Probability of reciprocation in repeated prisoner's dilemma games

Both social cooperation and self‐control require reciprocation. In social cooperation situations a single person's cooperative act, if not reciprocated by others, would be unreinforced both immediately and in the long term. Similarly, a single act of self‐control (refusing a single cigarette, for example), if not followed up by other such acts, would also be unreinforced immediately and in the long term. The present experiments varied probability of reciprocation in a prisoner's dilemma‐like game that could resemble a social cooperation or a self‐control situation. Participants earned points by playing against a computer. The computer offered the participant a choice between 5 or 6 points (‘cooperation’ by the computer) or between 1 or 2 points (‘defection’ by the computer). The participant's choice of the lesser alternative (‘cooperation’) or the greater alternative (‘defection’) on the current trial led, respectively, to cooperation or defection by the computer on the next trial with a probability (probability of reciprocation, PR) which could vary. When PR was greater than 63%, consistent cooperation maximized the participant's earnings. When PR was less than 63%, defection maximized earnings. Three conditions were studied: PR signaled by spinners; PR unsignaled; PR unsignaled with participants believing that they were playing with another person, not the computer. With PR = 100% (‘tit‐for‐tat’) and PR = 50%, the modal participant maximized earnings under all three conditions. With PR = 75%, participants maximized earnings only when PR was signaled. These results indicate that differences between people's tendency to cooperate with other people (social cooperation) and their tendency to cooperate with their own future interests (self‐control) may lie in differences in subjective PR. Copyright © 2001 John Wiley & Sons, Ltd.     

The ‘conjunction fallacy’ revisited: how intelligent inferences look like reasoning errors

Findings in recent research on the ‘conjunction fallacy’ have been taken as evidence that our minds are not designed to work by the rules of probability. This conclusion springs from the idea that norms should be content‐blind—in the present case, the assumption that sound reasoning requires following the conjunction rule of probability theory. But content‐blind norms overlook some of the intelligent ways in which humans deal with uncertainty, for instance, when drawing semantic and pragmatic inferences. In a series of studies, we first show that people infer nonmathematical meanings of the polysemous term ‘probability’ in the classic Linda conjunction problem. We then demonstrate that one can design contexts in which people infer mathematical meanings of the term and are therefore more likely to conform to the conjunction rule. Finally, we report evidence that the term ‘frequency’ narrows the spectrum of possible interpretations of ‘probability’ down to its mathematical meanings, and that this fact—rather than the presence or absence of ‘extensional cues’—accounts for the low proportion of violations of the conjunction rule when people are asked for frequency judgments. We conclude that a failure to recognize the human capacity for semantic and pragmatic inference can lead rational responses to be misclassified as fallacies. Copyright © 1999 John Wiley & Sons, Ltd.     

Patterns of Preference for Numerical and Verbal Probabilities

We report results of an experiment designed to test a principle formulated by Budescu and Wallsten (1995), that, when communicating uncertainty information, mode choices are sensitive to sources and degrees of vagueness. In addition, we examined subjects’ efficacy in using such uncertainty information as a function of communication mode, source, and vagueness. In phase one of the experiment, subjects in a dyad used precise (numerical) or imprecise (verbal) expressions to communicate to a remote partner precise or vague uncertainty about the likelihoods of events. Spinner outcomes were used to generate precise uncertainty while answers to almanac questions were used to elicit vague uncertainty. In phase two, subjects saw the events paired with their partners’ estimates of similar events, and were asked to gamble on one event from each pair. Communication mode preferences were measured as the relative frequency that subjects chose the numerical mode to either express or receive uncertainty information regarding the events. Efficacy was measured as the relative frequency that subjects choose from the pair the event associated with the objectively more probable uncertainty expression. Underlying uncertainty interacted with direction of communication to affect preferences for modes of expression of the probabilities. Subjects preferred precise (numerical) information, especially for precise events (spinners). For vague events (questions), their preference for precise (numerical) information was stronger when receiving than when communicating information. Similar preferences were reflected in the efficiency of subsequent gamble decisions based on the probability estimates. Specifically, decisions were more efficacious (i.e. consistent with Expected Utility) when degrees of precision in events and estimates matched. © 1997 by John Wiley & Sons, Ltd.     

THE epistemologies of parsimony: A review of Ockham's razors: A user's manual by Elliott Sober

Sober analyzes two paradigms of parsimony that have been used successfully in science. These are associated with two interpretations of probability: Bayesian and frequentist. Sober applies these paradigms to problems in biology, psychology, and philosophy. In the chapter on psychology, he argues that objective data consisting of environmental input and two or more concurrent responses could be used to refute empirically the radical behaviorist thesis that probability of learned responses can be accounted for solely on the basis of environmental variables. Sober believes that such data are readily available and offers a thought experiment to illustrate his point. Behavior analysts, however, would want actual experimental data, undoubtedly with animals, before accepting any such refutation. Nonetheless, Sober's philosophical point about the type of experiment that would be capable of refuting this thesis is valid. The behavior analytic program, however, does not depend upon the truth of this thesis.     

Do Politicians Take Risks Like the Rest of Us? An Experimental Test of Prospect Theory Under MPs

Political psychologists have been quick to use prospect theory in their work, realizing its potential for explaining decisions under risk. Applying prospect theory to political decision‐making is not without problems, though, and here we address two of these: (1) Does prospect theory actually apply to political decision‐makers, or are politicians unlike the rest of us? (2) Which dimension do politicians use as their reference point when there are multiple dimensions (e.g., votes and policy)? We address both problems in an experiment with a unique sample of Dutch members of parliament as participants. We use well‐known (incentivized) decision situations and newly developed hypothetical political decision‐making scenarios. Our results indicate that politicians’ deviate from expected utility theory in the direction predicted by prospect theory but that these deviations are somewhat smaller than those of other people. Votes appear to be a more important determinant of politicians’ reference point than is policy.     

The Generalized Quantum Episodic Memory Model

Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over‐distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over‐distribution effect and subadditivity have been widely observed in item and source‐memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal‐detection theory. A dual‐trace model called the over‐distribution (OD) model (Brainerd & Reyna, 2008) can explain the episodic over‐distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory (GQEM) model, which extends the Quantum Episodic Memory (QEM) model developed by Brainerd, Wang, and Reyna (2013). We test GQEM by comparing it to the OD model using data from a novel item‐memory experiment and a previously published source‐memory experiment (Kellen, Singmann, & Klauer, 2014) examining the over‐distribution effect. Using the best‐fit parameters from the over‐distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory.     

Implications of an initial empirical victory for the truth of the theory and additional empirical victories

Psychologists take two propositions for granted. Specifically, empirical verification of predictions derived from a theory (a) support that the theory is more likely to be true and (b) support that additional predictions derived from the theory have an increased probability of being sustained if subjected to empirical testing. In contrast, I argue that both propositions depend strongly on whether auxiliary assumptions are taken into account. When auxiliary assumptions are not taken into account, the first proposition is valid but the second is not. When auxiliary assumptions are taken into account, the first proposition is not valid, and the second proposition encounters additional problems. I use Venn diagrams and Bayesian principles to demonstrate these conclusions.     

迪昂问题及其解决

迪昂问题是当代科学哲学争论的主题之一。波普尔、拉卡托斯和库恩都曾经对此问题给予不同的对待或解决。本文对此背景给以扼要的介绍,然后着重介绍和评价一种新的解决方案——基于贝叶斯方法的解决。相比之下,后一方案较为令人满意。     

有关条件推理中概率效应的实验研究

通过预备实验选取了四种不同条件概率的条件规则和四种不同前后件概率组合的条件规则作为实验材料,以大学生为被试,考察了两种概率因素(条件概率和前后件概率)对条件推理的演绎形式(MP、DA、AC、MT)以及变通形式(四卡问题)的影响。结果表明,两种概率因素对四种条件推理的影响都非常显著,研究进一步证实了人们对四种推理的认可程度主要与范畴前提的概率成正比的结论;但概率因素对四卡问题的解决影响不明显。     

Conditioning against the Grain

This paper discusses counterexamples to the thesis that the probabilities of conditionals are conditional probabilities. It is argued that the discrepancy is systematic and predictable, and that conditional probabilities are crucially involved in the apparently deviant interpretations. Furthermore, the examples suggest that such conditionals have a less prominent reading on which their probability is in fact the conditional probability, and that the two readings are related by a simple step of abductive inference. Central to the proposal is a distinction between causal and purely stochastic dependence between variables.