"Who Gets What and Why" by Alvin E. Roth: Summary and Review

You cannot buy your way into a famous university, and you cannot buy a kidney. Yet both are allocated somehow, and the rules decide who gets what. Alvin Roth has spent his career studying such rules and changing them. In 2012 he shared the Nobel Prize in economics with Lloyd Shapley “for the theory of stable allocations and the practice of market design”. Who Gets What and Why, published in 2015, is his account of that work for general readers. It shows that markets are human inventions with rules, and that bad rules can be replaced by better ones.

Many markets are matching markets, where you must also be chosen

Roth starts with a distinction. In a commodity market, such as the market for wheat or shares, you do not care who sells to you. The price connects buyers and sellers, and anyone who pays the price gets the good. In a matching market, both sides choose. A company does not hire everyone who wants the job, and you do not work for every company that wants you. Universities, schools, jobs and marriage are all matching markets.

In these markets, price cannot do all the work. A university does not just raise its fees until only as many students apply as it has places. It wants particular students, and students want particular universities. Roth’s book asks how such two-sided choices can be organized well. The early chapters show that matching markets are everywhere, from breakfast to college admission. They also show that even ordinary markets depend on rules that someone designed.

Kidney exchange: saving lives without money

The book’s most moving example comes early. In the United States, more than 100,000 people were waiting for a kidney when Roth wrote the book. Selling organs is forbidden by the National Organ Transplant Act of 1984, and it is illegal almost everywhere. Iran is a rare country that allows payment to living donors.

Many patients have a relative or friend who wants to donate a kidney but cannot, because their blood or tissue types do not match. Two such pairs can swap. Swaps like this had been done before, but very rarely. In a 2004 paper, Roth and his colleagues Tayfun Sönmez and Utku Ünver showed how to organize them on a large scale. The donor of pair A gives to the patient of pair B, and the donor of pair B gives to the patient of pair A.

Putting this into practice was hard. In a later interview, Roth described the steps. First, his team had to build a shared database across 14 transplant centers in New England, which took about a year. Then hospitals had to learn to operate on the same day, because a donor might back out after the other patient had received a kidney. A swap between two pairs needs four operating rooms at once.

The breakthrough came with chains. A donor who is willing to give to any stranger starts a chain. That donor gives to the patient of pair A. Pair A’s donor then gives to pair B’s patient, and so on. Because the chain began with a free gift, it does not need all operations on the same day. Chains made much longer sequences of transplants possible.

Markets fail when they unravel

The middle of the book explains how markets break down. Roth names four problems. A market can happen too soon, move too fast, become congested, or be too risky for its participants. The first problem is unraveling. Competitors try to get ahead of each other by making offers earlier and earlier.

The classic case is American medicine. In the 1940s, hospitals competed for medical students by offering positions earlier each year. Sometimes they made offers years before graduation, before students knew which kind of medicine they wanted to practice. To get answers quickly, hospitals made exploding offers, offers that expire within a very short time. Students had to accept or reject an offer without knowing what else they might get.

Roth shows the same pattern in other markets, such as young lawyers applying to work for judges and doctors training in gastroenterology. The gastroenterology market even unraveled a second time in the 1990s, after it had left a central system. Roth contrasts these with American graduate schools. Most universities follow a rule that offers of admission and funding stay open until April 15. A student who accepts an earlier offer may still change their mind before that date. This rule makes early exploding offers almost useless, so that market does not unravel.

A thick market must also be quick, and safe

The second and third problems come from success. A market that attracts many participants is thick, which Roth sees as essential. But thickness creates congestion: there are too many options to consider in the time available.

Roth gives the example of New York City high schools. Until 2003, students ranked five schools, and schools then made offers in three rounds. That was far too few rounds for tens of thousands of students. As a result, about 30,000 students a year ended up at schools they had not listed at all.

Speed can also become a problem. Roth describes the race among trading firms on stock exchanges to be faster by a few thousandths of a second. The economists Eric Budish, Peter Cramton and John Shim proposed a fix called frequent batch auctions. Orders would be collected for a very short, fixed time and then processed together. Then a tiny speed advantage would no longer decide who trades first.

The last condition is safety. A good market must make it safe for people to say what they really want. Under the old school system in Boston, schools first filled their places with students who had ranked them first. A family that listed a popular school first and missed it often found its second choice already full. So parents had to guess which school to name first, and families who stated their true wishes could lose out.

Deferred acceptance: hold the best offer, but do not accept it yet

The book’s central tool is an algorithm that the mathematicians David Gale and Lloyd Shapley published in 1962. It is called deferred acceptance, because no offer is accepted until the very end. Its result is a stable matching. That means no applicant and school are left who would both rather be matched with each other than with their current partner.

Here is how it works when students apply to schools. Take three students and three schools with one seat each. Ann prefers North, then South, then East. Ben prefers North, then East, then South. Cara prefers South, then North, then East. North ranks Ben above Ann and Cara, and South ranks Ann above Cara.

1. Each student applies to their first choice. Ann and Ben apply to North, and Cara applies to South.
2. North holds Ben and rejects Ann. South holds Cara. Holding is not accepting.
3. Ann applies to her second choice, South. South prefers Ann, so it now holds Ann and rejects Cara.
4. Cara applies to her second choice, North. North still prefers Ben and rejects her.
5. Cara applies to East, which holds her. Nobody is rejected any more, so all held offers become final.

The result is Ben at North, Ann at South and Cara at East. Cara did not get her first choice, but no school she prefers would prefer her to its current student. So the result is stable. And because no offer was final until the end, every student could list their true preferences without risk.

In 1984, Roth discovered that the clearinghouse American hospitals had used since the early 1950s worked very much like this algorithm. He argued that this was why it had survived when many other systems failed.

In 1995 he was asked to redesign it. Together with Elliott Peranson, he built a version in which applicants make the offers. It also handles couples who want jobs in the same city, about 1,000 graduates a year. The new algorithm was adopted in 1997 and matches more than 20,000 positions a year. In New York, a similar design reduced the number of students placed at schools they had not listed by about 90 percent.

When applications are cheap, signals become valuable

A related chapter deals with signaling. When applying costs almost nothing, people apply everywhere. Then each application says very little about real interest, and the other side cannot tell who is serious.

One solution is to give each person a small number of signals that cost something because they are scarce. Roth describes how the American Economic Association introduced such signals in the job market for young economists. Each candidate can send a signal to only a few departments, so a signal shows real interest. Roth suggests similar signals for other crowded markets, including online dating.

This chapter connects to a different question about choosing. The secretary problem asks when one person should stop looking and accept the next good candidate. Roth’s markets are different, because both sides choose and many matches are made at the same time. Reading both shows two separate problems hidden in the word “matching”.

Some transactions are forbidden because people find them repugnant

The last part of the book deals with markets that many people refuse to allow. Roth calls such transactions repugnant. Some people want to make these transactions, but others think they should not be allowed, even when nobody else is directly harmed.

His examples come from a paper he published in 2007. California voters banned restaurants from serving horse meat in a 1998 referendum, although it is eaten in other countries. In France, the authorities banned dwarf tossing, a bar entertainment in which a large man throws a small man. A man who earned his living from it went to court to keep his job. The biggest case is the ban on paying for kidneys.

Roth does not say that these bans are foolish. He treats repugnance as a real limit that a designer must respect, just like a law or a technical limit. Kidney exchange is his best example. It increased transplants without any payment, so it worked within the limit rather than against it. In the final chapter he applies this view to markets in general. A free market, in his account, is not a market without rules. It is a market whose rules let people take part safely and freely.

How it differs from other books on markets

Most popular economics books, such as Tim Harford’s The Undercover Economist, explain how prices work. Roth’s book is about the many markets where prices are not enough. That makes it unusual among books for general readers.

The closest neighbor is John McMillan’s Reinventing the Bazaar. McMillan also argues that markets are built and need rules. His book covers more types of markets, while Roth’s goes deeper into a few cases he helped to design himself.

A third neighbor is Algorithms to Live By by Brian Christian and Tom Griffiths. It explains related mathematical ideas, such as the secretary problem, and applies them to personal decisions. Roth applies them to institutions instead. His great advantage is that he was there. He describes the meetings, the doubts and the practical problems from the inside, and he shows how much work happens after the theory is finished.

Where it falls short

The book’s strength is also its weakness. Roth tells the story of projects that he led, and he tells it as a success story. Critics of matching systems appear only briefly. For example, the medical match was challenged in court in 2002 by doctors who argued that it kept their wages low. The case was dismissed in 2004 after Congress passed a law protecting the match. Roth’s own research found no wage difference between medical fields with and without a match. Still, a reader learns little about that debate from the book.

School choice raises a similar question. Deferred acceptance makes honest ranking safe. But it cannot create more good schools. If a city has too few good schools, a better algorithm only distributes the shortage more fairly. Roth knows this, but the book gives the point less weight than it deserves.

Some examples are also dated. The book appeared before the large online platforms for jobs, housing and dating reached their present size. The principles still apply, but readers today will want newer cases.

How to read it

The book contains no formulas and is easy to follow, so the audiobook, read by Peter Berkrot, works well for most chapters. The chapters on the medical match and school choice are easier in print. There you can follow the steps of the algorithm on paper, as in the example above.

Read it as an insider’s account of what good market rules can achieve. Then look for one critical view, for example on school choice or the medical match, to see what the designer may have missed. For a reader who wants to see how mathematics changes real institutions, few books explain it this well.