Latent structure in random sequences drives neural learning toward a rational bias

Abstract

People generally fail to produce random sequences by overusing alternating patterns and avoiding repeating ones-the gambler's fallacy bias. We can explain the neural basis of this bias in terms of a biologically motivated neural model that learns from errors in predicting what will happen next. Through mere exposure to random sequences over time, the model naturally develops a representation that is biased toward alternation, because of its sensitivity to some surprisingly rich statistical structure that emerges in these random sequences. Furthermore, the model directly produces the best-fitting bias-gain parameter for an existing Bayesian model, by which we obtain an accurate fit to the human data in random sequence production. These results show that our seemingly irrational, biased view of randomness can be understood instead as the perfectly reasonable response of an effective learning mechanism to subtle statistical structure embedded in random sequences.gambler's fallacy | waiting time | neural network | temporal integration | Bayesian inference P eople are prone to search for patterns in sequences of events, even when the sequences are completely random. In a famous game of roulette at the Monte Carlo casino in 1913, black repeated a record 26 times-people began extreme betting on red after about 15 repetitions (1). The gambler's fallacy-a belief that chance is a self-correcting process where a deviation in one direction would induce a deviation in the opposite directionhas been deemed a misperception of random sequences (2). For decades, this fallacy is thought to have originated from the "representativeness bias," in which a sequence of events generated by a random process is expected to represent the essential characteristics of that process even when the sequence is short (3).However, there is a surprising amount of systematic structure lurking within random sequences. For example, in the classic case of tossing a fair coin, where the probability of each outcome (heads or tails) is exactly 0.5 on every single trial, one would naturally assume that there is no possibility for some kind of interesting structure to emerge, given such a simple and desolate form of randomness. And yet, if one records the average amount of time for a pattern to first occur in a sequence (i.e., the waiting time statistic), it is significantly longer for a repetition (head-head HH or tail-tail TT, six tosses) than for an alternation (HT or TH, four tosses). This is despite the fact that on average, repetitions and alternations are equally probable (occurring once in every four tosses, i.e., the same mean time statistic). For both of these facts to be true, it must be that repetitions are more bunched together over time-they come in bursts, with greater spacing between, compared with alternations. Intuitively, this difference comes from the fact that repetitions can build upon each other (e.g., sequence HHH contains two instances of HH), whereas alternations cannot. Statistically, the mean time and waiting time delineate the m...

Human Inferences about Sequences: A Minimal Transition Probability Model

“…For instance, subjects become faster and more accurate when they encounter a pattern that repeats the same instructed response, or that alternates between two responses, and they slow down and may even err when this local pattern is discontinued [12–23]. Finally, studies asking subjects to produce random sequences or to rate the apparent “randomness” of given sequences, show a notorious underestimation of the likelihood of alternations [24–29]. …”

Human inferences about sequences: A minimal transition probability model

“…For instance, subjects become faster and more accurate when they 14 encounter a pattern that repeats the same instructed response, or that alternates between two responses, and they slow down and may even err when this local pattern is discontinued [12][13][14][15][16][17][18][19][20][21][22][23]. Finally, studies 16 asking subjects to produce random sequences or to rate the apparent "randomness" of given sequences, show a notorious underestimation of the likelihood of alternations [24][25][26][27][28][29]. 18 Here, we propose a model that provides a principled and unifying account for those seemingly unrelated results, reported in various studies and subfields of the literature quoted above.…”

The neural basis of decision-making during sensemaking: Implications for human-system interaction

“…The Parietal Cortex (PC) represents spatial aspects of data and does some mathematical processing. The Temporo-Parietal Junction (TPJ) learns to recognize structure in new domains [14]. Section 3.1 and 3.2 present neurobiological explanations of two aspects of sensemaking controlled by mechanisms in these brain regions: number representation and gambler's fallacy.…”

“…Mean times and waiting times of patterns measure the temporal intervals between various encounters of the patterns. It has been argued that these statistics could be the driving force that underlies people's randomness perception, and cognitive biases such as the gambler's fallacy, the hot hand belief and the attributing representativeness heuristic [14,53]. Since memory is essentially a process of reconstructing the past towards efficient predictions of the future, we would expect that emergence of asymmetries, pattern dissociation, hypothesis structures, and cognitive biases are all consequences of these temporal perception mechanisms.…”