# Re: The Base Rate Fallacy

Date: Tue Jun 04 1996 - 15:55:29 BST

> From: "Elliott, Mark" <MAE195@psy.soton.ac.uk>
> Date: Fri, 24 May 1996 10:50:41 GMT
>
> The Base Rate Fallacy is the belief that probability rates are false.

The base rate fallacy is the failure to take base rates into acount when
judging probability. In such a task you are given statistics for a
population as well as for a particular case; both should be considered
together. People tend to ignore the population base rate.

Here is another version of the kind of problem with which this tends to
happen (from Koehler, quoting Tversky and Kahneman):

#3. The taxi cab problem, as described by Tversky and Kahneman
(1980, p. 62) is as follows: "A cab was involved in a hit-and-run
accident at night. Two cab companies, the Green and the Blue,
operate in the city. You are given the following data: (i) 85% of
the cabs in the city are Green and 15% are Blue. (ii) A witness
identified the cab as a Blue cab. The court tested his ability to
identify cabs under the appropriate visibility conditions. When
presented with a sample of cabs (half of which were Blue and half
of which were Green) the witness made correct identifications in
80% of the cases and erred in 20% of the cases. Question: What is
the probability that the cab involved in the accident was Blue
rather than Green?"

When people answer this, they tend to say that the probability it was
blue (the rare case) is about 80%, but the real probability is 41%,
because this takes into account the fact that there are may more green
cabs than blue ones. (For details, see Koehler's
http://cogsci.soton.ac.uk/~bbs/Archive/bbs.koehler.html
or
http://cogsci.ecs.soton.ac.uk/cgi-bin/newpsy?4.49
(the second is shorter and easier)

> When presented with statistics about the population as a whole, people
> tend to ignore them and think about themselves as completely different
> entities. For example someone has the symptoms of a disease which takes
> two forms, both fatal, requiring two different medicines. Only one
> medicine can be taken and medicine A does not work for form B of the
> disease and medicine B does not work for form A of the disease. Form A
> of the disease occurs 10% of the time in the population whilst form B
> occurs 90% of the time. After taking an 80% reliable A/B test it says
> that this person has form A of the disease.

So far, this is a correct description.

> Therefore this person is
> likely to take the treatment for form A of the disease dispite a 20%
> chance that he could have form B and only 10% of people in the
> population have form A.

Incorrect, his chances of having the common form are MUCH higher than
that; you have just committed the base rate fallacy, focusing only on
the test, and ignoring the population base rates!

> This is because people are not concerned with
> statistics, they are concerned with themselves.

They ARE concerned with statistics, but only the statistics they think
are about themselves; they think population baseline rates do not apply
to them when there are also statistics that are closer to them.

> People can learn base rate probabilities quicker through experience
> where-by a penalty is incurred each time they act in a certain way.

In other words, if the task were not to decide based on written
assessments of the statistics, but to do this repeatedly, as you learn,
from experience, that most people have form B, that the test is only
80% reliable, and that if you rely on the test and ignore the base
rates you will "die" much more often than otherwise, then you learn not
to ignore the base rates. Also, if the problem is given to you with
actual numbers of cases, rather than percentages, people are better at
saying the correct conditional probability (the probability that
someone the test says has the rare form actually has the common form)
than they are with percentages.

> For example if people were told that a fruit machine gave out a lot of
> money each time it was played on, they would probably think it was a
> lie and ignore the base rate.

This is not a base rate problem.

> However if they had a go on it and won
> some money they are more likely to believe it and carry on playing.
> Therefore it can be wrong to ignore base rates.

It is not yet clear that you understand base rates. Re-read the shorter
Koehler article in Psycoloquy.
http://cogsci.ecs.soton.ac.uk/cgi-bin/newpsy?4.49

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