On Feb 9, 2007, at 4:31 PM, Pei Wang wrote:
This is a better example of "conjunction fallacy" than the "Linda"
example (again, I don't think the latter is a fallacy), but still,
there are issues in the mainstream explanation:
Pei: If the Linda example** is presented in the context of
**betting**, then I
believe that it is definitely correctly classified as a fallacy.
If it's presented in the form of "which option is more likely", then
you can
validly argue that humans interpret "likely" as a combination of
intension
and extension, so that the so-called fallacious answer is not a
fallacy but
just a semantic mapping different from the standard extensional-
probability-theory-based
one.
But, if it's presented in the form of "which option would you bet on
being the case",
then the human behavior typically called a "fallacy" actually **is**
a fallacy --
people are applying mixed intension/extension where not appropriate...
ben
__________
** for those who don't know... Here is the fallacy.
"Linda is 31, single, outspoken, and very bright. She majored in
philosophy in college. As a student, she was deeply concerned with
discrimination and other social issues, and participated in anti-
nuclear demonstrations. Which statement is more likely?
a. Linda is a bank teller.
b. Linda is a bank teller and active in the feminist movement.
"
The problem is, a lot of people say that b is more likely. This is
intensional rather than extensional comparison.
A variant is
"Which statement would you bet more money on?"
which has also been tested, and reveals the same fallacy, though with
lesser frequency.
(1) This example can be explained by "availability", which should not
be taken as a heuristic (that people choose to use), but a restriction
(that people have to follow).
(2) I bet the result will be very different if the two problems are
presented together, rather than independently, since that will reduce
(though not completely) the difference in available evidence.
Pei
On 2/9/07, Eliezer S. Yudkowsky <[EMAIL PROTECTED]> wrote:
Some of them, but not others. For an example of the more
difficult case:
**
Two independent sets of professional analysts at the Second
International Congress on Forecasting were asked to rate,
respectively,
the probability of "A complete suspension of diplomatic relations
between the USA and the Soviet Union, sometime in 1983" or "A Russian
invasion of Poland, and a complete suspension of diplomatic relations
between the USA and the Soviet Union, sometime in 1983". The
second set
of analysts responded with significantly higher probabilities.
**
This is a type of conjunction fallacy where, arguably, an AI can
beat a
human in this specific case, but only by expending more computing
power
to search through many possible pathways from previous beliefs to the
conclusion. In which case, given a more complex scenario, one that
defeated the AI's search capabilities, the AI would fail in a way
essentially analogous to the human who conducts almost no search.
--
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence
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