Who "believes" in the Gambler's Fallacy and why?

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.

It is probably a pattern: does spontaneous focusing on regularities in preschool predict reasoning about randomness four years later?

The many studies with coin-tossing tasks in literature show that the concept of randomness is challenging for adults as well as children. Systematic errors observed in coin-tossing tasks are often related to the representativeness heuristic, which refers to a mental shortcut that is used to judge randomness by evaluating how well a set of random events represents the typical example for random events we hold in our mind. Representative thinking is explained by our tendency to seek for patterns in our surroundings. In the present study, predictions of coin-tosses of 302 third-graders were explored. Findings suggest that in third grade of elementary school, children make correct as well as different types of erroneous predictions and individual differences exist. Moreover, erroneous predictions that were in line with representative thinking were positively associated with an early spontaneous focus on regularities, which was assessed when they were in second year of preschool. We concluded that previous studies might have underestimated children's reasoning about randomness in coin-tossing contexts and that representative thinking is indeed associated with pattern-based thinking tendencies.

Sample decisions with description and experience

Decision makers weight small probabilities differently when sampling them and when seeing them stated. We disentangle to what extent the gap is due to how decision makers receive information (through description or experience), the literature’s prevailing focus, and what information they receive (population probabilities or sample frequencies), our novel explanation. The latter determines statistical confidence, the extent to which one can know that a choice is superior in expectation. Two lab studies, as well as a review of prior work, reveal sample decisions to respond to statistical confidence. More strongly, in fact, than decisions based on population probabilities, leading to higher payoffs in expectation. Our research thus not only offers a more robust method for identifying description-experience gaps. It also reveals how probability weighting in decisions based on samples — the typical format of real-world decisions — may actually come closer to an unbiased ideal than decisions based on fully specified probabilities — the format frequently used in decision science.

Is there a need for personal gambling licences?

Licensing is currently the most popular option among regulators for controlling gambling operations. However, approximately 20% of operators are still public monopolies. Many forms of gambling (especially lotteries) are government operated even in countries with a licensing system. This creates an inherent conflict of interest, given that government is supposed to protect the well-being of its citizenry and to reap the benefits of gambling at the same time. At least in the gambling monopoly, however, addressing the unavoidable harm that results from gambling should be a priority. Industry self-regulation and reliance on "responsible gambling" rely too much on individuals to control their own gambling. It is suggested in this contribution that it is possible to provide more comprehensive consumer protection, recognising both the duty of governments to take care of their own citizens and the fact that industry self-regulation is not enough. Pre-commitment cards have been tested in various contexts, and have shown promise in terms of providing tools for individuals to restrict their own gambling. However, given the known shortcomings such as allowing the use of other cards that are not one's own, and other venues, it is clear that in themselves they do not guarantee effective prevention. Personal licensing is therefore explored as a move forward in this literature-based discussion. Although the system may be applicable to other contexts, the focus is on the Nordic countries. Given that the underlying justification for gambling monopolies is to control gambling-related harm, in the cases of Finland and Norway licensing could be combined with loyalty cards introduced by monopoly operators. This would provide a feasible alternative to current practices of responsible gambling.

Changes in parents' perceived injury risk after a medically-attended injury to their child

Unintentional injuries are a major cause of hospitalization and death for children worldwide. Since children who sustain a medically-attended injury are at higher risk of recurrence, it is crucial to generate knowledge that informs interventions to prevent re-incidence. This study examines when, in the year following a medically-attended injury, parents perceive the greatest risk of injury recurrence. Since perception of injury risk is associated with parental preventive behavior, this can inform decisions on the timing of parent-targeted interventions to prevent re-injury. Study participants were 186 English-fluent parents of children 0 to 16 years, presenting at the British Columbia Children's Hospital for an unintentional pediatric injury. Parents were excluded if their child had a disability or chronic health condition. Perceived risk of the same and of any injury recurring were elicited from parents, when they sought treatment at the hospital, as well as one, four, and twelve months later. The study ran between February 2011 and December 2013. Mixed-effects models were used to analyze changes in parents' responses. Analysis indicates that perceived risk of the same injury recurring did not change. However, perceived risk of any injury recurring increased from baseline to first follow-up, then decreased during the rest of the year. Overall, perceived risk of any injury was higher for parents whose child had a history of injuries. Visits to the Emergency Department for a pediatric injury may not be optimal timing to deploy injury prevention interventions for parents. Follow-up visits (when parents' perceived risk is highest) may be better.

Generating randomness: making the most out of disordering a false order into a real one

Randomness is far from a disturbing disorder in nature. Rather, it underlies many processes and functions. Randomness can be used to improve the efficacy of development and of systems under certain conditions. Moreover, valid unpredictable random-number generators are needed for secure communication, rendering predictable pseudorandom strings unsuitable. This paper reviews methods of generating randomness in various fields. The potential use of these methods is also discussed. It is suggested that by disordering a "false order," an effective disorder can be generated to improve the function of systems.

Randomization and serial dependence in professional tennis matches: Do strategic considerations, player rankings and match characteristics matter?

In many sports contests, the equilibrium requires players to randomize across repeated rounds, i.e., exhibit no temporal predictability. Such sports data present a window into the (in)efficiency of random sequence generation in a natural competitive environment, where the decision makers (tennis players) are both highly experienced and incentivized compared to laboratory studies. I resolve a long-standing debate about whether professional players’ tennis serve directions are serially independent (Hsu, Huang & Tang, 2007) or not (Walker & Wooders, 2001) using a new dataset that is two orders of magnitude larger than those studies. I examine both between- and within-player determinants of the degree of serial (in)dependence. Evidence of the existence of significant serial dependence across serves is presented, even among players ranked Number 1 in the world. Furthermore, significant heterogeneity was found with respect to the strength of serial dependence and also its sign. A novel finding is that Number 1 and Number 2 ranked players tend to under-alternate on average, whereas in line with previous findings, the lower-ranked the players, the greater their tendency to over-alternate. Within-player analyses show that high-ranked players do not condition their randomization behavior on their opponent’s ranking. However, the under-alternation of top players would be consistent with a best-response to beliefs that the population of opponents over-alternates on average. Finally, the degree of observed serial dependence is not systematically related to other match variables proxying for match difficulty, fatigue, and psychological pressure.

A re-examination of "bias" in human randomness perception

Human randomness perception is commonly described as biased. This is because when generating random sequences humans tend to systematically under- and overrepresent certain subsequences relative to the number expected from an unbiased random process. In a purely theoretical analysis we have previously suggested that common misperceptions of randomness may actually reflect genuine aspects of the statistical environment, once cognitive constraints are taken into account which impact on how that environment is actually experienced (Hahn & Warren, Psychological Review, 2009). In the present study we undertake an empirical test of this account, comparing human-generated against unbiased process-generated binary sequences in two experiments. We suggest that comparing human and theoretically unbiased sequences using metrics reflecting the constraints imposed on human experience provides a more meaningful picture of lay people's ability to perceive randomness. Finally, we propose a simple generative model of human random sequence generation inspired by the Hahn and Warren account. Taken together our results question the notion of bias in human randomness perception. (PsycINFO Database Record

Perceptions of randomness in binary sequences: Normative, heuristic, or both?

When people consider a series of random binary events, such as tossing an unbiased coin and recording the sequence of heads (H) and tails (T), they tend to erroneously rate sequences with less internal structure or order (such as HTTHT) as more probable than sequences containing more structure or order (such as HHHHH). This is traditionally explained as a local representativeness effect: Participants assume that the properties of long sequences of random outcomes-such as an equal proportion of heads and tails, and little internal structure-should also apply to short sequences. However, recent theoretical work has noted that the probability of a particular sequence of say, heads and tails of length n, occurring within a larger (>n) sequence of coin flips actually differs by sequence, so P(HHHHH) <P(HTTHT). In this alternative account, people apply rational norms based on limited experience. We test these accounts. Participants in Experiment 1 rated the likelihood of occurrence for all possible strings of 4, 5, and 6 observations in a sequence of coin flips. Judgments were better explained by representativeness in alternation rate, relative proportion of heads and tails, and sequence complexity, than by objective probabilities. Experiments 2 and 3 gave similar results using incentivized binary choice procedures. Overall the evidence suggests that participants are not sensitive to variation in objective probabilities of a sub-sequence occurring; they appear to use heuristics based on several distinct forms of representativeness.