Re: Twenty Beautiful Women

At 20:54 7/27/96, Mike Duvos wrote:
>ichudov@algebra.com (Igor Chudov @ home) writes:
>
> > Also, I would appreciate if someone specified what exactly
> > the goal function is.
>
>Me too.

For clarification, the problem is often stated in textbooks similar like this:

You ask someone to write one number each on ten pieces of paper without you
being able to see the numbers. The person may use any number from 1 to
10^99, but may not use a number twice. The person turns over the ten
papers.

You goal is to determine the paper with the highest number [rules apply as
described in the original post]

The general solution is to flip over 1/e papers and choose the paper that
has a higher number on it than any of the 1/e papers turned over at first.



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Lucky Green writes:

> For clarification, the problem is often stated in textbooks similar like this:
> 
> You ask someone to write one number each on ten pieces of paper without you
> being able to see the numbers. The person may use any number from 1 to
> 10^99, but may not use a number twice. The person turns over the ten
> papers.
> 
> You goal is to determine the paper with the highest number [rules apply as
> described in the original post]
> 
> The general solution is to flip over 1/e papers and choose the paper that
> has a higher number on it than any of the 1/e papers turned over at first.

Stated this way, I suppose strategy A is better than strategy B if after
an arbitrarily large number of trials, N(A>B) > N(B>A).

It is still unclear that such a notion translates smoothly into notions
like "lowest gas price", where buying once at a station that is half
the price beats buying a dozen times at a station that is only one 
cent less.  

It does translate perfectly well into the original problem of picking
subjectively beautiful women, however, which is also non-parametric in
a similar way.  It would be nice to see a short proof that for the
optimal solution, the threshold is the max of the first 1/e elements, 
and is not a function of how many steps have been taken. 

--
     Mike Duvos         $    PGP 2.6 Public Key available     $
     mpd@netcom.com     $    via Finger.                      $

> 
> At 20:54 7/27/96, Mike Duvos wrote:
> >ichudov@algebra.com (Igor Chudov @ home) writes:
> >
> > > Also, I would appreciate if someone specified what exactly
> > > the goal function is.
> >
> >Me too.
> 
> For clarification, the problem is often stated in textbooks similar like this:
> 
> You ask someone to write one number each on ten pieces of paper without you
> being able to see the numbers. The person may use any number from 1 to
> 10^99, but may not use a number twice. The person turns over the ten
> papers.
> 
> You goal is to determine the paper with the highest number [rules apply as
> described in the original post]
> 
> The general solution is to flip over 1/e papers and choose the paper that
> has a higher number on it than any of the 1/e papers turned over at first.

Can someone explain the theory behind this?


-- 
"Of all tyrannies a tyranny sincerely  exercised for the good of its victims  
 may be the most  oppressive.  It may be better to live under  robber barons  
 than  under  omnipotent  moral busybodies,  The robber baron's  cruelty may  
 sometimes sleep,  his cupidity may at some point be satiated; but those who  
 torment us for own good  will torment us  without end,  for they do so with 
 the approval of their own conscience."    -   C.S. Lewis, _God in the Dock_ 
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