The Adjusted Winner (AW) procedure is a conflict resolution mechanism designed to ensure a fair and equitable division of assets between two parties. Developed by Steven Brams and Alan Taylor in the mid-1990s, this mathematical approach addresses the complexities of dividing both divisible and indivisible items in a manner that is envy-free, equitable, and Pareto-optimal.

Historical Background

The AW procedure emerged from the broader study of fair division in game theory, a field within mathematics and economics concerned with dividing goods or resources among individuals in a way that each person believes they have received their fair share. Brams and Taylor introduced this method in their 1996 book "Fair Division: From Cake-Cutting to Dispute Resolution," which expanded on previous efforts exploring fair division algorithms.

The procedure has its roots in game theory and cooperative negotiation principles, aiming to provide a structured method for resolving disputes and dividing resources in a way that is mathematically fair and acceptable to all parties involved. Although initially theoretical, the AW procedure has been applied to a variety of contexts, including divorce settlements, inheritance disputes, business and labor negotiations, as well as international treaties.

Definition and Basic Mathematics

The AW procedure begins with each party assigning a certain number of points (typically 100) to the items being divided, reflecting the subjective value each party places on each item. These points are then used to determine the initial allocation of items to the parties.

The steps of the procedure are as follows:

• Bid Allocation: Each party assigns points to items according to their individual valuations using pair-wise comparison.
• Initial Allocation: Items are initially allocated to the party that values them the most, ensuring that each item is allocated to the party that has assigned the highest number of points to it.
• Adjustment Phase: If one party receives more than half of the total points, adjustments are made to equalize the allocations. If the item is indicated as divisible, this is done by transferring parts of item(s) from one party to the other. The transfer is made in such a way that the perceived value of the transferred items is equalized between both parties. If the item is not divisible, the optimum combination of whole items is transferred to get as close to equality as possible.

The AW procedure guarantees that the final allocation 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 at least as good for the other party.
• Involves Splitting at Most One Good: Only one item may need to be divided to achieve the above properties.

Use in Peace Negotiations

One of the notable applications of the AW procedure is in peace negotiations, particularly in resolving territorial disputes. An example is the theoretical application to the Israeli-Palestinian conflict. The procedure involves defining the contested territories (such as the West Bank, Gaza Strip, and Jerusalem) and allowing each side to assign points based on their valuations of these territories.

The AW procedure then provides a solution that allocates the territories in a way that meets the fair division criteria. For instance, one possible outcome could be that one party receives control over the West Bank and another receives Gaza, while Jerusalem might be shared or split to ensure equitability. This method highlights the potential of the AW procedure to offer a structured and fair approach to resolving complex international disputes.

Potential Use in Civil Law Cases

The AW procedure's applicability extends beyond international disputes to various civil law cases, such as divorce settlements and inheritance disputes. In divorce settlements, for instance, the procedure can help divide marital assets, including property, investments, and personal items, in a way that both parties feel is fair. Each spouse assigns points to the assets, and the procedure ensures that the final division is both envy-free and equitable.

Similarly, in inheritance disputes, the AW procedure can be used to divide the estate among heirs. Each heir assigns points to the items in the estate based on their personal valuations, and the procedure ensures a fair distribution that considers the subjective values of each heir.

Conclusion and Future Prospects

The Adjusted Winner procedure represents a significant advancement in the field of fair division and dispute resolution. Its mathematical foundation and structured approach offer a reliable method for achieving fair and equitable outcomes in a variety of contexts. While the procedure has been theoretically validated and applied in simulated scenarios, its adoption in real-world cases has been limited.

Looking to the future, the AW procedure has the potential to become a more widely used tool in legal and negotiation settings. NextLevel Mediation has implemented the AW procedure as part of its suite of integrated tools to assist the mediator / neutral. We believe as awareness of its benefits grows, it will be integrated into online dispute resolution mechanisms, providing a fair and efficient method for resolving conflicts.