This protocol for fair cake division works, but only just, for more than 2 people:
Note that if each
participant is supremely
egotistical,
none of them can
complain: each of the non-slicers cannot afford to wait for a
piece larger than an
equal share (else she
risks 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.