Saturday, September 13, 2014

Dividing Unequal Assets: Sperner's Lemma

I came across this article in the NY Times which I found pretty interesting. It pretty much what my title is, which is how to divide an unequal asset.

The example scenario that they gave is dividing up rent for an apartment where the rooms are of unequal size or have different characteristics, such as view or furnishing. Instead of each person paying an equal amount for each room, it actually makes sense for it to be split in an uneven manner.

Of course, the person currently getting the best room at the same equal rent contribution would not want to consider this. I think this exercise is best done by people before deciding to rent a place together, or by people who believe in fairness.

There is an interactive tool that allows people to do run this exercise.

It is called Sperner's Lemma and the detailed paper can be found here.

I have to admit that I have never heard of this before, thought I've always wondered about it. This can be used and applied to a lot of other things as well, not just the division of rent. Pretty much any unequal asset.

I am sure I will find a use to apply this formula in the future. Oh well, just some food for thought on a lazy Saturday night!

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