on the efficacy of the agent’s actual and counterfactual choices (Experiments 1–3), individual differences in responsibility assignment strategies (Experiment 4), and how people conceptualize decisions involving trade-offs among multiple goals (Experiments 5–6). We also find similar results using everyday decision problems (Experiment 7). Taken together, these experiments show that attributions of responsibility depend not only on what decision-makers do, but also on the quality of the options they choose not to take.     

Ambiguity aversion: the explanatory power of indeterminate probabilities

Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem in terms of a psychological effect: ambiguity aversion. The ‘comparative ignorance’ hypothesis articulates how this effect works and explains why it is important to an understanding of the typical pattern of responses associated with Ellsberg’s two-color problem. In the first part of this article we challenge Fox and Tversky’s explanation. We present first an experiment that extends Ellsberg’s two-color problem where certain predictions of the comparative ignorance hypothesis are not confirmed. In addition the hypothesis seems unable to explain how the subjects resolve trade-offs between security and expected pay-off when vagueness is present. Ellsberg offered an explanation of the typical behavior elicited by his examples in terms of these trade-offs and in section three we offer a model of Ellsberg’s trade-offs. The model takes seriously the role of imprecise probabilities in explaining Ellsberg’s phenomenon. The so-called three-color problem was also considered in Fox and Tversky (1995). We argue that Fox and Tversky’s analysis of this case breaks a symmetry with their analysis of the two-color problem. We propose a unified treatment of both problems and we present a experiment that confirms our hypothesis.     

Distinguishing indeterminate belief from “risk-averse” preferences

I focus my discussion on the well-known Ellsberg paradox. I find good normative reasons for incorporating non-precise belief, as represented by sets of probabilities, in an Ellsberg decision model. This amounts to forgoing the completeness axiom of expected utility theory. Provided that probability sets are interpreted as genuinely indeterminate belief (as opposed to “imprecise” belief), such a model can moreover make the “Ellsberg choices” rationally permissible. Without some further element to the story, however, the model does not explain how an agent may come to have unique preferences for each of the Ellsberg options. Levi (1986, Hard choices: Decision making under unresolved conflict. Cambridge, New York: Cambridge University Press) holds that the extra element amounts to innocuous secondary “risk” or security considerations that are used to break ties when more than one option is rationally permissible. While I think a lexical choice rule of this kind is very plausible, I argue that it involves a greater break with xpected utility theory than mere violation of the ordering axiom.