National Post

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Saturday, July 17, 1999

Divorce, by the numbers
Two New York professors have devised a formula they say can guarantee a fair and 'envy-free' marital breakup. Their 'Adjusted Winner' algorithm could even be used to solve international conflicts

Robert Uhlig, with files from Elena Cherney and Steve Smith
The Daily Telegraph,with files from the National Post

Marcelo Del Pozo, Reuters
Mick Jagger and Jerry Hall ended their marriage recently with Hall reportedly agreeing to a $23-million settlement. Hall had consulted Anthony Julius, a top divorce lawyer who negotiated Princess of Wales multimillion-dollar split from Prince Charles. The Adjusted Winner formula of professors Steven Brams and Alan Taylor might have saved the two famous couples some money, or at least let them part 'envy-free.'

Agence France-Presse
Jerry Hall in a purple satin evening gown at Vivianne Westwood's 1997 spring-summer fashion show at the Louvre Carrousel.

Divorce lawyers may now be on the verge of obsolescence. Two American academics have devised, and patented, a mathematical formula that can take the stress and envy out of dividing property when a marriage breaks up.

Steven Brams, a political scientist at New York University, and Alan Taylor, a mathematician at Union College in Schenectady, N.Y., believe their algorithm, which they call "Adjusted Winner," can guarantee fair shares for both sides in a financial or alimony dispute.

The two professors came up with the formula after working on a simple mathematical conundrum -- how to divide a cake equally between three or more people.

One of the problems in dividing anything is to make sure the division is "envy-free." With cake, even when all of the pieces are the same size, some pieces might have more icing or decorations, leading to envy among the sharers of the cake.

Using the Adjusted Winner formula, everyone leaves the table believing they have the best piece of cake, (and they get to eat it, too), said Prof. Brams.

But divorce is a more complicated matter than dessert, and avoiding envy can be more difficult and consequential. The Adjusted Winner formula claims to make the split automatically.

It takes into account more than just the financial value of the assets at stake. It also assesses their relative emotional and practical value to each side. Here's how it works:

Both parties in a divorce must first allocate points to each of the items under dispute. The total number of points must add up to 100. Each item goes initially to whoever allocated it the most points, after which there is an adjustment process to square any inequalities.

Take a hypothetical divorcing couple, called Adam and Barbara, who own a townhouse, a holiday cottage and a sports car.

Adam loves the car and gives it 60 points. The townhouse, which he quite likes, he assigns 25 points, and the cottage, which does not particularly interest him, gets his remaining 15 points.

Barbara wants the townhouse and gives it 65 points, followed by the car, to which she assigns 25 points. Like Adam, she is unimpressed by the cottage, and assigns it her remaining 10 points.

Because each item initially goes to whoever gave them the most points, Adam gets the car and cottage and Barbara gets the townhouse. But this is not fair, because Adam has received two items, worth 75 of his 100 points, while Barbara obtained just one, worth 65.

This is where the adjustment is made. In this part of the process, the item rated most similarly by both Adam and Barbara -- the cottage, at 15 and 10 respectively -- is taken from Adam's share, so his total drops to 60.

Then simple algebra takes over. The cottage gets sold off, and Adam keeps three-fifths of its selling price, worth nine points to him, and Barbara gets the remaining two-fifths, worth four points to her. Both end up with the same final total of 69 points.

As well as being fair, the method is also envy-free as both ended up with the bulk of what they wanted.

There can, of course, be problems. One partner could start anticipating the number of points the other would assign certain possessions. But "the greater the difference in preferentials, the more we can mutually gain," said Prof. Brams.

A typical conflict resolved using the Adjusted Winner allows all parties to walk away with two-thirds to three-quarters of what they wanted, he added.

The process of getting what they want may also be less painful. In their recent book about their formula, The Win-Win Solution, the two professors chronicled the very public and messy breakups of Donald Trump and Marla Maples and of the Prince of Wales and Diana, the late Princess of Wales. "The Trumps and Charles and Di did work out settlements. But this would facilitate and [expedite] an agreement," says Prof. Brams.

The use of cold, hard numbers can be especially useful in situations where the parties involved are passionate enemies who can't bear to compromise in any way that might actually please the other person.

One mediator who has used Adjusted Winner in divorce cases, while lauding the process, noted that he has adapted the abstract theory to suit the human reality which confronts him in his office.

"When you apply a mathematical theory to something that involves people, you have to take human emotion into account," said Norman G. Lavery, who has used Adjusted Winner to mediate between 40 and 50 divorce cases at his Missoula, Mont., conflict-resolution practice.

Sometimes, for example, the point values a person assigns to objects act as a kind of alarm alerting Mr. Lavery to underlying issues that need to be resolved. "If they're worried about the chaise lounge they bought 22 years ago the day after they got married, and the chaise now has no wheels and is rusted out, we're not talking about a chaise anymore. Behind that there are some psychological, emotional things that need to be worked out."

Professors Brams and Taylor acknowledge the algorithm is not a panacea, but say it does minimize feelings of losing out.

"It takes much of the worry out of being an inept bargainer by providing a guarantee of fairness," said Prof. Brams. "The techniques help disputants resolve their differences and reach amicable agreements by having them decide how much they value things, rather than having a court or an arbitrator decide."

The academics say it can also be used by corporate executives to solve business disputes, divide assets and help settle problems with corporate mergers. It can be used for all kinds of interpersonal conflict, in fact, such as family feuds over estates.

And their ambitions for their algorithm go even further. They say Adjusted Winner can even be used in international conflicts such as that of Northern Ireland.

"We think it's a universal tool that could solve anything, from household disputes to international conflicts," said Prof. Brams.

"When parties are at loggerheads, such as in Northern Ireland, it can achieve a breakthrough."

And soon, software that runs the algorithm will be available for sale, so that Adam and Barbara can buy their divorce in a box. While New York University holds the patent, Prof. Brams would share any proceeds from his idea. But even though Adjusted Winner could prove lucrative in a world driven by both domestic and political strife, Prof. Brams pointed out that his formula can be used with only pencil and paper. "You don't really need the computer," he said.

But at least one Canadian family law expert said he does not believe that a math formula, no matter how elegant, could offer relief from the ugly reality of a marital dissolution.

Thomas Harding, Chairman of the Canadian Bar Association's Westminister Family subsection in Vancouver, scoffed at the idea of the Adjusted Winner formula, which he said makes no sense. He said Prof. Brams and Prof. Taylor are misguided to think the formula can stem a divorcing couple's envy.

"What they're saying is they're going to change the personality characteristics of the human race by playing a game of Monopoly," said Mr. Harding. "That seems pretty naive.

"Whether there is going to be envy relates more to the personalities involved than the division of the assets."

Mick Jagger and Jerry Hall ended their marriage recently with Hall reportedly agreeing to a $23-million settlement. Hall had consulted Anthony Julius, a top divorce lawyer who negotiated Princess of Wales multimillion-dollar split from Prince Charles. The Adjusted Winner formula of professors Steven Brams and Alan Taylor might have saved the two famous couples some money, or at least let them part 'envy-free.'

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