Re: Hidden information question


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.

That seems to be a VERY STRONG assumption, unlikely to be
realized in any real situation except in a newsgroup discussion in
the form of a riddle.

KISS.

Just use the employer's report to the IRS and report the average or
median as every State Academic Instituion does. In fact, in a
State in which I worked, every one whose salary exceeds a certain
threshold is PUBLIC information, released by the State each year,
and available to all faculty members.

That's when everyone finds out how much the football coach makes
and how many times it's higher (usually about 10 times) than the
salary of the President of the University or the Governor of the
State, or the President of the US for that matter. It really reflexes
the priority of the Educational System in collegiate sports by
hiring professionals

WARNING: LONG rant prompted by this salary problem

Start RANT: I was in an "academic institution" which hired an entire
professional team in Africa to win several National championships
in soccer; other universities now learned where they could
recruit players too; the biggest problem with these professional
atheletes disguised as college students was how to keep them
from spending their entire "scholarship" in the first week, and had
no money left for the rest of the semester.

The same unviversity hired football players <by illegally stuffing
money under the table; won a National Championship; fired
the coach when the payoff was discovered by the NCAA and
put the university on probation for three years> The coach
who was fired had a contract that had to be bought out. So,
he sat out several years as a coach with his nearly $1 million
buy-out (if he gets another coaching job in the interim, he
would forfeit the buy out for the unserved contract years).
The fired coach was a celebrity. During his short years of
buyout, I happened to see him in Cozumel, escorting a group
of Old Ladies from a cruiseship. When I greeted him (he
used to be a neighbor of mine, in choice real estimate lake
front properties where my lot was between the his lot and
that of the Head basketball coach. :-)) he waved the old
ladies to wait for him down the street, sat down at the
ocena front Las Palmeras restaurant with us, chatted a
bit, and discreetly asked, "where IS Cozumel?" while he
was leading as the Tour Guide the old ladies IN Cozumel. :-)

Everyone remembers the National CHampionship; nobody
remembers, or cares about the lack of sportsmanship or
NCAA violations. Other universities followed the same pattern.
National Championship; NCAA violations and probation. Plenty
examples of it in our so called "collegiate sports" when nearly
every university have illiterate, professional players with perhaps
two exceptions, Duke and Stanford.

END RANT about intercollegiate sports.

the mandatory release of salary information also gives every
faculty member the data to complain how under-paid they are,
even for the highest paid ones.

-- Bob.

Get piece of paper.
First person picks a random number (+ or -) known only to him/her and
adds it to his/her salary. Writes only the total on piece of paper.
Paper goes around the room with everyone else adding his/her salary to
the total.
When it comes back to the first person s/he subtracts the random number.

(This has to be done in such a way that no one can follow the running
total. Perhaps everyone has a piece of paper. S/he keeps the one that
comes to him/her, passing on a *** with only one number: the sum of
the number that came to him/her plus his/her salary.)

How does one calculate the mean for a set of random variables, if one
does not know:
1. the value of the variables, or
2. the parameters (i.e. mean, std dev) of the distribution?

.