Thinking and Deciding

ACCURACY OF PROBABILITY JUDGMENTS 141
childbirth taken together).
They noted that the probability scale is limited at the top. It does not allow people
to go beyond 100%, so any error may tend to make people give a spuriously large
number of 100% judgments. To test this theory, they asked subjects to express their
judgments as odds instead of percentages. It then became impossible to indicate
100% confidence, for that would correspond to infinite odds. This helped a little, but
the basic effect was still present.
Another possible explanation of biased confidence judgments is that people have
little idea what probability means: “People’s inability to assess appropriately a probability
of .80 may be no more surprising than the difficulty they might have in estimating
brightness in candles or temperature in degrees Fahrenheit. Degrees of
certainty are often used in everyday speech (as are references to temperature), but
they are seldom expressed numerically nor is the opportunity to validate them often
available” (Fischhoff et al., 1977, p. 553).
This argument does not explain all the results. Even if people do not have a good
feeling for what “80% confidence” means, they must have a good idea of what 100%
confidence means: It clearly means absolute certainty — no chance at all of being
incorrect — yet these extreme expressions of confidence are the judgments that show
the most bias.
In addition to the finding of overconfidence at 100%, another finding suggests
that overconfidence is not merely a result of misuse of the probability scale. People
themselves are willing to act on their judgments. Fischhoff and his colleagues
asked the subjects whether they would be willing to play a game. After making the
confidence judgments (still using odds for their estimates), the subjects were told (p.
558):
Look at your answer sheet. Find the questions where you estimated the
odds of your being correct as 50 to 1 or greater.... We’ll count how
many times your answers to these questions were wrong. Since a wrong
answer in the face of such high certainty would be surprising, we’ll call
these wrong answers ‘your surprises.’
The researcher then explained:
I have a bag of poker chips in front of me. There are 100 white chips and
2 red chips in the bag. If I reach in and randomly select a chip, the odds
that I will select a white chip are 100 to 2, or 50 to 1, just like the odds
that your ‘50 to 1’ answers are correct. For every ‘50 to 1 or greater’
answeryougave,I’lldrawachipoutofthebag.... Sincedrawingared
chip is unlikely, every red chip I draw can be considered ‘my surprise.’
Every time you are surprised by a wrong answer ..., you pay me $1.
Every time I am surprised by a red chip, I’ll pay you $1.
Of course, since the subjects’ confidence was usually greater than 50 to 1, they
stood to come out ahead if their estimates were well calibrated. Of forty-two subjects