An algorithm designed to divide property, such as in a matrimonial dissolution, or in contract negotiations between management and labor, such as in the current Hollywood writers strike, is a pillar of a new commercial enterprise that seeks to reach fair and equitable outcomes more efficiently than those resulting from traditional negotiations. The algorithm, or “Adjusted Winner” system, is one of three systems currently offered by Fair Outcomes, Inc. (, two of which were co-invented by Steven Brams, a professor of politics at NYU. Fair Outcomes, Inc. is a Boston-based company founded and operated by attorneys, game theorists, and computer scientists.

Fair Outcomes, Inc. focuses on three methods of dispute resolution using its proprietary systems:

  • Fair Buy-Sell: This patent-pending system is used by joint owners of property-such as business partners, shareholders, and married couples-who wish to bring their joint ownership to an end on terms that are mutually acceptable and legally enforceable.
  • Fair Proposals: This patent-pending system is employed in matters in which one party is seeking money or other concessions from another party, such as in a lawsuit, and allows each party to propose a resolution that it deems fair in a manner that is credible but non-prejudicial.
  • Fair Division: The patented “Adjusted Winner” system seeks to divide up multiple items of property or resolve multiple issues in disputes. Adjusted Winner, described in Brams’ co-authored The Win-Win Solution: Guaranteeing Fair Shares to Everybody (W.W. Norton), has been applied to conflicts ranging from divorce to international border disputes.

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In cases in which two parties must divide up multiple items or resolve multiple issues, Adjusted Winner enables them to do so in a fair and efficient manner. It embodies a bidding process that guarantees each party at least 1/2 of what that party considers to be the total value of all of the items or issues in question-and usually allows each party to receive between 2/3 and 3/4 of that value-facilitating a win-win outcome.

Traditionally, fair division of property has used the “you cut, I choose” method. As with a birthday cake divided between two people, one person cuts the cake while the other chooses the piece he or she prefers. However, “cut-and-choose” lacks equitability-that is, the subjective value that the two people place on the pieces they get may not be the same. For example, suppose one-half of the cake is frosted with vanilla icing and the other with chocolate icing, and suppose the cutter values chocolate icing twice as much as vanilla. It is possible that the cutter’s valuation of the piece she gets will be less than the chooser’s valuation of the piece he gets, making the division inequitable.

Brams, Michael Jones of Montclair State University, and Christian Klamler of Austria’s University of Graz developed two methods to make such divisions equitable: the Surplus Procedure (SP) and the Equitability Procedure (EP). Their work was originally described in the December 2006 issue of the Notices of the American Mathematical Society.

Using SP, a mathematical algorithm, two parties can divide property in a way that leaves each with a 50 percent share plus some part of the surplus that remains. The algorithm takes into account which features of a commodity are valued most by each party. For a division among three or more parties, the EP method gives all parties more-than proportional shares. Both SP and EP are “strategy-proof”: the players cannot assuredly manipulate these procedures to their advantage. Brams and his co-authors offer division of land as an example of how their algorithm works. For example, land bordering water might be more valuable to one party, while land bordering a forest might be more valuable to another. The SP method shows how to divide the land in such a way that the both parties receive approximately the same value from the parcels of land they get.

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