The equiprobability bias from a mathematical and psychological perspective

Abstract

The equiprobability bias (EB) is a tendency to believe that every process in which randomness is involved corresponds to a fair distribution, with equal probabilities for any possible outcome. The EB is known to affect both children and adults, and to increase with probability education. Because it results in probability errors resistant to pedagogical interventions, it has been described as a deep misconception about randomness: the erroneous belief that randomness implies uniformity. In the present paper, we show that the EB is actually not the result of a conceptual error about the definition of randomness. On the contrary, the mathematical theory of randomness does imply uniformity. However, the EB is still a bias, because people tend to assume uniformity even in the case of events that are not random. The pervasiveness of the EB reveals a paradox: The combination of random processes is not necessarily random. The link between the EB and this paradox is discussed, and suggestions are made regarding educational design to overcome difficulties encountered by students as a consequence of the EB.

Keywords: complexity; equiprobability bias; randomness; subjective probability; uniformity.

Figure 1.

Examples of 12-item binary strings arranged according to their entropy and complexity. Each string is represented by an array of squares (grey squares for 1s and white squares for 0s). Although entropy and complexity are linked, some strings exhibit high entropy and low complexity, such as 010101010101 (bottom right).