alvin roth

Nobel Prizes: Al Roth and Lloyd Shapley

Great choices. Al Roth for matching and the design of new types of markets. Lloyd Shapley for fundamental contributions to game theory and mathematical economics including the Gale-Shapley algorithm which is a cornerstone of the matching methods Al Roth pioneered. I am especially pleased about this because of Roth’s great work on improving kidney allocation. Here is Roth’s blog, Market Design and here he is giving a talk at Google. Here is what I wrote in 2010 about Roth

Roth has applied heavy-duty theory to the very practical problems of matching doctors to residency programs, children to schools, economists to departments and kidneys to patients in a way that is stable, incentive-compatible, and maximizes the gains from exchange.  In my view, Roth is the most influential economist working today. Influential among other economists?  Yes.  But what I really mean is influential in the world.

Previous posts on MR about Roth (also here). Roth’s papers.

More soon.

Al Roth: Entrepreneurial Economist

“I’ve always been interested in using mathematics to make the world work better.”

That’s Al Roth from a profile in Forbes.  Roth has applied heavy-duty theory to the very practical problems of matching doctors to residency programs, children to schools, economists to departments and kidneys to patients in a way that is stable, incentive-compatible, and maximizes the gains from exchange.  In my view, Roth is the most influential economist working today. Influential among other economists?  Yes.  But what I really mean is influential in the world.

Roth’s homepage has many introductory papers as well as more technical material, here is his blog, Market Design and here is good video, Roth at Google

*Where Economics Went Wrong: Chicago’s Abandonment of Classical Liberalism*

That is the new book by David Colander and Craig Freedman, here is one short bit:

The best way of conveying our conception of what is at least suggestive of a Classical Liberal stance is to present a handful of economists who, in our view, reflect this attitude.  We have chosen six economists: Edward Leamer, Ariel Rubinstein, Alvin Roth, Paul Romer, Amartya Sen, and Dani Rodrik.  Each have, in our view, displayed a Classical Liberal attitude to methodology in important aspects of their work.

I am very much in favor of what the authors propose here, although I might reserve the term classical liberal for the more traditional political distinction.

Dear Canada: Don’t Ban Paid Blood Plasma Donation

The United States has been called the OPEC of blood plasma because it exports hundreds of millions of dollars worth to other countries. Why does the US dominate the blood plasma industry? Because in the U.S. it’s legal to pay donors which increases supply. Some provinces in Canada have also allowed paid donors but 80% of the blood plasma given to Canadians is imported from the United States and, to make matters worse, some provinces have banned or are considering banning paid donation. A very good letter opposes the ban:

We are professional ethicists in the fields of medical ethics, business ethics, and/or normative ethics, and academic economists who study how incentives and other mechanisms affect individual behaviour. We all share the goal of improving social welfare.

We have strong reservations regarding any Act or legislation (hereafter: “Acts”) that would prohibit compensation for blood plasma donations…….Both the ethical and the economic arguments against a compensatory model for blood plasma for further manufacture into PDMPs are weak. Moreover, significant ethical considerations speak in favour of the compensatory model, and therefore against the Acts.

The letter carefully discusses many of the objections such as that paid donations will drive out unpaid:

The compensatory model leaves open the possibility of donors’ opting out of compensation, or the operation of a parallel non-compensatory model. The United States does just this, and has an approximately 50% higher voluntary, unpaid, per capita blood donation rate than Canada. Germany, Austria, and the Czech Republic, where plasma donors can be compensated, likewise all have higher rates of voluntary, unpaid per capita blood donation than Canada.

Is paid blood plasma less safe?

Dr. Graham Sher, the CEO of Canadian Blood Services, has said, “It is categorically untrue to say, in 2015 or 2016, that plasma-protein products from paid donors are less safe or unsafe. They are not. They are as safe as the products that are manufactured from our unremunerated or unpaid donors.”

The letter is signed by two Nobel Prize winners in economics, Alvin Roth and Vernon Smith, by philosophers like Peter Jaworski, who did most of the heavy lifting, and by experts who have studied incentives and blood donation closely like Nicola Lacetera and Mario Macis. I am also a signatory.

Arrived in my email

The book itself has not yet come to my pile, though perhaps it still will.  This one is self-recommending, so here is the basic information, it is due out June 2:

Alvin Roth, Who Gets What — and Why: The New Economics of Matchmaking and Market Design.

If you do not know why this is self-recommending, here are previous MR posts on Alvin Roth.  And here is the book’s home page.

The economics of reclining your airplane seat

I believe Josh Barro started this mess of a debate.

I would emphasize the endogeneity of transaction costs.  The airlines could do a lot to encourage Coasean bargaining between fliers, but they don’t.  How about handing out little cards?: “Have a friendly haggle with the person behind you.  Last year the average price for a non-reclined seat was $16.50.”  They could print up standardized contracts, like how they distribute customs forms, including contracts for trading seat assignments or distance from the bathrooms or how you shush your child, or not.  Imagine being nudged toward a deal through the in-flight internet system, so you don’t have to turn around to face the other party in the bargain.  They could take a cue from Alvin Roth and his matching algorithms or help you set up complex multi-party deals, like how the Denver Nuggets used to construct (and then dismantle) their rosters.

Nada.

The disutility of bargaining in this environment is high relative to the value at stake.  The chance of irritation or hurt feelings is non-negligible, and perhaps people on a flight are crankier anyway.  So the airlines deliberately keep the transactions costs high, as the gains from the potential bargain are low relative to the ickiness of the process.  The airlines wish to keep a lot of people away from the process altogether, if only out of fear of having to arrest people, divert flights, and so on.

That implies the more we debate this problem, the worse it becomes.  It also gives us the true Coasean answer to what is best.  Relative to current norms, who does more to make the whole question “an issue” — the seat recliner or the purchaser of the recliner-blocker?  Clearly it is the purchaser of the blocker and thus Josh Barro is broadly in the right, the norm should continue to allow people to recline their seats as that minimizes fuss, which is more important than getting the right outcome with the seat itself.

If you don’t like that, United does sell coach seats with extra space, which makes the recline of the person in front of you less bad.

Noble Matching

In honor of the Nobel prizes to Al Roth and Lloyd Shapley, here is a primer on matching theory. Matching is a fundamental property of many markets and social institutions. Jobs are matched to workers, husbands to wives, doctors to hospitals, kidneys to patients.

The field of matching may be said to start with the Gale-Shapley deferred choice algorithm. Here is how it works, applied to men and women and marriage (n.b. the algorithm can also work for gay marriage but it’s a little easier to explain and implement with men and women). Each man proposes to his first ranked choice. Each woman keeps her top-ranked suitor but defers accepting the proposal. Each woman also rejects her lower ranked suitors. Each rejected man proposes to his second ranked choice. Each woman rejects again any lower-ranked suitors, which may include previous suitors who have now become lower-ranked. The process repeats until no further proposals are made; each woman then accepts her top-ranked suitor and the matches are made.

A similar process works when proposal receivers may accept more than one suitor, not that useful for marriage in most of the United States but very useful for when students are applying to schools and each school accepts many students.

Now what is good about this algorithm? First, Gale and Shapley proved that the algorithm converges to a solution for a very wide range of preferences. Second, the algorithm is stable in the sense that there is no man and no woman who would rather be matched to each other than to their current match. There are of course, men who would prefer to marry other women and there are women who would prefer to marry other men but no mutually preferable match is possible. Thus, the algorithm produces a stable match.

The application to men and women is somewhat fanciful, although Match.com should clearly adopt this idea!, but the application to students and schools is very real. Gale and Shapley concluded their paper by writing:

It is our opinion, however, that some of the ideas introduced here might usefully be applied to certain phases of the admissions problem.

Indeed, this is exactly what has happened. Students in New York and in Boston are now matched to schools using versions of this algorithm. Even before Gale and Shapley the algorithm had been used, without much theorizing, by doctors allocating residents to hospitals and since Gale-Shapley and Roth the idea has been used much more extensively all over the world .The algorithm, by the way, has been picked up and extended by computer scientists notably including Knuth.

I said above that the men propose to the women–this matters because when the women propose to the men you also get a stable match but it may be a somewhat different match and in general it is better to be the one proposing. Matching becomes more difficult when, as in modern times, both men and women may propose. Fortunately, in many problems, such as with students and schools, the proposers and receivers can be fixed.

Another question is whether the algorithm can be strategically manipulated. In an Impossibility Theorem with much the same flavor as Arrow’s Theorem and the Gibbard-Satterthwaite theorem, Roth and Roth and Sotomayor proved that there is always some possibility for manipulation but the G-S algorithm can be said to minimize the opportunity for strategic manipulation; in particular for the proposers, men or say students applying to schools. it is a dominant strategy to reveal one’s true preferences.

The importance of a stable matching algorithm can be seen in what happens when such algorithms are not used. In trying to allocate residents to hospitals, for example, what typically happens when a stable algorithm is not used is unraveling and chaos. Unraveling occurs when offers are made earlier and earlier in an attempt to get a jump on the competition. Prior to the currently used National Residency Matching Program, for example, hospitals were making offers to residents up to two years in advance! All kinds of chaos arose as hospitals would make exploding offers, accept now or the offer explodes! Such offers would inevitable lead to recriminations and backing out of the offers as better matches were sought.

What Roth has done is extend the Gale-Shapley algorithm to more complicated matches and to actually design such algorithms to solve real problems. In the 1970s, for example, the medical residency algorithm began to run into trouble because of a new development, the dual career couple. How to match couples, both doctors, to hospitals in the same city? By the 1990s assortative matching in the marriage market was beginning to derail matching in the doctor-hospital market! Roth was called in to solve the problem and moved from being a theorist to a market designer. Roth and Peranson designed the matching algorithm that is now used by Orthodontists, Psychologists, Pharmacists, Radiologists, Pediatric surgeons and many other medical specialties in the United States.

Most famously, Roth has worked on improving kidney allocation. I first wrote about this in 2004 (see also these posts):

Your spouse is dying of kidney disease. You want to give her one of your kidneys but tests show that it is incompatible with her immune system. Utter anguish and frustration. Is there anything that you can do? Today the answer is yes. Transplant centers are now helping to arrange kidney swaps. You give to the spouse of another donor who gives to your spouse. Pareto would be proud. Even a few three-way swaps have been conducted.

But why stop at three? What about an n-way swap? Let’s add in the possibility of an exchange that raises your spouse on the queue for a cadaveric kidney. And let us also recognize that even if your kidney is compatible with your spouse’s there may be a better match. Is there an allocation system that makes all donors and spouses better off (or at least no worse off) and that maximizes the number of beneficial swaps? In an important paper (Warning! Very technical. Requires NBER subscription.) Alvin Roth and co-authors describe just such a mechanism and show that it could save many lives. Who says efficiency is a pedestrian virtue?

Since that time we have seen many such swaps including this record of 60 people and 30 kidneys. Truly a noble match.

Minor editing Oct. 23.

2012 Nobel Laureates in economics

Alvin Roth and Lloyd Shapley!

Great picks.  Both have done work on matching theory, bargaining theory, allocation theory, and market design. Here is Roth’s blog, he often reads MR by the way and sometimes sends us links.  I now need to repack and travel, my apologies, but Alex is likely to have more to say.  Alex in particular has many excellent past posts on Roth.  Here is an excellent overview of the contributions of Shapley.  Here is Wikipedia on Shapley.  Here is a Forbes profile of Roth.  Here is the Swedish information.

I think of this as a prize about how theory can be turned into usable results, how trade and matching can be made more efficient in concrete ways, how trade is a coordination game, and the intimate connection between issues of trade and issues of distribution.

Richly deserved by both men.

Handicapping the 2012 Nobel

This article mentions Alvin Roth, Bob Shiller, Richard Thaler, Robert Barro, Lars Hansen, Anthony Atkinson, Angus Deaton, Jean Tirole, Stephen Ross, and William Nordhaus.

I’ll predict a triple prize to Shiller, Thaler, and Eugene Fama.  Fama clearly deserves it, can’t win it solo (too strongly EMH in an age of financial crisis), but can be bundled with two people from behavioral finance and irrational exuberance theories.

Barro will get it, but not in an election year.  Hansen and Ross are good picks but I don’t see them getting it before Fama does.  Paul Romer deserves mention but this is probably not his year because of politics in Honduras.

William Baumol cannot be ruled out.  A neat idea — but unlikely — is Martin Feldstein and Joseph Newhouse for their pioneering work in health care economics, plus for Feldstein there is public finance too.

Tirole and Nordhaus are deserving perennials, with various bundlings (e.g., Oliver Hart, or for Nordhaus other names in environmental).  I hope the Krueger-Tullock idea is not dead but I would bet against it, same with Armen Alchian and Albert Hirschman.  Dale Jorgensen has a shot.

I believe Duflo and Banerjee (and possibly Michael Kremer too, maybe even Robert Townsend) will get it sooner than people are expecting, though not this year as they just presented in Stockholm.  Next year I think.

Not once in the past have I been right about this.

Addendum: Here is the talk from Northwestern.

The Matchmaker

The Boston Globe’s Leon Neyfakh has a good piece on Alvin Roth:

Roth has always been interested in the idea that sophisticated theories can be used to solve practical problems. As a graduate student at Stanford University, he earned a doctorate in operations research, which uses math to help organizations run more smoothly. Roth was just 19 when he started at Stanford, having quit high school without graduating at the age of 16 and finished Columbia University in three years. At just 22, he got a job as an assistant professor at the University of Illinois, and in 1977, at just 25, he was granted tenure there….

In the years since, Roth has emerged as a rare figure in the academic world: a theorist willing to dive into real-world problems and fix them. After helping the med students, he designed a better way to assign children to public schools — the system now used by both Boston and New York. He also helped invent a system for matching kidney donors with patients, dramatically increasing the number of donations that take place each year. More recently, he and one of his students have been talking with Teach for America about improving the system it uses to deploy volunteers around the country.

… Inspired by Roth’s work, these rising economists are also setting their sights on real-world problems. Some are looking at dating websites; others are interested in how universities could do better at scheduling their students’ classes. Like Roth, all of them envision a world in which economists, as unlikely as it may seem, are recognized as society’s mechanics.

One minor note, kidney exchanges are great but I wouldn’t describe the increases as “dramatic.” We will need, in addition, other ideas to alleviate the shortage of transplant organs.

The practical value of economics as a science

I know of three very good books on the actual (or sometimes hypothetical) application of economic ideas to real world problems:

1. Alex Tabarrok's Entrepreneurial Economics: Bright Ideas from the Dismal Science.

2. Some other book I haven't read and can no longer remember.

There is now a third:

3. Better Living Through Economics, edited by John J. Siegfried.  It covers emissions trading, the EITC, trade liberalization, welfare reform, the spectrum auction, airline deregulation, antitrust, the volunteer military, and Alvin Roth algorithms for deferred acceptance.  The contributions are uniformly excellent and written by top economists.

More Assorted Links

Austin Frakt reviews Modern Principles: Macroeconomics.  Austin's blog, The Incidental Economist, covers game theory, investment planning and health economics among other topics.

Here is an updated version of my paper Life Savings Incentives: Consequences, Costs and Solutions to the Organ Shortage.  Did you know that it is legal to offer compensation for donating a whole body (e.g. for research purposes) but not legal to compensate an organ donor to save a life?  Crazy.  Alvin Roth links to a survey of transplant surgeons indicating increasing support for legalizing some forms of compensation (Roth also links to a recent radio interview with yours truly.)

House built from Lego, yes really.  

The Shortage of Transplant Organs

The Wall Street Journal has a front-page article and a debate between Julio Elias and Alvin Roth on alleviating the shortage of transplant organs.  This interactive graphic was good at explaining the idea of kidney swaps.  Elias and Roth should have discussed no-give, no-take rules and Lifesharers

I will be speaking to Congressional and agency staff about the organ shortage this Thursday at noon (this event is not open to the public.)

Addendum: Transplant surgeon Arthur Matas, mentioned in the WSJ article, is no
libertarian but argues for live kidney sales in a new Cato Policy
Report
.

Kidney swaps II

The Wall Street Journal reports (subs. required) that the kidney swap idea I wrote about earlier is beginning to be implemented. Here are they key points:

Last year, 43% of kidneys transplanted in the U.S. came from living donors, up from 28% a decade ago.

But a biological barrier often blocks a transplant from a relative. In about a third of all would-be pairs, blood types are incompatible. In others, the sick person has antibodies that can initiate a rejection of the donated organ. It’s heartbreaking “to have the treasure of the live donor and then have that not go forward because of a biological obstacle,” says Massachusetts General Hospital transplant surgeon Francis DelMonico.

Occasionally, transplant centers spot a way out: One New England father with blood type A couldn’t donate a kidney to his daughter with blood type B. So he gave a kidney to a teenager with blood type A, and the teenager’s sister gave a kidney for the man’s daughter.

Such swaps, however, typically occur only when happenstance alerts surgeons to the possibility. Economist Alvin Roth and co-authors have devised an algorithm, however, that computes all the possible swaps and which is incentive-compatible.

…when Dr. Saidman gave the economists details on 45 pairs in which the would-be donor was unable to give a kidney to the intended recipient. Even though each of the 45 had a donor willing to spare a kidney, all were stuck waiting for the right person to die. With swaps involving two kidneys, the economists found, eight transplants were possible. If swaps involving three kidneys were possible, then 11 transplants were possible.

Addendum: Alert readers will note that kidney swaps are quite similar to organ clubs an idea for saving lives that has been implemented by Lifesharers.

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