The Equiprobability Bias from a Mathematical and Psychological Perspective

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.

Fair charging strategies for EVs connected to a low-voltage distribution network

The development of smart grid technologies and appropriate charging strategies are key to accommodating large numbers of Electric Vehicles (EV) charging on the grid. In this paper a general framework is presented for formulating the EV charging optimization problem and three different charging strategies are investigated and compared from the perspective of charging fairness while taking into account power system constraints. Two strategies are based on distributed algorithms, namely, Additive Increase and Multiplicative Decrease (AIMD), and Distributed Price-Feedback (DPF), while the third is an ideal centralized solution used to benchmark performance. The algorithms are evaluated using a simulation of a typical residential low voltage distribution network with 50% EV penetration. © 2013 IEEE.