Although widely investigated and used in psychology, the concept of randomness is beset with philosophical and practical difficulties. In this paper, I propose a resolution to a long-standing problem in psychological research by arguing that the inability to comprehend and produce random behavior is not caused by a defect on the part of the observer but is a consequence of conceptual confusion. Randomness describes a state of high complexity which defies analysis and understanding. The well-known biases in predictive behavior are (...) not caused by the observers’ inability to comprehend randomness but reflect a natural pattern-seeking response to high-complexity situations. Further, I address the circularity at the heart of the randomness debate. Replacing randomness with complexity in psychology and cognitive science would eliminate many of the current problems associated with defining, investigating and using this elusive term. (shrink)

Two old problems in probability theory involving the concept of randomness are considered. Data obtained with one of them--Bertrand's chord problem--demonstrate the equivocality of this term in the absence of a definition or explication of assumptions underlying its use. They also support two propositions about probabilistic thinking: (1) upon obtaining an answer to a question of probability, people tend to see it as the answer, overlooking tacit assumptions on which it may be based, and tend not to consider the possibility (...) of other assumptions from which different answers would follow; (2) perceptual balance--moderate uniformity of density of distribution--is a determinant of the degree to which a two-dimensional pattern is perceived as random. (shrink)

People commonly use terms like ‘random’, ‘by chance’, or ‘accidentally’ when they describe occurrences that sidestep the normal course of events, with no apparent causal link to ongoing activities. Such intrusive events are typically perceived as happening all of a sudden. This was demonstrated in seven experiments (N = 1299) by asking people to identify statements they believed belonged to stories about chance events, and by comparing chance vs. non-chance events from their own life and from the lives of others. (...) Suddenness also appeared to be more strongly associated with beginnings than with endings of an episode. Thus, statements about sudden beginnings of a career or a relationship were more readily believed to happen ‘by chance’ than ‘not by chance’. But life-changing events did not become more accidental simply by being placed in the beginning of a ‘life chapter’. These studies highlight a central but neglected feature of perceived randomness. (shrink)

We argue that approaches adhering to normative systems can be as fruitful as those by descriptive systems. In measuring people's perception of randomness, discrepancies between human behavior and normative models could have resulted from unknown properties of the models, and it does not necessarily lead to the conclusion that people are irrational or that the normative system has to be abandoned.

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...) between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

Color charts, or grids of evenly spaced multicolored dots or squares, appear in the work of modern artists and designers. Often the artist/designer distributes the many colors in a way that could be described as “random,” that is, without an obvious pattern. We conduct a statistical analysis of 125 “random-looking” art and design color charts and show that they differ significantly from truly random color charts in the average distance between adjacent colors. We argue that this attribute generalizes results in (...) subjective randomness in a black/white setting and gives further evidence supporting a connection between subjective randomness and what is esthetically pleasing. (shrink)

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. (shrink)

Pereboom’s ‘wild coincidences’ argument against agent-causal libertarianism is based on the claim that in a world governed by statistical laws, the dovetailing of indeterministic physical happenings with the free actions of agent causes would be a coincidence too wild to be credible. In this paper it is shown that the conclusion is valid for deterministic laws, but that it fails for statistical laws. Therefore, the ‘wild coincidences’ argument does not provide the promised empirical refutation of agent-causal libertarianism.

The statistics of small samples are often quite different from those of large samples, and this needs to be taken into account in assessing the rationality of human behavior. Specifically, in evaluating human responses to environmental statistics, it is the effective environment that matters; that is, the environment actually experienced by the agent needs to be considered, not simply long‐run frequencies. Significant deviations from long‐run statistics may arise through experiential limitations of the agent that stem from resource constraints and/or information‐processing (...) bounds. The article draws together recent work from a number of areas in judgment and decision making ranging from randomness perception (Hahn & Warren, ), information sampling (Hertwig & Pleskac, ; Kareev et al., ), and consequences of choice for exploration or exploitation (e.g., Denrell, ) to demonstrate how proper consideration of these deviations leads to reevaluation of behaviors that are otherwise deemed irrational. (shrink)

Normative theories can be useful in developing descriptive theories, as when normative subjective expected utility theory is used to develop descriptive rational choice theory and behavioral game theory. “Ought” questions are also the essence of theories of moral reasoning, a domain of higher mental processing that could not survive without normative considerations.

The subjective feeling of free choice is an important feature of human experience. Experimental tasks have typically studied free choice by contrasting free and instructed selection of response alternatives. These tasks have been criticised, and it remains unclear how they relate to the subjective feeling of freely choosing. We replicated previous findings of the fMRI correlates of free choice, defined objectively. We introduced a novel task in which participants could experience and report a graded sense of free choice. BOLD responses (...) for conditions subjectively experienced as free identified a postcentral area distinct from the areas typically considered to be involved in free action. Thus, the brain correlates of subjective feeling of free action were not directly related to any established brain correlates of objectively-defined free action. Our results call into question traditional assumptions about the relation between subjective experience of choosing and activity in the brain’s so-called voluntary motor areas. (shrink)

Erroneous gambling-related beliefs can be defined as beliefs that imply a failure to recognise how commercial gambling activities are designed to generate a guaranteed loss to players. In t...

The present paper explores the role of motivation to observe a certain outcome in people’s predictions, causal attributions, and beliefs about a streak of binary outcomes. In two studies we found that positive streaks lead participants to predict the streak’s continuation, but negative streaks lead to predictions of its end. More importantly, these wishful predictions are supported by strategic attributions and beliefs about how and why a streak might unfold. Results suggest that the effect of motivation on predictions is mediated (...) by a serial path via causal attributions to the teams at play and belief in the hot hand. (shrink)

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)