Sunday, June 28, 2009

Fair Division in Treaty Negotiations

Raiffa in "the art and science of negotiation" describes the Panama Canal treaty negotiations in 1974. He got the value each country attached to each issue from the US negotiating team. In the fair division book chapter 5 describes this negotiation using their Adjusted winner algorithm. One weakness with this algorithm is that all items must be divisible.
There is no way to fix issues as non divisible as there is in my program (you will need to remove s.t. wor3 and s.t. wor4).
So if you take the data as

data;
param m := 2;
param n := 9;
param o := 1;

/*m people, n divisible items, o non divisible items*/
/*
1 non divisible items expansion routes
US Panama
US defense rights 22 9
use rights 22 15
Land and water 15 15
expansion rights 14 3
duration 11 15
expansion routes 6 5
compensation 4 11
jurisdiction 2 7
US military rights 2 7
defense role of Panama 2 13
*/

param c : 1 2 3 4 5 6 7 8 9 :=
1 22 22 15 14 11 4 2 2 2
2 9 15 15 3 15 11 7 7 13;

param d : 1 :=
1 6
2 5;
end;

where expansion routes is not divisible.

US gets item number us defense rights, use rights, expansion rights,expansion routes
Panama gets duration, expansion routes, compensation, jurisdiction and us military rights. For Land and water the US gets .1333 of this and Panama get 0.86667 which is ok as land and water are the sorts of things that can be divided up. Each country got 66% of what they wanted, In this case my program gets the same results as the Adjusted winner program.

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