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

spike spike66 at comcast.net
Fri Oct 21 23:28:18 UTC 2005

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> -----Original Message-----
> From: extropy-chat-bounces at lists.extropy.org [mailto:extropy-chat-
> bounces at lists.extropy.org] On Behalf Of spike
...
>
> Here's another interesting twist: the test answers
> *might* be wrong.  The proles could send me a
> wrong answer, and if I don't catch it, well... too
> bad.  ...  Remember this is just a game, an experiment. spike

Another idea occurred to me.  I could include a
question that has no perfectly right answer, but
rather one to which confidence levels must be
assigned.  For instance:

Assign confidence levels to these scenarios

a)  OJ did it and Fuhrman planted the glove
b)  OJ did it and Fuhrman did not plant the glove
c)  OJ did not do it and Fuhrman planted the glove
d)  All other possible scenarios

You can see that no one can know the right answer,
not even OJ or Fuhrman.  OJ cannot be 100% certain
that Fuhrman was the glove planter, Fuhrman cannot
be 100% certain that OJ was the Nicole slayer.
The only theoretical person who could be 100%
certain is one who both slew Mrs Simpson
and planted the glove, and OJ is on his trail
I can assure you.

The game then would be to see how a contestant
would distribute the confidence levels.  The
head-prole test maker must assign probability
levels to each possible answer, then multiply
the responses probability distribution by the
pre-decided distribution, then normalize the
score to 1.  We want a perfect score on this
kind of test to be 1.

But for the first go-around, let us have only
unambiguous questions, like the three-coins
example.  Someone posted me offlist a line
of reasoning that had not occurred to me:

<quote from someone else> "For the three coins,  The odds of pulling out one
of the three coins and  putting down a Head is fifty percent.  Since HH, HT,
TT include three heads and three tails to proceed with.  Since we know only
two of the coins has a head on it, the odds of flipping it over and having
tails is fifty percent.  Then we multiply the two percentages and come to a
conclusion at twenty-five percent.  The answer to the probability of pulling
a coin to reveal heads then tails is twenty-five percent." <end quote>

So now we know there exist lines of reasoning that