A new study is looking into how superstitions pop up — and why they endure.

Horseshoe.

Image credits Benjamin Nelan.

If we’re being honest, we’re not always the most logical of species. Roman leaders looked to the patterns of flying birds for guidance on important decisions, and builders today still sometimes omit the thirteenth floor from building plans. Humanity has harbored superstition for a long, long time now, and we’ll probably keep doing it for a while yet.

We know the number 13 doesn’t really invite bad luck, so why do we keep these superstitions going? Well, in a surprising twist of fate, a new paper reports that it is, sometimes, rational, to hold onto irrational behaviors. That is, if most other people hold onto them, too.

We’re wrong, but we’re wrong together!

“What’s interesting here is that we show that, beginning in a system where no one has any particular belief system, a set of beliefs can emerge, and from those, a set of coordinated behaviors,” says Erol Akçay, an assistant professor of biology at Penn, and the paper’s second author.

The researchers analyzed superstitions by applying the principles of game theory. They devised a model that shows how groups of people, each starting with distinct belief systems, can evolve a coordinated set of behaviors. These behaviors, in time, become enforced by consistent social norms.

Game theory is a branch of science that tries to model and predict how people interact and how they make decisions in a group or social setting. Akçay, alongside Bryce Morsky, a postdoctoral researcher, focused specifically on ‘correlated equilibria’ — scenarios in which all actors are given correlated signals that dictate their response to any given situation — to look into the issue.

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A classical example of a correlated equilibria scenario, Akçay explains, “is a traffic light.” If two people are approaching an intersection, he goes on to say, one will see a ‘stop’ signal and the other one a ‘go’ signal, and both actors know this is the case. The rational way forward, then, is for both actors to obey the signal they see. In this example, the traffic light acts a ‘correlating device’ or a ‘choreographer’, as it informs the behavior of all actors combined.

What the team wanted to see was how this would go down if the correlating device was taken out of the picture. If people had to pay attention to other signals that could direct their actions, and then shape their beliefs according to the success of their actions, would coordinated behaviors arise? Essentially, this would show the team whether evolution can act as a “blind choreographer” of sorts.

“What if a cyclist is riding toward an intersection, and instead of a traffic light they see a cat,” Akçay says. “The cat is irrelevant to the intersection, but maybe the person decides that if they see a black cat, that means they should stop, or that maybe that means the approaching cyclist is going to stop.”

What color the is cat obviously has no bearing on anything else happening in the intersection. A black cat won’t make it more likely that a cyclist enters the intersection any more than a white cat would make it less likely that he wouldn’t. But, and here’s the crux, different colors of cats would have a consistent effect if enough people believed different-colored cats had an effect. It’s a type of conditional strategy that might result in a higher payoff to the cyclist if it is correlated with superstitions of other cyclists, the team explains.

The team’s model assumes that individuals are rational and don’t blindly follow norms, but will do so when the norms seem to have a beneficial effect. They would thus change their beliefs to more closely resemble those of successful people. In effect, this creates a dynamic similar to natural evolution where norms “compete” against one another inside the group.

This process eventually leads to the formation of new social norms. Whether or not these norms are stable, the team also found, comes down to whether they are consistent — meaning that they successfully coordinate individual behavior even in the absence of an external “choreographer.”

“Slowly, these actors accumulate superstitions,” adds Morsky, the study’s first author. “They may say, ‘Ok, well I believe that when I observe this event I should behave this way because another person will behave that way,’ and over time, if they have success in using that kind of a strategy, the superstitions catch on and can become evolutionarily stable.”

“Sometimes it may be rational to hold these irrational beliefs.”

Norms that are able to prescribe how one actor should behave while also giving them a reliable idea of how others will behave in any given situation give rise to superstitions because they help us coordinate large groups even in the absence of outside choreographers, such as traffic lights. To further explore their findings, the researchers hope to engage in social experiments to see whether individuals might start devising their own superstitions or beliefs when none are provided.

“What I like about this work,” says Morsky, “is that these beliefs are made-up superstitions, but they become real because everybody actually follows them, so you create this social reality. I’m really interested in testing that further.”

The paper “Evolution of social norms and correlated equilibria” has been published in the journal Proceedings of the National Academy of Sciences.