Abstract
Psychological research has found that human perception of randomness is biased. In particular, people consistently show the overalternating bias: they rate binary sequences of symbols (such as Heads and Tails in coin flipping) with an excess of alternation as more random than prescribed by the normative criteria of Shannon's entropy. Within data mining for medical applications, Marcellin proposed an asymmetric measure of entropy that can be ideal to account for such bias and to quantify subjective randomness. We fitted Marcellin's entropy and Renyi's entropy (a generalized form of uncertainty measure comprising many different kinds of entropies) to experimental data found in the literature with the Differential Evolution algorithm. We observed a better fit for Marcellin's entropy compared to Renyi's entropy. The fitted asymmetric entropy measure also showed good predictive properties when applied to different datasets of randomness-related tasks. We concluded that Marcellin's entropy can be a parsimonious and effective measure of subjective randomness that can be useful in psychological research about randomness perception.
Highlights
IntroductionExplaining how people make inductive reasoning (e.g., inferring general laws or principles from the observation of particular instances) is a central topic within the psychology of reasoning
In this paper we investigated the potentiality of Marcellin’s asymmetric entropy for predicting randomness judgments
Fitting Marcellin’s entropy to randomness rating, we observed a better fit compared to subjective randomness measures based on classical Shannon’s entropy and on Renyi’s entropy, which represents a generalized form of such measures of uncertainty comprising many different kinds of symmetric entropies
Summary
Explaining how people make inductive reasoning (e.g., inferring general laws or principles from the observation of particular instances) is a central topic within the psychology of reasoning. Perceiving a situation as non-random requires some kind of subjective explanation which entails the onset of inductive reasoning (Lopes, 1982). During World War II the German air force dropped on London V1 bombs: many Londoners saw particular patterns related to the impacts and they developed specific theories about German strategy (e.g., thinking that poor districts of London were privileged targets). A statistical analysis of the bombing patterns made after the end of the war revealed that the distribution of the impacts was not statistically different from an actual random pattern (Hastie and Dawes, 2010). The opposite mistake happens when an observer fails to detect a regularity, attributing to chance a potential relation noticed (Griffiths, 2004): before Halley, no one had ever thought that the comets observed in 1531, 1607, and 1682 were the very same comet (Halley, 1752)
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