A cab was involved in a hit and run. There are two cab companies, red and blue. What is the probability the cab involved in the accident is blue?

Respondents neglect the base rate (most common answer = 80%) when the story is phrased:

- 85% of cabs are green and 15% are blue

- A witness identified the cab as blue. During the cross examination, the witness correctly identified one of the two colors 80% of the time and failed 20%

Respondents give answers close to the Bayes rate (41%) when the story is phrased:

- The two companies operate the same number of cabs, but green cabs are involved in 85% of accidents

- A witness identified the cab as blue. During the cross examination, the witness correctly identified one of the two colors 80% of the time and failed 20%

Mathematically the problems are exactly the same, but in the second explanation of the story, a psychological causal link between green cabs and accidents is established because of the wording.

The Green and Blue cab example of causes trump statistics

They provide us with a stereotypical trait about an individual and a feature of the situation that significantly affects the outcome. Studies have shown this leads to more correct inferences and improved judgement

Why are causal base rates effective?

Statistical results that have accompanying causal interpretations have a stronger effect on our thinking  than non-causal information. However even information that is framed causally can't overcome personal beliefs reinforced by experience

Learning through causal explanations

They are base rates framed in a way that changes your view about how the case at hand came to be.

University of Michigan - Ann Arbor

The associative mechanisms in the brain (system 1) seek causes to explain and rationalize events. This is part of the reason why we are bad intuitive statisticians: statistics often deals in probabilities - relating what did happen to what could've happened.

Psychology of Cause and Change

Kahneman, Daniel. Thinking, Fast and Slow. Nota, 2013.

Thinking Fast and Slow by Daniel Kahneman

Even statistical experts do not recognize if a sampling effects played a large role in an outcome, when using their intuition.

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