Adjusted winner procedure
Adjusted winner procedure
Adjusted Winner (AW) is an algorithm for envy-free-item-allocation. Given two parties and some discrete goods, it returns a partition of the goods between the two parties that is: # Envy-free: Each party believes their share of the goods is as good as or better than their opponent's; # Equitable: The "relative happiness levels" of both parties from their shares are equal; # Pareto-optimal: no other allocation is better for one party and still at least as good for the other party; and # Involves splitting at most one good between the parties.
It is the only procedure that can satisfy all four properties simultaneously. Despite this, however, there are no accounts of the algorithm actually being used to resolve disputes.
The procedure was designed by steven-brams and alan-d.-taylor, and published in their book on fair division and later in a stand-alone book. Adjusted Winning was previously patented in the United States, but expired in 2016.
Algorithm Each party is given the list of goods and an equal, fixed number of points to distribute among them. They then assign values to each good and submit their (sealed) list of bids to an arbiter, who assigns each item to its highest bidder.
If the combined value of one party's goods are then greater than the other's, the algorithm then orders the higher-valued-party's goods in increasing order based on the ratio <math display="block">\frac{\text{value for higher-combined-value party}}{\text{value for lower-combined-value party}},</math> and begins transferring them from the higher-combined value party to the lower-combined value party until their valuations are almost equal (moving any more goods would cause the lower-combined-value party to now have a higher combined value than the other). The next good is then divided between the parties such that their values become the same. For the Israeli–Palestinian conflict; For the Spratly Islands dispute; the Panama Canal Treaties; and the 1980 Jolis v. Jolis divorce case.
Any two of these three properties can be satisfied simultaneously: An envy-free and equitable allocation could be found by giving each party an equal amount of each good. An envy-free and Pareto-optimal allocation could be found via Pareto-efficient envy-free division or weller's-theorem. * An equitable and Pareto-optimal allocation could be found via linear programming. Moreover, it is possible to find an allocation that, while being Pareto-optimal/envy-free or Pareto-optimal/equitable, would minimize the number of objects that have to be shared between two or more parties. This it usually considered the generalization of the Adjusted Winner procedure to three or more parties.
Adjusted Winner is designed for agents with positive valuations over the items. It can be generalized for parties with mixed (positive and negative) valuations, however.
Related procedures The brams–taylor-procedure was designed by the same authors, but it is instead a procedure for envy-free-cake-cutting: it handles heterogeneous resources ("cake") which are more challenging to divide than Adjusted Winning's homogeneous goods. Accordingly, BT guarantees only envy-freeness, not any other attributes.
The article on fair-division-experiments describes some laboratory experiments comparing AW to related procedures.