b9 wrote:
there is no difference between there being 2 or 3 or more people.
if the cutter does not get to choose until last, they will cut the cake as equally as they can, as any inequality in the cuts will result in a "smallest piece", and that is the piece the cutter would get.
Thank you all for your responses. That was a very interesting (and often entertaining) read !
b9's answer is pretty much what I also thought.
However, I then read another suggestion similar to Free-Hinter-System's, that convinced me I was initially wrong.
Free-Hinter-System wrote:
I think the best method is this: One person cuts three pieces. The two others name those that they would be willing to take. If their selections do not necessarily conflict (ie, both would accept two of the existing three) then each takes one of those they had named and the divider takes the remaining piece. If they do necessarily conflict (ie both would only accept the same one), then the divider takes one of the other two pieces and the two remaining pieces are "recompiled", cut by one of the two choosers, and the other of the two then chooses a piece, leaving one for the second cutter.
I guess I neglected the fact that, even if Person1 has an incentive to cut things "fairly" because he takes the last piece, the solution is still not "fair", because the measure of "fairness" of Person2 and Person3 may be different than Person1's.
I guess I initially assumed you could get to an absolutely exact 1/3, which is not realistic.
Then you could also add a bit of "game theory" by assuming that Person1 knows that Person2 and Person3 are polite and will not take the biggest piece. He would then have an incentive to cut one piece larger than the others.
19 Aug 2010, 2:49 pm
