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The paper, authored by New York University's Steven Brams, Wilfrid Laurier University's D. Marc Kilgour, and the University of Graz's Christian Klamler and published this month in Notices of the American Mathematical Society, outlines a pair of algorithms that are based on the self-identified priorities of the parties.
Journal Reference:
Steven J. Brams, D. Marc Kilgour, Christian Klamler. Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm. Notices of the American Mathematical Society, 2014; 61 (02): 130 DOI: 10.1090/noti1075
Interesting, although I'm not sure I agree. Let's take a look at the application given:
Quote:
For example, assume players A and B rank four items, going from left to right, as follows:
A: 1 2 3 4 B: 2 3 4 1
Now, if we give A item 1 and B item 2 (their most preferred), the next unallocated item on both their lists is item 3. Who should get it? The algorithm gives it to A and gives item 4 to B, which is an envy-free allocation because each player prefers its items to the other player's:
A prefers item 1 to 2 and item 3 to 4 B prefers item 2 to 3 and item 4 to 1
The way I read this, in the first round A and B each get their first choice. So far, so good.
Once items 1 and 2 are eliminated, though, the items left are 3 and 4. According to these facts, both A and B prefer 3 to 4, so if A gets item 3 and B gets item 4, A is getting an item that B would have wanted above the item that B winds up with. Why wouldn't B come out of this thinking "I'm glad I got item 2, but I thought item 3 was way better than item 4, so I'm not happy that I got stuck with item 4"?
Location: On the "Left Coast", somewhere in "the Land of Fruits & Nuts"
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Quote:
Originally Posted by nifear
The paper, authored by New York University's Steven Brams, Wilfrid Laurier University's D. Marc Kilgour, and the University of Graz's Christian Klamler and published this month in Notices of the American Mathematical Society, outlines a pair of algorithms that are based on the self-identified priorities of the parties.
Journal Reference:
Steven J. Brams, D. Marc Kilgour, Christian Klamler. Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm. Notices of the American Mathematical Society, 2014; 61 (02): 130 DOI: 10.1090/noti1075
Obviously the authors have never been involved in what's euphemistically known as a "Hi-Conflict Divorce", frequently where one partner has BPD (Borderline Personality Disorder), and notions of "equity", "fairness", "logic", "agreements", and even "envy", become totally irrelevant!
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