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How To Share a Cake Over the Internet
mikejuk writes "The problem to be solved sounds trivial — cut up a cake so that each person thinks they get a fair share. This classical problem gets even more difficult if the 'players' can't all see what is going on at the same time — for example because they are negotiating via the internet. Now there is an asynchronous algorithm that is guaranteed to be fair and it all depends on using an encrypted auction. The new algorithm is simple and easy to use, and might be the solution to any number of difficult situations where people need to share things so that everyone comes away happy."
The Cake is a Lie
I suspect that the deeper problem is that virtually nobody, even if they use the word 'fair' to describe the outcome they want, actually wants what this outcome provides...
The classic 'cake slicing' analogy holds in situations where it is agreed that the cake ought to be sliced evenly and there is simply the problem of doing the slicing. It does not cover the situations where ownership of the cake is my Manifest Destiny, where the cake was given to you by God, where possession by those subhumans of any part of the cake would be unacceptable, or where it is only just that the invisible hand allocate the cake...
My intended point was not that it is impossible to cope with utility functions in general; but that many real-world actors have hard minimums that add up to greater than one cake across the group you are dividing for. Sometimes, their utility functions even appear to be dependent on the deprivation of others of the cake, not of the possession of the cake themselves(and, in the somewhat-less-fucked-up-but-not-much-more-helpful, intermediate case you have the 'keeping up with the Joneses' where people continually recalibrate their utility functions based on the shares allocated around them).
There are certainly unequal-utility cases that are solvable, I just suspect that those don't include many of the real ones...