Re: Hidden information question
- From: "Reef Fish" <Large_Nassau_Grouper@xxxxxxxxx>
- Date: 30 May 2006 21:41:01 -0700
Nigel wrote:
shiling99@xxxxxxxxx wrote:
Reef Fish wrote:
Jerry Dallal wrote:
Schizoid Man wrote:
Several coworkers would like to know their average salary. How can they
calculate it, without disclosing their own salaries?
It's perhaps a semantic thing, but in the scheme proposed by you, and
earlier by xhos. everyone disclosed their own salaries except YOU, who
thinks you are smarter than the rest of them.
The proposed scheme is bogus.
If YOU can play the game of adding a random number to YOUR salary,
then assuming that your are working in a think-tank that everyone can
come up with the same idea, and adjust the average from his OWN
fake noise (random or not is irrelevant).
That is, if EVERYONE enters Si + Ei where Ei is known only to person
i, then nobody will ever know the true average salary. In order for
the
scheme to work, one has to make the tacit assumption that there is
ONE, and ONLY ONE, smart donkey in the group, who thinks he is
smarter than the rest, and the rest is indeed as dumb as he thinks by
telling the truth of their salary when you think you are smart enough
to
fool them.
Even if everyone adds his noise as Si + Ei
as long as Ei is independent of all Si i=1,2,3,.. n
or more precisely,
E(E|S)=0;
The average will be a unbiase estimate. For efficient estimate the
sencond moment assuption may be needed.
This reply by Schizold Man is commensurate with the nonsense of the
problem posed.
What I still find puzzling is HOW Jerry Dallal and xhos not only
thought
the problem was legitimate, but came up independently with the same
bogus solution that is silly under ANY reasonable assumption,
I think you need to ask why the coworkers want to know their average
salary. I can think of scenarios which would make it beneficial for the
coworkers to profer inflated figures for their salaries.
That only adds other dimension of silliness to the problem. Why would
the coworkers WANT to know the average salary? How would that
information help them (as an individual who knows his own salary), in
any way, especially since the AVERAGE is almost NEVER used as
location measure of the "center" of any salary distribution, because of
its over-sensitivity to large outliers in a skewed long-tail
distribution?
What's the redeeming value of the PROBLEM? Never mind the
solution.
-- Bob.
.
- References:
- Hidden information question
- From: Schizoid Man
- Re: Hidden information question
- From: Jerry Dallal
- Re: Hidden information question
- From: Reef Fish
- Re: Hidden information question
- From: shiling99
- Re: Hidden information question
- From: Nigel
- Hidden information question
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