The Psychology of Religious Intuitions: Randomness & Chance

This series explores the psychology of intuition and cognitive illusion, specifically as applied to religious intuitions.  See background and representativeness. 

Randomness & Chance

Consider two questions:

1) You flip a fair coin six times.  Which of the following two sequences is more likely to occur:  H-T-H-T-T-H or H-H-H-H-T-H?

2) A basketball player is on a major hot streak, landing him a spot on the cover of Sports Illustrated. Soon afterwards, his performance drops and he is no longer noteworthy.  Is this evidence for the "Sports Illustrated Jinx," according to which appearing on the cover of Sports Illustrated jinxes athletes to bad performance?

1) If you're like most people surveyed in the experiments of famed psychologists Daniel Kahneman and Amos Tversky, you probably think the answer to question 1 is the first sequence: it just looks more random, right?  The correct answer is that they are both about equally likely under the laws of chance.

A random series of coin flips is expected to be half heads and half tails only in the very long run. But, people use a mental shortcut (the representativeness heuristic) that expects short runs to be representative of long runs: we think any sequence of coin flips should look as fair as a long run.  This leads to a systematic bias called the clustering illusion: people think clusters are meaningful patterns even when they are frequently produced by chance, because that's not what we expect chance to look like.  We are terrible intuitive statisticians.  Randomness actually creates clusters, according to the laws of probability--but we intuitively think it won't.

Religious intuitions often involve claims about patterns that "could not possibly be due to chance."  (I don't have in mind evolution here, because evolution is actually a systematic process, not a chance process--a point often misunderstood by creationists.)  People cite supposed miracles or facets of the world that "could not be coincidence;" they see shapes of Jesus in crackers when elements cluster together more than they intuitively expect, and see divine signs in the world around them.  But as we have seen, people are notoriously bad at judging intuitively what randomness looks like: we are very prone to seeing patterns where there are none.  The only way to ascertain randomness is by using formal statistical procedures; logic and scientific thinking are trustworthy where intuition leads astray. 

2) If you are like many people, you might intuitively think the Sports Illustrated jinx is real, or at least eery.  But, it is easily explained by an overlooked fact called regression toward the mean. A basketball player's performance is due both to his actual skill level and to some degree of luck--aka random chance.  If someone is suddenly performing well enough to make the cover of SI, they probably have been experiencing unusually good luck. Since unusually good luck is...well, unusual, we don't expect it to continue, meaning that they go back (regress) to how they normally play (their mean). Appearing on the cover of SI just coincides with the time of unusually good luck, which we expect to end anyway. The SI jinx is an example of a general tendency people have: we are very good at seeing cause and effect (or inventing explanations) when random fluctuations are actually at work.

In his book How We Know What Isn't So, psychologist Thomas Gilovich relates an experience he had on a trip to Israel:

"A flurry of deaths by natural causes in the northern part of the country led to speculation about some new and unusual threat. It was not determined whether the increase...was within the normal fluctuation in the death rate that one can expect by chance. Instead, remedies for the problem were quickly put in place.  In particular, a group of rabbis attributed the problem to the sacrilege of allowing women to attend funerals, formerly a forbidden practice. The remedy was a decree that subsequently barred women from funerals in the area. The decree was quickly enforced, and the rash of unusual deaths subsided" (Gilovich, 1991, pg. 28.)

A string of deaths can be expected by chance fluctuations, just like the string of "heads" above. But, people saw a meaningful pattern because we wrongly expect randomness not to come in clusters. Meanwhile, the actual death rate at a given moment is due to the average death rate plus some degree of luck (chance); if the death rate rose unusually, it means there was a string of unusually bad luck that is unlikely to continue (the death rate should regress to its mean). So, surprise, surprise: the rabbis enacted their decree while there was unusually bad luck and the death rate went down to normal, and--voilá!--they see cause and effect.

The moral of the story is that people are biased to see patterns and cause and effect where there is randomness, leading to religious intuitions. Scientific thinking must be employed to understand complex phenomena and the nature of the universe.  In this case, carefully applied statistics can tell us what is random and what is not, when our intuitions turn us into hyperactive pattern-detectors.
  

Further reading:
Gilovich, T. (1991) How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life. Chapter 2: Something Out of Nothing: The Misperception and Misinterpretation of Random Data.

Kahneman, D., & Tversky, A. (1972) Subjective Probability: A Judgment of Representativeness. Cognitive Psychology.