[extropy-chat] monty hall paradox again

[Brett Paatsch]

David wrote:

> Spike wrote:
> 
> > David wrote:
> >
> >>Call the larger envelope value LV,
> >>the smaller envelope SV,
> >>the minimum possible amount of zorgs is z.
> >>and i is some integer.
> >>
> >>SV must be i * z.
> >>But LV = 2 * SV , therefore SV can only increment in steps of 2z.
> >>
> >>This means that for any given range there are twice as many
> >>possible SV values as there are LV values.
> >>This means that the chance that the other envelope is the
> >>smaller one is twice the chance that it is the larger one.
> >>
> >>expected value becomes 2/3 * 5 + 1/3 * 20 = 10.
> >>    
> >>
> >
> >I am examining this argument carefully, for it is
> >tempting indeed.  The phrase "for any given range" makes me
> >squirm a little, for I fear that it incorrectly causes the zorg
> >version of the puzzle to collapse to the less interesting
> >real dollars version, which is solved by Eliezer's solution.
> >The real dollars version is merely a poker match. 
> >
> >On the other hand, I suppose that even with zorgs, there
> >must me *some* finite range.  Do let me ponder, thereby
> >dumping even more perfectly good life into this maddening
> >time-sink.
> >
> >spike
>
> "any given range" immediately becomes applicable when you
> open the first  envelope.
> The range is 2 * the value of the envelope you open.

I also baulked at "range" but I thought that David had it right.

 ie. He restated one interpretation of what you *seemed* to
want in terms you *seemed* to want.  

I'd be curious to see if you can fault him. 

With dollars we have an idea what the units are. Although
they could be say US dollars or Australian dollars or dollars in
some other country's denomination. With zorgs instead of dollars
we don't have such potentially messy preconceptions about
purchasing power etc but the ratios don't change. 5 zorgs.
10 zorgs. 20 zorgs. Same as 1 zorg. 2 zorgs, 4 zorgs isn't it? You
are just preserving the ratio while removing the preconception of
a how much a dollar can bye aren't you? Wasn't that the point ?

So you can plug whatever you want into "zorg" including dollars
if you want. Just as the person choosing the evelope could. Only
thing is you have to be consistent in what you plug in to preserve
the ratio you want. One zorg has to always equal a zorg. 5 zorgs
has to be half of 10 zorgs and a quarter of  20 zorgs whatever 
you decide a zorg is.  Whether a zorg is a simple familiar dollar
or dollar processed by any mathematical function to convert it 
into some other currency.

I'd like to see what you think of David's offering Spike.

Brett