A formula that promises a fair way for divorcing couples to divide their property has been devised by a mathematician and a political scientist.
“Adjusted Winner” uses a basic mathematical conundrum how to divide a cake equally between three or more people to guarantee fair shares for both sides in a financial or alimony dispute.
Instead of looking at the financial worth of the property, the patented method assesses its relative emotional and practical value to each party. It can also be used by corporate executives to solve business disputes.
The challenge is to ensure the division is “envy-free,” so that the parties feel they have a slice at least as good as anyone else, said Steven Brams, a political scientist at New York University, and Alan Taylor, a mathematician at Union College in Schenectady, N.Y.
With a cake, a fair, envy-free division is easy to achieve. But in divorce settlements and corporate mergers, avoiding envy can be difficult. “Adjusted Winner” claims to make the split automatically.
“It takes much of the worry out of being an inept bargainer by providing a guarantee of fairness,” said Mr. 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 method relies on each party allocating points out of 100 to each of the items of property under dispute. Each item goes initially to whoever allocated it the most points, after which there is an adjustment process to square any inequalities.
In the case of a divorcing couple called Adam and Barbara who own a town house, a holiday cottage and a sports car, Adam loves the car and gives it 60 points.
The town house, which he quite likes, he assigns 25 points, and the cottage, which does not particularly bother him, gets his remaining 15 points.
Barbara wants the town house 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.
As each item initially goes to whoever allotted it the most points, Adam gets the car and cottage and Barbara gets the town house. But this is not fair as Adam has two items, and 75 of his 100 points, while Barbara obtained just one, worth 65.
In the adjustment 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.
If the cottage is sold with Adam keeping three-fifths of its selling price, worth nine points to him, and Barbara getting 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.
Hilary Siddle, chairman of Britain’s Family Law Committee of the Law Society, said she doubted if the formula could deal with complexities such as dividing up homes suffering from “negative equity.” For instance, it might seem that Jerry Hall received an inequitable share of Mick Jagger’s fortune when she agreed to a settlement believed to be worth around $16 million.
It is well known that the couple’s favorite home is La Forchette, a chateau in the Loire Valley. Had they used “Adjusted Winner,” both parties are likely to have scored it highly.
Downe House, a Georgian mansion on Richmond Hill, west London, would probably have been more highly prized by Miss Hall than Mr. Jagger.
Mr. Jagger is thought to value their Japanese home on the Caribbean island of Mustique and their town house in Manhattan. As an avid classic car enthusiast, he is likely to have rated his $3.2 million collection more highly.
Mr. Jagger is also said to be very attached to his impressive collection of art and furniture, which is worth an estimated $48 million.
On this basis, a possible outcome is that Miss Hall assigned 40 points to La Forchette, 35 to Downe House, 10 each to the Mustique and New York residences, three points to the art collection and two points to the classic cars.
Mr. Jagger, using the same method, could also have assigned 40 to La Forchette, 25 to Mustique, 10 to New York and five points each to Downe House, the classic cars and the art collection.
Thus, Mr. Jagger gets Mustique, the cars and art, worth 35 points, while Miss Hall receives Downe House alone, also worth 35 points.
This leaves Mr. Jagger and Miss Hall to take equal shares of La Forchette and the New York residence, either financially or as a time-share arrangement.