L'Ombre de l'Olivier

The Shadow of the Olive Tree

being the maunderings of an Englishman on the Côte d'Azur

05 September 2007 Blog Home : September 2007 : Permalink

The Cake Cutting Metaphor

In his interesting book on Copyright “Bounty Hunters”, Greg London has section about "cake cutting" where he describes ways that two people can agree to cut a cake so they each get a fair share:

The basic cake cutting algorithm works like this: There is a cake treated as common property between two people. These two people want to find a way to cut the cake such that both of them get a fair piece. A solution is to have one person of the two cut the cake, and then allow the other person to pick which piece they want.

This is a fairly robust algorithm because it will produce a fair result under most circumstances, regardless of how selfish or selfless the actors are. The person cutting the cake has incentive to cut fairly because if one piece is noticeably bigger, the other person will naturally tend to pick that piece, and the person who cut the cake will get a smaller piece. Selfish cake cutters are given incentive to cut fairly.

But there are other algorithms that you could use to cut the cake. For example, you could have one person cut the cake and pick which piece they get. This produces a fair result only if the cake-cutter is a reasonably fair person. The model shows that this algorithm will produce an unfair result if the cake-cutter serves only their self-interest.

Another approach is to bring in a third person to act as an impartial cake-cutter, have them cut the cake, and distribute it accordingly. This is also subject to abuse when unfair players are in the system. The third person acting as impartial cake cutter is an actor the same as any of the other players, and could be filled by various people across the spectrum of selfish to selfless.

A model that relies on finding a “fair” or “impartial” individual for the algorithm to achieve a fair result is not nearly as robust as an algorithm that doesn't care about the internal drives of the players but achieves a fair result anyway.

It occurs to me that, as a rough approximation, the "one person cuts, the other chooses" algorithm describes the market based approach where you have roughly equal numebrs of buyers and sellers, the "one person cuts AND chooses" one describes a mnopoly (or monopsony) and the "third party decides" one descibes the classic government intervention case.

The more I think about it the more I realise that the metaphor is surprisingly good. All of these algorthms can scale quite well to handle cases where the number of parties is greater than 2 without much thought and all of them have sufficient relationship to real life that it becomes easy to imagine that an unfair player can find a way to get more than he should. It is easiest of course in the monopoly case but it is quite easy to imagine a crooked "neutral party" in the third choice and a person who threatens his opposite number(s) in the first choice - "You want me to use this knife on you too? no? well pick the smaller portion ok?"

But it occurs to me that the metaphor also explains nicely why socialism and big government doesn't work. These two rely on a neutral third party for goodness and it should be obvious that neutral third parties, even if perfect and impartial, do not come for free. In other words they must somehow take a rake off to survive and that explains why the government solution is only to be preferred as a last resort - it is inherently wasteful.