Two observations I find interesting: 1. Order matters. In the the-slice solution, it is much better to be Charlie. This is because there is a chance you will g

Two observations I find interesting: 1. Order matters. In the the-slice solution, it is much better to be Charlie. This is because there is a chance you will get more than your expected share if value of the cake, because you start out with a guaranteed 1/3 value (from your perspective) plus a chance of extra if Bob trims. This seems to break the "no envy" clause in a very human way: it is true that no player is envious of the other person's choice (that is, no one wants to swap), but Alice and Bob may be envious of Charlie's increased happiness, feeling it unfair. (It sounds like this may have changed in the new algorithm, with the sending away of dominant players. But I believe it then may be better to be A or B.) 2. Along similar lines, none of the algorithms concern themselves with maximizing total happiness. Point 2 can be seen even in the two-player version: Say a cake is half chocolate and half vanilla. Suppose A adores vanilla and assigns zero value to chocolate, while B can't even tell the difference between them. If A cuts first, she will need to divide it in half across the two flavors to make two "equal" slices of chocolate-and-vanilla ("equal" in her eyes). B choose at random and gets half a cake's worth of happiness, while A gets a quarter of a cake's worth, leading to an inefficiency of a quarter cake. If B cut first (presumably in half at random, since he doesn't distinguish between the flavors), there is a good chance A's happiness will increase, although there's very little chance it will come out perfect.