[extropy-chat] Coin Flip Paradox
gts
gts_2000 at yahoo.com
Wed Jan 31 19:02:28 UTC 2007
> There is great beauty in principles such as the Principle of
> Indifference...
Here is another example of where this "beautiful principle" fails
miserably:
This is from a text on decision theory [1], in which the author rejects
the principle as a decision-making rule on two grounds:
1) it is illogical and philosophically untenable (if we have no reason to
expect one outcome more than another then we have no reason to assume they
are equiprobable, either)
and, perhaps more critically,
2) the principle can lead to disaster...
A decision must be made between action 1 (A1) and action 2 (A2). One of
two scenarios will unfold (S1 or S2). We are ignorant of the probabilities
of S1 and S2, so we invoke the principle of indifference (also called the
principle of insufficient reason, as in this text) and assign each
scenario a probability of 50%.
As below, the expected utility (EU) of A1 is therefore 100, calculated as
(.5 * -100) + (.5 * 300) = 100. The expected utility of A2 is 20,
similarly calculated.
S1 S2 EU
----------------------------------
A1| -100 300 100
A2| 10 30 20
We choose A1 as this action offers the highest expected utility.
The author writes, "The principle of insufficient reason could lead us to
disaster... If, unbeknownst to us, the probability of S1 were, say, .9,
the expected utility of A1 would be significantly less than that of A2. In
a life or death situation the principle could be totally disastrous."
It's beautiful, though. :-)
-gts
1. Choices: An Introduction to Decision Theory By Michael D. Resnik
http://books.google.com/books?vid=ISBN0816614407&id=4genrKNUkKcC&pg=RA2-PA35&lpg=RA2-PA35&ots=wE4Uxk7bqE&dq=principle+of+insufficient+reason&sig=PsMUy3fqcMgFha8Kyx2HLaC-EA8
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