Subjective randomness and natural scene statistics (original) (raw)
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Assessing the “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 over-represent certain sub-sequences 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. In the present study we provide a preliminary test of this account, comparing human-generated against unbiased process-generated binary sequences. Crucially we apply metrics to both sets of sequences that reflect constraints on human experience. In addition, sequences are compared using statistics that are shown to be more appropriate than a standard expected value analysis. We find preliminary evidence in support of our theoretical account and challenge the notion of bias in human randomness perception.
Advances in Applied Mathematics, 1991
Psychologists have studied people's intuitive notions of randomness by two kinds of tasks: judgment tasks (e.g., "is this series like a coin?" or "which of these series is most like a coin?"), and production tasks (e.g., "produce a series like a coin"). People's notion of randomness is biased in that they see clumps or streaks in truly random series and expect more alternation, or shorter runs, than are there. Similarly, they produce series with higher than expected alternation rates. Production tasks are subject to other biases as well, resulting from various functional limitations. The subjectively ideal random sequence obeys "local representativeness"; namely, in short segments of it, it represents both the relative frequencies (e.g., for a coin, 50%-50%) and the irregularity (avoidance of runs and other patterns). The extent to which this bias is a handicap in the real world is addressed. o 1991 Academic press, ~nc. Randomness is a concept which somehow eludes satisfactory definition. Devices which are random by definition, such as fair coins, can nonetheless generate series of outcomes which lack the appearance of randomness (e.g., a very long string of heads), while some digit series, although clearly patterned, define normal numbers, namely, numbers whose decimal form provably passes all tests for randomness (e.g., the infinite series obtained from writing down all the counting numbers in order: 1234567891011121314151617181920212223...).
Psychological conceptions of randomness
Journal of Behavioral Decision Making, 1989
This article presents a critique of the concept of randomness as it occurs in the psychological literature. The first section of our article outlines the significance of a concept of randomness t o the process of induction; we need to distinguish random and non-random events in order to perceive lawful regularities and formulate theories concerning events in the world. Next we evaluate the psychological research that has suggested that human concepts of randomness are not normative. We argue that, because the tasks set to experimental subjects are logically problematic, observed biases may be an artifact of the experimental situation and that even if such biases d o generalise they may not have pejorative implications for induction in the real world. Thirdly we investigate the statistical methodology utilised in tests for randomness and find it riddled with paradox. In a fourth section we find various branches of scientific endeavour that are stymied by the problems posed by randomness. Finally we briefly mention the social significance of randomness and conclude by arguing that such a fundamental concept merits and requires more serious considerations.
Psychonomic Bulletin & Review
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 h...
Making sense of randomness: Implicit encoding as a basis for judgment
Psychological Review, 1997
People attempting to generate random sequences usually produce more alternations than expected by chance. They also judge overalternating sequences as maximally random. In this article, the authors review findings, implications, and explanatory mechanisms concerning subjective randomness. The authors next present the general approach of the mathematical theory of complexity, which identifies the length of the shortest program for reproducing a sequence with its degree of randomness. They describe three experiments, based on mean group responses, indicating that the perceived randomness of a sequence is better predicted by various measures of its encoding difficulty than by its objective randomness. These results seem to imply that in accordance with the complexity view, judging the extent of a sequence's randomness is based on an attempt to mentally encode it. The experience of randomness may result when this attempt fails. Judging a situation as more or less random is often the key to important cognitions and behaviors. Perceiving a situation as nonchance calls for explanations, and it marks the onset of inductive inference (Lopes, 1982). Lawful environments encourage a coping orientation. One may try to control a situation by predicting its outcome, replicating, changing, or even by avoiding it. In contrast, there seems to be no point in patterning our behavior in a random environment. Although people feel that they know what they mean when speaking of randomness (Kac, 1983) and they communicate in everyday and professional affairs using their shared intuitive understanding of the term, it.is one of the most elusive concepts in mathematics. Randomness resists easy or precise definition, nor is there a decisive test for determining its presence (Ayton,
Why are people bad at detecting randomness? A statistical argument
Journal of Experimental Psychology: Learning, Memory & Cognition.
Errors in detecting randomness are often explained in terms of biases and misconceptions. We propose and provide evidence for an account that characterizes the contribution of the inherent statistical difficulty of the task. Our account is based on a Bayesian statistical analysis, focusing on the fact that a random process is a special case of systematic processes, meaning that the hypothesis of randomness is nested within the hypothesis of systematicity. This analysis shows that randomly generated outcomes are still reasonably likely to have come from a systematic process, and are thus only weakly diagnostic of a random process. We tested this account through three experiments. Experiments 1 and 2 showed that the low accuracy in judging whether a sequence of coin flips is random (or biased towards heads or tails) is due to the weak evidence provided by random sequences. While randomness judgments were less accurate than judgments involving non-nested hypotheses in the same task domain, this difference disappeared once the strength of the available evidence was equated. Experiment 3 extended this finding to assessing whether a sequence was random or exhibited sequential dependence, showing that the distribution of statistical evidence has an effect that complements known misconceptions.
Perception and identification of random events
2012
The cognition of randomness consists of perceptual and conceptual components. One might be able to discriminate random from non-random stimuli, yet be unable to identify which is which. In a series of experiments, we compare the ability to distinguish random from nonrandom stimuli to the accuracy with which given stimuli are identified as "random." In a further experiment, we also evaluate the encoding hypothesis according to which the tendency of a stimulus to be labeled "random" varies with the cognitive difficulty of encoding it . In our experiments, the ability to distinguish random from non-random stimuli is superior to the ability to correctly label them. Moreover, for some stimuli, difficulty of encoding fails to predict the probability of being labeled "random," providing evidence against one version of the encoding hypothesis.
PEOPLE'S INTUITIONS ABOUT RANDOMNESS AND PROBABILITY: AN EMPIRICAL STUDY4
2006
What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable process. Three groups of subjects differing according to their background knowledge
Subjective patterns of randomness and choice: Some consequences of collective responses
Journal of Experimental Psychology: Human Perception and Performance, 2009
Any individual's response intended to be random should be as probable as any other. However, 3 experiments show that many people's independent responses depart from the expected chance distribution. Participants responding to instructions of chance and related concepts favor the available options unequally in a similar way. Consequently, in hide-and-seek games, hiders converge on certain locations and are thereby detected beyond chance by seekers who share their preferences. People agree on salient and on nonsalient options, both of which are preferred under different instructions and even in the absence of instructions. Group responses strongly correlate under diverse, even opposing (e.g., competitive and cooperative) directions. Apparently, common default tendencies, combining random and aesthetic choices, are only somewhat modified under specific instructions. Maximal agreement with others is obtained by implementing one's own aesthetic preferences. These results broadly replicate in one-and two-dimensional tasks. Implications of the findings, their possible roots, and their connection to constructs from, e.g., game theory and subjective-complexity research, are discussed.
Perceptions of randomness: Why three heads are better than four
Psychological Review, 2009
A long tradition of psychological research has lamented the systematic errors and biases in people's perception of the characteristics of sequences generated by a random mechanism such as a coin toss. It is proposed that once the likely nature of people's actual experience of such processes is taken into account, these "errors" and "biases" actually emerge as apt reflections of the probabilistic characteristics of sequences of random events. Specifically, seeming biases reflect the subjective experience of a finite data stream for an agent with a limited short-term memory capacity. Consequently, these biases seem testimony not to the limitations of people's intuitive statistics but rather to the extent to which the human cognitive system is finely attuned to the statistics of the environment.