Tuesday, February 13, 2007
The Timeless Problem of Fair Division -vvw vvx

I usually avoid putting mathematics-related posts here but I think this one might interest some people who usually find math distasteful.

Here's an interesting article I came across some weeks ago.

Sharing Your Cake--and Eating it, Too

It's about the age old problem of sharing a piece of resource, e.g. cake, fairly between two or more parties. For the simpler version of two parties, the traditional solution of "you cut, I choose" works quite well. Except what if the cake is half chocolate and half strawberry, and person A hates chocolate while person B has no preference over either flavours? You might end up having one or more person feeling he got ripped off even though he did physically receive half a cake. The article talks about some guys who came up with a procedure that ensures each guy feels as though he gets at least half the cake.

Actually, it seems like the method was not really about fair division but rather, about dividing in such a way that nobody feels cheated. In my terms, I would say it depends on the individual's assigned utility on each part of the cake (assuming it's not homogeneous). In fact, I think it's trivial (my word for bloody obvious) that people assign different utility to different things. While optimization may not be a simple matter, to improve from simple physically equal division to a more optimal division (with equal or greater utility for each individual) should be quite easy.

Unfortunately, the property of obviousness is subjective. This is where I shall complain, like all Singaporeans do, about the stupidity of some systems, in this case, assigned duties in NS. Somehow, people have the idea that it is good and fair to divide duties such that everyone has the same proportion of guard duties and COS duties. This is retarded, just like in the cake cutting problem. Perhaps someone loves doing guard duties and another loves doing COS. It seems pretty obvious that a swap is one step towards the optimum but nooooooooooo. No wonder they say "military intelligence" is an oxymoron.

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Yiheng made 10:06 PM

1 Comments:

Hey! I once deliberated this concept of assigning duties in the army before. It works like SP or EP in which the people in the roster submit their disutilities/utilities in doing COS and guard duty anonymously, then impartially allocate duties ensuring maximum utility for everyone.

But I submit to you 2 problems in why this wouldn't work out in the army, other than the 'military intelligence part' One aspect is that the disutility of duty is dependant not just on personal preferences but our inevitable comparison with the disutilities of others. I mean, 2 COS duties won't seem too bad at first, but you do feel shittier if most of your friends are getting lesser. People still tend to be stuck in the quantity over quality mindset.

I can almost imagine Royston kao-pehing why he has two COS duties when Celester only has 1 thursday guard duty, yet if you ask him if he wants to swap, he would refuse.

Second is the fact that most people can't comprehend this exercise of assigning utility. Let alone people from the army. They might potentially see it as a system we cleverly devised for the scholars to somehow benefit from.

let's face it: People who aren't inducted in this still remain as terrible decision makers.
By  Soqcrates, at 11:28 PM  

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