Making Light:  Open thread 162 ::: August 08, 2011, 04:18 PM

On the Lemurian coins, I found a lot of interesting comments, but not
the two that leapt out at me.

First, the stipulation that unidentified coins are "no more likely
to be silver than gold" suggests to me that we should consider the
possibility that the unidentified coins may be less likely to be
silver than gold.  That leads to solutions parameterized by the
probability of the unidentified coins being silver, which makes
the restriction moot.

The second consideration is one I've discussed before, perhaps even
in the dim past of Making Light if such a problem has come up here.
Suppose in an alternate universe Mr. Jones comes to the meeting with
two silver coins.  I propose that it's most likely he'd say,

  I have two Lemurian coins in my hand.  At least one is silver.

given what we know of the sort of utterances he is prone to.  So what
happens if he finds that he has one silver coin and one gold?  I don't
see any reason why he should prefer proclaiming his possession of
a gold coin to one of silver, or vice versa.  So my interpretation
of the problem is that half of the time he has two matching coins,
determining which statement he makes, and the other half of the
time he has one of each, and chooses equiprobably between the two
statements.  Given that in the given instance he makes a statement
about having a gold coin, he is equally likely to have two gold coins
as he is to have one of each metal.