[extropy-chat] Coin Flip Paradox

gts gts_2000 at yahoo.com
Wed Jan 31 19:02:24 UTC 2007

Jef, I promised yesterday to answer in more detail a post of yours which  
you wrote in reply to my post about the problem in decision theory. Your  
message is interesting but you did not actually answer mine directly,  
except with your usual argument about context.

You wrote:

> Gordon, principles cannot "fail miserably".  People can fail miserably
> when they try to apply principles out of context.

But otherwise you wrote nothing more about the problem.

You seem to claiming here that the decision theorist who wrote that text  
on decision theory was somehow wrong in his application or misapplication  
of the principle of indifference, but yet you did not tell me why or how  
he should have proceeded.

Will you please address the problem directly? Why do you think this  
decision theorist was wrong to warn his readers to stay clear of the  
principle of indifference? In what way did he "apply principle out of  

Why was he wrong to conclude that in a life or death situation, the  
principle could lead to disaster?

Here it is again:

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. :-)


1. Choices: An Introduction to Decision Theory By Michael D. Resnik

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