A well-known method of dividing a cake between two people is to have the first person to cut the cake and have the second person to have the first pick. This will guarantee that the first person will cut the cake in half so that the second person cannot leave him with a smaller piece.
Now we want to divide the cake among n people. Let's make the following assumptions:
(a) Each person cannot cut the cake more than once
(b) Everyone is logical
(c) Everyone wishes to get the largest possible piece
(d) Everyone wishes to narrow the gap with those who have a bigger piece than he does
(e) No one cares about anyone who has a smaller piece than themselves.
Can you generalize the strategy to n people? Give your logical steps/proof that this strategy will yield a fair result.
(In reply to
One fair cut deserves another by Steve Herman)
I think it's pretty clear that whoever is cutting has to cut a
one-person slice. If, for instance, there are 4 people, and the
first cutter tries to cut the cake in half, and one "half" is slightly
larger than the other, then whoever has to share the smaller "half"
with the cutter has been damaged through no fault of his/her own.
re: One fair cut deserves another
