[extropy-chat] three coins in a fountain, part 3: the test

spike spike66 at comcast.net
Sun Oct 23 02:02:12 UTC 2005

> -----Original Message-----
> From: extropy-chat-bounces at lists.extropy.org [mailto:extropy-chat-
> bounces at lists.extropy.org] On Behalf Of Chris Hibbert
> Sent: Saturday, October 22, 2005 4:28 PM
> To: ExI chat list
> Subject: Re: [extropy-chat] three coins in a fountain, part 3: the test
> Hal wrote:
> > I looked a bit at the mathematics of a slightly different form of the
> > puzzle and got a (possibly) surprising result.
> Economists (and I don't know who else) are quite interested in eliciting
> people's best estimates.  It turns out that if you use what's called a
> log-based scoring rule, the respondents' best strategy is to give their
> best likelihood estimate... Chris Hibbert

Ja I realized over dinner that we overlooked the
obvious.  We are so accustomed to adding scores
on tests that it isn't intuitive to use logs
when multiplying scores.  

Earlier today I wrote:

>I guess we must decide then exactly what we are trying to optimize...

If we maximize the log of our score, then all the
irrelevant criteria involving other students, monkeys,
payoff matrices, all disappear.  It becomes clear why 
one would avoid assigning zero probability anywhere, 
since the log of zero is negative infinity.  Adding 
anything to negative infinity gives negative infinity, 
so one's average is forever stuck at negative infinity.

A perfect score would be zero (the log of 1), but 
to accomplish this perfect zero, one must risk a 
negative infinity, which will forever wreck one's 


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