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Better Ways to Cut a Cake

Posted by garym on November 6, 2006 - 12:14pm

I'm not sure if this is political news, or just good advice in general, but the long and short of it is a new paper by NYU mathematicians who have methodically set out the recipies for truly fair ways to carve a cake:

a new 2-person surplus procedure (SP), which induces the players to be truthful in order to maximize their minimum allocations, leads to a proportionally equitable division of the surplus -- the part that remains after each player receives 50% -- by giving each person exactly the same proportion of the surplus as he or she values it.
For n > 2 persons, a new equitable procedure (EP) yields a maximally equitable division of a cake. This division gives all players the highest common value that they can achieve and induces truthfulness, but it may not be envy-free. The applicability of SP and EP to the fair division of a heterogeneous, divisible good, like land, is briefly discussed.
[ via Better Ways to Cut a Cake ]

Yes, it is typically academically dense and opaque, but vital conflict resolution fare nonetheless. If you'd really rather the executive summary, you can read the English Version here.

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Faulty Logic

Submitted by Dodge on November 6, 2006 - 5:17pm.

The hypothesis falls apart because the authors failed to consider the case where the number of cuts is n-n where n is the number of cake eaters. Their assumption that n-1 is always the case is wrong.

n-n cuts is the case where someone wants to have their cake and eat it too. All of it. The result in this case is always the same no matter what the value of n.

Freaken philosophers eh! Even worse if they know some mathematics and can apply for grant money.

Faulty Disproofs

Submitted by garym on November 6, 2006 - 8:10pm.

Actually, unless I'm mistaken on my Game Theory, the case you describe is covered too, only it is covered by a different rule, and I think that rule might be the Nash Equalibria made famous by the movie A Beautiful Mind: Greed is self-deprecating; everybody loses. This is perhaps a Darwinistic reason for our human propensity to cling to and defend groups, even those groups into which we have been arbitrarily assigned: the community gains most where the participants will give up advantage to the whole.

There is, however, still a very valid criticism of the Game Theory approach to conflict resolution, that being how the sense of value in humans may not be discernable, for example, Prisoners Dilema fails to account for the advantages to mobsters of longer sentencing vs vendettas post-release.

There's still one further criticism to the whole notion of Game Theory, and for that I turn to the eminent Danish mathematician Piet Hein:

Solutions to problems
are easy to find:
the problem's a great
contribution.
What's truly an art
is to wring from your mind
a problem to fit
a solution.

garym: ict evangelist - musician - whatever