Superstition and Rational Learning

We argue that some but not all superstitions can persist when learning is rational and players are patient, and illustrate our argument with an example inspired by the code of Hammurabi. The code specified an “appeal by surviving in the river” as a way of deciding whether an accusation was true, so it seems to have relied on the superstition that the guilty are more likely to drown than the innocent. If people can be easily persuaded to hold this superstitious belief, why not the superstitious belief that the guilty will be struck dead by lightning? We argue that the former can persist but the latter cannot by giving a partial characterization of the outcomes that arise as the limit of steady states with rational learning as players become more patient. These “subgame-confirmed Nash equilibria” have self-confirming beliefs at information sets reachable by a single deviation. According to this theory a mechanism that uses superstitions two or more steps off the equilibrium path, such as “appeal by surviving in the river,” is more likely to persist than a superstition where the false beliefs are only one step off of the equilibrium path.

Inevitable magic – reason, magic and manipulation

Magical thinking occurs when supernatural causes, as opposed to rational ones, are assumed in events that defy reasonable probability. To investigate magical thinking, 64 adults were tested in a novel experiment where they were told they were playing an online game with opposing players. However, neither the “Game” nor the opposing players were real. It was a presentation designed to provide an illusion of game play. The “game” consisted of two sessions, each showing three opposing players (six rounds each). Half the opposing players were “seen” (pre-recorded videos with confederates posing as players) and the other half were “unseen”. To play the “game”, participants were asked to choose a card (from a set of five) and then observe the opposing player attempt to guess that card without being able to see it. Participants were then shown that one-third of opposing players displayed “good luck” (many correct guesses, defined by an above average score), one-third “neutral luck” (some correct, defined by an average score), and one-third “bad luck” (almost none correct, defined by a below average score). After the game, participants were asked to score each player on how likely they are to choose that player for a second stage of the game (in reality, there was no second stage). In the results, there was a significant effect of “luck” (with higher preferences for higher luck). There was also a significant effect of visibility (seen players preferred over unseen). Participants also completed two questionnaires to assess their disposition for magical thinking. There was a weak effect of questionnaire scores on the preference for luck. Results are considered in the context of research in anthropology and psychology

Steady State Learning and the Code of Hammurabi

The code of Hammurabi specified a “trial by surviving in the river” as a way of deciding whether an accusation was true. This system is puzzling for two reasons. First, it is based on a superstition: We do not believe that the guilty are any more likely to drown than the innocent. Second, if people can be easily persuaded to hold a superstitious belief, why such an elaborate mechanism? Why not simply assert that those who are guilty will be struck dead by lightning? We attack these puzzles from the perspective of the theory of learning in games. We give a partial characterization of patiently stable outcomes that arise as the limit of steady states with rational learning as players become more patient. These “subgame-confirmed Nash equilibria” have self-confirming beliefs at certain information sets reachable by a single deviation. We analyze this refinement and use it as a tool to study the broader issue of the survival of superstition. According to this theory Hammurabi had it exactly right: his law uses the greatest amount of superstition consistent with patient rational learning.

Short-term plasticity as cause-effect hypothesis testing in distal reward learning

Asynchrony, overlaps and delays in sensory-motor signals introduce ambiguity as to which stimuli, actions, and rewards are causally related. Only the repetition of reward episodes helps distinguish true cause-effect relationships from coincidental occurrences. In the model proposed here, a novel plasticity rule employs short and long-term changes to evaluate hypotheses on cause-effect relationships. Transient weights represent hypotheses that are consolidated in long-term memory only when they consistently predict or cause future rewards. The main objective of the model is to preserve existing network topologies when learning with ambiguous information flows. Learning is also improved by biasing the exploration of the stimulus-response space towards actions that in the past occurred before rewards. The model indicates under which conditions beliefs can be consolidated in long-term memory, it suggests a solution to the plasticity-stability dilemma, and proposes an interpretation of the role of short-term plasticity.Comment: Biological Cybernetics, September 201

Illusions of causality: How they bias our everyday thinking and how they could be reduced

Illusions of causality occur when people develop the belief that there is a causal connection between two events that are actually unrelated. Such illusions have been proposed to underlie pseudoscience and superstitious thinking, sometimes leading to disastrous consequences in relation to critical life areas, such as health, finances, and wellbeing. Like optical illusions, they can occur for anyone under well-known conditions. Scientific thinking is the best possible safeguard against them, but it does not come intuitively and needs to be taught. Teaching how to think scientifically should benefit from better understanding of the illusion of causality. In this article, we review experiments that our group has conducted on the illusion of causality during the last 20 years. We discuss how research on the illusion of causality can contribute to the teaching of scientific thinking and how scientific thinking can reduce illusion