Re: [Phys-L] Inference Lab Design

[John Denker <jsd@av8n.com>]

On 08/19/2012 01:22 PM, Marty Weiss wrote:
> So, here's where explanation breaks down... in the normal high school
> class, there will always be some wise guy who asks,  "What's the
> penalty for guessing wrong?"  You say,  "There is no penalty."  So
> the kids says,  "He guessed a white hat because he has a 50-50 chance
> of getting it correct and it doesn't make any difference if he got it
> wrong anyway."

Obviously that kid has a bright future in tabloid journalism, where it
is more important to be first than to be right.

More seriously:  There are plenty of real-world situations where
making a somewhat-ill-informed decision quickly is the winning strategy, 
in preference to making a perfectly-well-informed decision after it is 
too late to do any good.  As a particularly spectacular example:  you
quarantine people who have been exposed to the Ebola virus *before* you 
know whether they are actually infected or not.  Less-spectacular examples
are a dime a dozen.

  OTOH this principle must not be used as a pretext for willful ignorance,
  recklessness, or deceit (e.g. WMD).

In the hat game, if the payoff for guessing correctly is a million dollars,
and the cost of playing the game and guessing incorrectly is less than
half a million dollars, then making an immediate 50/50 guess is a fine
strategy.  So I would say that student is more "wise" than "wise guy".

I would go even further and make a symmetry argument:  There is no basis
for assuming the odds are 50/50.  The folks who set up the contest would 
probably prefer to make all hats the same color, so as not to give an 
arbitrary unfair advantage to one of the players.

> So, I ask everyone, suppose the penalty is DEATH."  ??    Then what's
> the logic in being the first one to guess white?"

That just goes to show that the problem as originally stated was
seriously underspecified.  As I said, it purports to be a pure logic
problem, but really it is much more than that.