Icedawn
May 20th, 2008, 06:38 PM
Just wanted to post in support of the locked thread "what is the proper way to split this?" (http://www.redflagdeals.com/forums/showthread.php?t=590423)
It's actually not a stupid question, and instead, a question of a type that is the subject of considerable study by game theorists.
The question asked is analagous to asking how to generalize from a standard "shotgun auction" designed to achieve a fair valuation of an undividable asset between two people. http://en.wikipedia.org/wiki/Shotgun_clause
To rephrase the OP, the question is how, without objective measurements, can an asset be divided between N individuals fairly.
The common solution for n=2 is as stated, simply have one party divide the asset and the second party choose between the assets. (although in a variety of situations, this is actually non-optimal)
Off the top of my head, I don't know the solution for any given n.
However, to illustrate the complexity of the problem, I DO have a pseudo-solution for n = 2^x.
What you could do is simply repeat the procedure multiple times, by first dividing the 2^x people into two groups of 2^(x-1). The first group decides by consensus how to divide the asset, the second group then chooses.
Then, for each group, this process is repeated on the part of the asset assigned to them. That is, apply a recursive solution until you get back to the "solved" n=2 case.
just my two cents.
*edit* actually, just need solutions for n = prime number. So long a number is not prime, and if solutions exist for all n = prime number, then you can recurse down using the appropriate algorithm for each factor of n.
It's actually not a stupid question, and instead, a question of a type that is the subject of considerable study by game theorists.
The question asked is analagous to asking how to generalize from a standard "shotgun auction" designed to achieve a fair valuation of an undividable asset between two people. http://en.wikipedia.org/wiki/Shotgun_clause
To rephrase the OP, the question is how, without objective measurements, can an asset be divided between N individuals fairly.
The common solution for n=2 is as stated, simply have one party divide the asset and the second party choose between the assets. (although in a variety of situations, this is actually non-optimal)
Off the top of my head, I don't know the solution for any given n.
However, to illustrate the complexity of the problem, I DO have a pseudo-solution for n = 2^x.
What you could do is simply repeat the procedure multiple times, by first dividing the 2^x people into two groups of 2^(x-1). The first group decides by consensus how to divide the asset, the second group then chooses.
Then, for each group, this process is repeated on the part of the asset assigned to them. That is, apply a recursive solution until you get back to the "solved" n=2 case.
just my two cents.
*edit* actually, just need solutions for n = prime number. So long a number is not prime, and if solutions exist for all n = prime number, then you can recurse down using the appropriate algorithm for each factor of n.