2. Charlie cuts the cake into three pieces that are equally valuable from his perspective
3. Alice identifies her first choice.
4. Bob identifies his first choice from the remaining two. Charlie gets the remaining one.
5. Bob trims either his or Alices piece.
6. Alice identifies her first choice.
Simpler. Is there a fault i don't see?
What if Alice thinks that the piece Bob gave to Charlie was the 2nd best piece, and after Bob's trimming, the remaining pieces are both worse than what Charlie has?
Edit: come on, are we really expected to read TFA or even to read carefully the first comment in the thread where it was clearly written “so that none of them envies other pieces” before commenting? (Seriously: I was obviously wrong. As punishment I leave my original comment here and now I’ll read the article five times.)
Alice picks one piece, Bob picks another, Charlie gets the third.
Now Bob thinks his piece is a bit too small compared to Alice's and transfers Alice's butter rose onto his piece.
Alice either swaps or doesn't.
Charlie now sees that either Alice or Bob has a cake piece with TWO butter roses and is VERY envious.
Charlie has the first cut, so he can cut horizontally and make a tiny piece with 3 butter roses on top. he either gets his three butter roses or a bigger piece of cake, their relative value is still the same for him.
One devides and gets the worst based on the others opinions, then leaves with his piece. repeat.