But how can this site take into account just how much (more) I deserve?
The āI cut, you chooseā method was the classic way to divide a weed bag fairly and ensure everyone got the same amount of herb. You know, back when it was illegal. Oh, itās still illegal in your state? Iām so sorry to hear that.
No, but this site can. 
I joke, I jokeā¦
This looks like they took the general ideas of the estate division chapter of Neal Stephensonās Cryptonomicon and ran with it into a fully operational system.
Atoms?
Krypton will always be envious of Barium
Many think the source of the word āatomā is ānot divisibleā, but scholars of ancient Greek agree that in contemporary contexts, it meant ānot divisible fairlyā.
Decorations are an interesting question, but my favorite scales-to-any-number-of-people solution to cake cutting it in http://www.amazon.com/How-Cut-Cake-Mathematical-Conundrums/dp/0199205906
- Make a single cut.
- Life the knife and slowly rotate clockwise.
- At any time, anyone may say āCut.ā
- When they do, make a cut, and that person who spoke gets the piece.
At the end, anyone who thinks their piece is too small must think someone elseās is too large, so they could have said ācutā before it got that large. Or, they think there wasnāt enough cake in the first place, which is not a problem that any division method can solve.
I was thinking just that. Although itās a little more complicated for the cases with both benefit and cost (they only show that as āSplitting Rentā, but it could be generalized to many more things), because instead of just saying how much you want something, you say how much youād be willing to pay for it. So itās maximizing two variables, your desire and the amount of money you ultimately end up spending.
That seems a much better method than the generalized n>2 method I always heard for cutting cake fairly.
The method I heard was that person A cuts a slice. Then person B either cuts a new slice, or cuts a slice out of Aās. Each person moving forward can cut a slice from the cake or from anyone elseās slice.
The problem with this method that I never saw mentioned is that it doesnāt solve the problem of being a dick. To wit: Person A precisely cuts a 1/nth piece, and then Person B cuts himself 99% of Aās slice just to be a dick.
You solution doesnāt seem to allow that.
(Perhaps my version could be amended by allowing multiple rounds until it all settles. But I think the existence of the dick may preclude the possibility of settling.)
Cupcakes.
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