3QD Monday Musing: Cake Theory and Sri Lanka's President

Even though we are for the most part a "links" blog, the editors of 3 Quarks Daily have decided that we will take turns writing a short column each Monday, where we can talk about whatever we feel like. No one else wanted to do the first one so it has fallen to me by default, and I'll take this opportunity to just ramble on about a bunch of things...

Last fall, the President of Sri Lanka, Chandrika Bandaranaike Kumaratunga, gave a very good speech on conflict resolution at the Asia Society in New York City, at which I was present, and in which, among other things, she commented that:

Conflict resolution has become today, a high profile subject taught in universities and lectured on, at many a seminar and conference. Experts in this field are held in awe in some circles in many countries. Yet, conflict resolution is not new. It has only been packaged differently in our age.

Afterwards, there was a reception and a friend introduced me to the President, to whom I said that although she was right about there being a lot of fancy repackaging of age-old wisdom in the academic field of conflict resolution, there have been some interesting intellectual developments, in mathematics, for example, which do provide new tools for avoiding or even resolving conflicts. As an example, I brought up cake theory.

Cake theory basically looks at methods of how to divide a cake among n persons so that each of them feels they got a fair share. For example, for two persons, one method would be to have one person cut the cake into two pieces, after which the other person gets to choose which piece she wants. This obviously gives the first person great incentive to carefully cut the cake into equal halves, otherwise she will get stuck with the smaller one. It gets a little more complicated for greater numbers of persons, but the problem has been solved for arbitrary n.

One method for dividing the cake into an arbitrary number of portions is described in the Wikipedia this way:

Another method begins with the first person portioning off 1 / n of the resource (for n people). Each following person then examines the portion in turn, removing a part for themselves if they believe the portion to be larger than 1 / n. The last person to remove part receives the portion. The process continues until the entire resource has been fairly divided.

The problem may be modified by requiring the division to be envy-free: that is, each recipient should not only believe that they have at least 1 / n of the resource (according to their measure) but that no other recipient has received more than they have.

The President seemed interested, so I went on to point out that this method has already been used in the Law of the Sea Treaty to divide under-sea mining resources between industrialized and developing countries:

The Convention of the Law of the Sea, which went into effect in 1994, incorporates such a scheme to protect the interests of developing countries when a highly industrialized nation wants to mine a portion of the seabed underlying international waters. The country seeking to mine would divide that area into two portions. An independent agency representing the developing countries would then choose one of the two tracts, reserving it for future use. [See more here.]

At this point, Madam President's philistine handlers decided that she had been subjected to a long enough insane-sounding harangue on "cakes" and "the sea" by me, and she was dragged off to be introduced to someone more polite. But she was interested, and subsequently had my wife, Margit, and me over to the Presidential Palace in Columbo for drinks when we were visiting friends in Sri Lanka later in the year.

Anyhow, we had a great time in Sri Lanka, and were saddened to hear that, among so many lives and so much else, the beautiful old hotel we stayed at on the beach in the coastal city of Galle was destroyed by the tsunami. But even that most horrific of disasters may have a silver lining in terms of our theme of conflict resolution, making possible more fruitful negotiations between the Sri Lankan government and the Tamil Tigers (the LTTE): there is more about that here.

I was reminded of all this by a great post yesterday at Something Similar by Jeff Hodges, about The Fair Division Calculator.

Have a good week!