Let's assume our three players are Alice, Bill, and
Cindy. Furthermore by some
random means, they have decided that Alice is going to be the first
person to cut. Here is how the Selfridge-Conway Envy Free method of
fair division works.
The Method
- Alice cuts the cake into, in her opinion, three equal pieces
and hands them to Bill.
- Bill can trim at most one of the three pieces so as to create
at least a two-way tie for the largest piece. The trimmings are set
aside. The three pieces (possibly one piece might have been trimmed)
are then handed to Cindy.
- Cindy now chooses a piece she thinks is tied at least tied for
largest.
- Bill chooses next, from the remaining pieces, one that he considers
to be at least tied for largest, with one condition, if the piece that
was trimmed in Step 2 by Bill himself was not taken by
Cindy, then he has to
take it.
- Alice gets the piece that is left over.
Who Envies Whose Piece?
What about the Trimmed Part?