🚀 go-pugleaf

In article <727745474snz@panache.demon.co.uk> raph@panache.demon.co.uk
(Raphael Mankin) wrote:

>The general rule is that the player who divides does not choose.
>This negative feedback prevents bias in the divisions -- assuming
>that there are no collusions.  A Byznatine generals' solution would
>be much more complex.

A what?  What's a Byznatine (or even Byzantine) generals' solution?

>Player 1 divides the pile into a 1-portion and a (n-1)-portion.
>Player 2 decides whether he or player 1 gets the 1-portion.  Whoever
>gets it drops out.  The division continues with n-1 players and the
>(n-1)-portion.

That ensures that each person is satisfied with his own share but the
new version of the problem requires that each person be satisfied that
nobody else has a better portion.

Player 3 may think that the 1-portion was too big but he has no chance
to object according to the above algorithm.

I believe the problem is insoluble because anyone who is not involved
in making a division can always veto it.  There is thus no incremental
approach which successively excludes people from the decision making.
This means that everyone must simultaneously agree to all divisions
but that is just a restatement of the problem.
--
Denis Howe <dbh@doc.ic.ac.uk>
Who is the potter and who the pot?