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

Rachlin's extended self: Influences on a Brazilian research group

We pay tribute to Rachlin's work stating that researching and writing for posterity is an act of self-control and altruism. We show how Rachlin's work influenced a series of seminars at the University of São Paulo (Brazil) based on his book from 1989, Judgment, Decision, and Choice. This influence is illustrated through two empirical exercises conducted during our seminars, where students were actively involved in data collection and analysis. The first exercise is about judgment of randomness involving coin tossing. The second is a replication of a procedure by Jones and Rachlin (2006) about social discounting of monetary quantities. We use these empirical examples to highlight some of Rachlin's major contributions to the science of behavior and their implications to our seminars and to ourselves as researchers.

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.

Regular and random judgements are not two sides of the same coin: Both representativeness and encoding play a role in randomness perception

The overalternating bias is that people rate sequences with an excess of alternation as more random than prescribed by information theory. There are two main explanations: the representativeness heuristic (Kahneman & Tversky Cognitive Psychology, 3, 430-454, 1972) and the implicit encoding hypothesis (Falk & Konold Psychological Review, 104, 301-318, 1997). These hypotheses are associated with different reaction times predictions. According to the encoding hypothesis, reaction times should increase as the complexity of the sequence increases, whereas the representativeness heuristic predicts fast reaction times only for more complex sequences that appear more random. We asked participants to guess the generating source of pairs of sequences of dichotomous elements in two different conditions: selecting the string generated by a random source or selecting the string generated by a nonrandom source. Results suggest that both the encoding strategy and the representativeness heuristic have a role in randomness perception and that the two criteria may have a different weight when determining the randomness versus the regularity of a string.

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.