The Fairest Way to Cut Cake

Question: How can your work on fair division theory be applied to political problems?


Steven Brams: Well we actually did apply one of our procedures to the 1978 Camp David Agreement between Israel and Egypt, which eventuated in a peace treaty in 1979. And there were several major issues dividing Israel and Egypt; the return of the Sinai after the ’73 war, which had been captured in the ’67 war for Israel, was recognitioned, diplomatic recognition by the Egyptians. And there were several other issues. And we assessed how important winning on these issues, getting one’s way, was to Israel was on the one hand and Egypt on the other. And we had given these attributions of importance using the algorithm to determine who would win on what issues. And it pretty much matched the actual agreement which took many months to negotiate; actually many years. And we think it would have been a much more efficient way to use the algorithm to determine who would win on what issues. And it pretty much matched the actual agreement, which took many months to negotiate, actually many years, and we think it would have been a much more efficient way to use this procedure and have countries indicate their interests using the procedure and then the procedure, the algorithm, would say who wins on what issues.


And it also can be used in more mundane circumstances, in dividing the marital property in a divorce. Again, you indicate how important it is to get the car, the house, the boat, the children, and so on, and it tells who gets what. And what we’ve found using these procedures is that most disputants can get between two-third and three-quarters of what they want because they want different things.


So, if you use an algorithm that does things fairly, makes the division what we call “envy free” so you don’t envy what the other person got because you got at least as much, it makes it equitable so that you both get the same amount, about 50%, that because the parties want often different things, they both can win. So, we actually call this a win-win solution. But we give more than that, an algorithm for making this division. So that’s some of the work that we’ve done on fair division.


And then we’ve done more theoretical work. This is work primarily with Allen Taylor, the mathematician at Union College. We came up with an algorithm for cutting a cake. Not just dividing separate goods like the house, the car, the boat, and so on. But what if the cake is something divisible, like land. How do you divide the land so that it satisfies these fairness properties and we came up with a cake cutting algorithm that basically generalizes the procedure everybody knows; I cut, you choose. That’s for two people. One person cuts 50/50 in terms of his preferences, and the other person will chose one half or the other. But her preferences are likely to be different from his preferences. So, she’s going to see one piece is worth more than 50%, but he, the cutter, has protected himself by dividing it 50/50. So I think we are all familiar with that. But how do you extend that to three persons, or four persons? So that’s what the algorithm did with the cake cutting algorithm. It’s actually very complicated so we’re not recommending this to be used practically to divide cake. So we came up with other procedures that are more practicable. And NYU, my university, actually patented one of these algorithms. It’s called Adjusted Winner. It’s a point allocation algorithm. So I’m the only political scientist I know with a U.S. Patent, and it’s an unusual patent. I think it was the first patent every issued for a legal dispute resolution procedure. Now, NYU has licensed the patent to a Boston law firm and a company has been formed called Fair Outcomes, Incorporated. It has a portfolio of these algorithms for settling disputes. And it’s in its embryonic stage, so I can’t report much on what’s happened. But I think that it’s a better way to solve disputes than the usual legal proceedings, which can be very costly to the litigants. They end up paying the lawyers most of their fees and it’s also usually quicker to use an algorithm than to litigate or simply negotiate sometimes over weeks, sometimes over months with a party you don’t particularly get along with. So, I’d like to see more of this actually used. And I’ve talked to bar associations and lawyers groups about this, and while some lawyers, of course, see their billable hours going down the drain if an algorithm is used rather than they’re using their great negotiating skills. But others see this as a procedure which would help them. And they could use their hours for more constructive purposes; advising people and to use this algorithm well. It’s a very simple algorithm. And to publicize it, we wrote this book, a popular book called The Win-Win Solution, which has not been translated into six languages. So, it seems to be attractive to people around the world. And we hope the company sells this idea and makes dispute resolution less burdensome and less trying for people.


Question: Will you apply your solution to the cake-cutting problem on your 70th birthday this year?


Steven Brams: Oh, well what I’m – in birthday parties, not necessarily my own, I’m usually the one asked to cut the cake, because I have done these kinds of things. But no, it’s a little too complicated if there are a lot of people. So, I am not recommending that this particular algorithm be used. But the one whereby you allocate points is very simple. It’s applicable to basically two-party disputes; those tend to be the most common. And we get some very nice properties out of it. We get the fact that not only is it envy-free, not only do both parties get the same amount – get more than the other party, but they get the same amount, about 50%. And it’s efficient, which means that there’s nothing better for both of them out there. So it has these kinds of guarantees which I think make the solution very attractive. And we’ve actually tested this in the laboratory and it’s been used in real life in a few cases, and it seems to work very well. So, we hope more people come around to the idea that this is, I think, the way to settle disputes. The alternative it’s actually called alternative dispute resolution, ADR, tends to take a more psychological approach. There’s a famous book called “Getting to Yes,” by Fisher and Ury, that says that if you communicate clearly, if you take into account the other side’s interests, you both can win also. I think the problem is that this is kind of naïve because people have strong incentives to exaggerate or to posture in negotiations. And what algorithms do is prevent that. It’s in your interests to be truthful, otherwise you may hurt yourself. In the absence of algorithms and in the absence of this kind of discipline, given my algorithm, you can give advice that you should be honest and communicate clearly, but that might not be in your best interests. That might not be rational. So, I think we need something more than what I call the “feel-good” approach.

Recorded on February 2, 2010
Interviewed by Austin Allen

Steven Brams’ solution to math’s "cake-cutting problem" can be applied to everything from divorce settlements to land disputes in the Middle East. But does he use it on his own birthday?

An organism found in dirt may lead to an anxiety vaccine, say scientists

Can dirt help us fight off stress? Groundbreaking new research shows how.

University of Colorado Boulder
Surprising Science
  • New research identifies a bacterium that helps block anxiety.
  • Scientists say this can lead to drugs for first responders and soldiers, preventing PTSD and other mental issues.
  • The finding builds on the hygiene hypothesis, first proposed in 1989.

Are modern societies trying too hard to be clean, at the detriment to public health? Scientists discovered that a microorganism living in dirt can actually be good for us, potentially helping the body to fight off stress. Harnessing its powers can lead to a "stress vaccine".

Researchers at the University of Colorado Boulder found that the fatty 10(Z)-hexadecenoic acid from the soil-residing bacterium Mycobacterium vaccae aids immune cells in blocking pathways that increase inflammation and the ability to combat stress.

The study's senior author and Integrative Physiology Professor Christopher Lowry described this fat as "one of the main ingredients" in the "special sauce" that causes the beneficial effects of the bacterium.

The finding goes hand in hand with the "hygiene hypothesis," initially proposed in 1989 by the British scientist David Strachan. He maintained that our generally sterile modern world prevents children from being exposed to certain microorganisms, resulting in compromised immune systems and greater incidences of asthma and allergies.

Contemporary research fine-tuned the hypothesis, finding that not interacting with so-called "old friends" or helpful microbes in the soil and the environment, rather than the ones that cause illnesses, is what's detrimental. In particular, our mental health could be at stake.

"The idea is that as humans have moved away from farms and an agricultural or hunter-gatherer existence into cities, we have lost contact with organisms that served to regulate our immune system and suppress inappropriate inflammation," explained Lowry. "That has put us at higher risk for inflammatory disease and stress-related psychiatric disorders."

University of Colorado Boulder

Christopher Lowry

This is not the first study on the subject from Lowry, who published previous work showing the connection between being exposed to healthy bacteria and mental health. He found that being raised with animals and dust in a rural environment helps children develop more stress-proof immune systems. Such kids were also likely to be less at risk for mental illnesses than people living in the city without pets.

Lowry's other work also pointed out that the soil-based bacterium Mycobacterium vaccae acts like an antidepressant when injected into rodents. It alters their behavior and has lasting anti-inflammatory effects on the brain, according to the press release from the University of Colorado Boulder. Prolonged inflammation can lead to such stress-related disorders as PTSD.

The new study from Lowry and his team identified why that worked by pinpointing the specific fatty acid responsible. They showed that when the 10(Z)-hexadecenoic acid gets into cells, it works like a lock, attaching itself to the peroxisome proliferator-activated receptor (PPAR). This allows it to block a number of key pathways responsible for inflammation. Pre-treating the cells with the acid (or lipid) made them withstand inflammation better.

Lowry thinks this understanding can lead to creating a "stress vaccine" that can be given to people in high-stress jobs, like first responders or soldiers. The vaccine can prevent the psychological effects of stress.

What's more, this friendly bacterium is not the only potentially helpful organism we can find in soil.

"This is just one strain of one species of one type of bacterium that is found in the soil but there are millions of other strains in soils," said Lowry. "We are just beginning to see the tip of the iceberg in terms of identifying the mechanisms through which they have evolved to keep us healthy. It should inspire awe in all of us."

Check out the study published in the journal Psychopharmacology.

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