This protocol for fair cake division works, but only just, for more than 2 people:
Note that if each participant
is supremely egotistical
of them can complain
: each of the non-slicers cannot afford to wait for a piece
larger than an equal share
(else she risk
s another one of the non-slicers cutting in
, and getting more than her
fair share). And the slicer is assured by this that all pieces are equal, hence he's not cheated, either.
Of course, problems start when if you assume that coalitions are allowed. In particular, the non-slicers can gang up against the slicer, and by cooperating get each more than her share. But that requires a certain degree of cooperation, which is usually not assumed in cake-sharing situations.