The quickest trick to play on the brain to demonstrate that a human brain does not process probability is to say, “You Gotta Play to Win.” This sets up in the brain a simple equation: If you don’t play, you won’t win and if you do play, you will win. Well, maybe not every time….
The phenomenon called probability has intrigued mariner for some time. The brain operates strictly on a cause and effect mode – information in, information out. Probability, however, does not operate that way. Probability is free to behave randomly in terms of cause and effect expectations.
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The weatherman says there is a ten percent chance of rain. To take the statement literally as a cause and effect event, everyone will receive ten percent of all the rain today. Alternatively, one could deduce that the weatherman has said this many times before and it did not rain so the probability in the listener’s mind is quite different from ten percent. Bayes’ Theorem, which will be discussed later, is able to discern the difference between what is expected and what may happen.
A recent book and a Nobel Prizewinner for economics, “Thinking Fast and Slow,” by Daniel Kahneman, has an excellent chapter that discusses why the brain is so easily fooled by probability. A key concept in the book is the “anchor” effect. The first piece of information the brain receives becomes an anchor that unduly affects proper judgment as later information is added. Kahneman’s example:
“The initial price offered for a used car sets the standard for the rest of the negotiations, so that prices lower than the initial price seem more reasonable even if they are still higher than what the car is really worth.”
The anchor effect is isolated quite nicely by Nate Silver in his book, “The Signal and the Noise,” which is about identifying the correct anchor in sports betting. Silver takes the reader through many examples of mistaken anchors that did not consider the appropriate first piece of information and therefore led to gambling losses. It is in Silver’s book that he simplifies Bayes’ Theorem, which is a massive and complex set of calculations.
Silver sets up a simple set of questions:
X = prior assumption (first piece of information):
Do you think your husband cheats on you? The woman thinks
it is unlikely and says maybe 5%. X=.05
Y = a new event occurs: a strange pair of panties is discovered in the
husband’s car. Is this true evidence or an unexplained
circumstance? What are the chances it is circumstantial?
The wife thinks maybe 20%. Y=.20
Z= What are the chances it is true evidence that the husband has been cheating? The wife thinks maybe 80% Z=.80
Nate Silver sets up the following equation:
___XY____ .01___ = .013 XY+Z (1-X) .81 (.95)
Roughly one chance in a hundred that the husband is cheating. The equation demonstrates the power of the anchor effect. The wife had a very low value (.05) as the first piece of information. This made the later values less effective even though the panties were a strong piece of evidence.
In reality, the husband will have a lot of explaining to do because the brain does not think in terms of probabilities.
Ancient Mariner