Who Gets What - And Why: The Hidden World of Matchmaking and Market Design

by Alvin E. Roth

Step 0. Applicants and employers privately submit preferences to a clearinghouse in the form of rank order lists. Step 1. Each employer offers jobs to its top-choice candidates, up to the number of its available positions. Each applicant looks at all the offers he or she has received, tentatively accepts the best one (the one highest on her preference list), and rejects any others (including any offers of jobs that were judged unacceptable and left off the applicant’s rank order list). … Step n. Each employer that had a job offer rejected in the previous step offers that job to its next choice, if one remains. Each applicant considers the offer he or she has been holding together with his or her new offer(s) and tentatively accepts the most preferred (highest-ranked) of these. The applicant rejects any remaining offers — including possibly the one that had been tentatively accepted earlier but is no longer the best offer received. (Note that applicants take no account of the step of the algorithm in which an offer was received; they look only at whether they prefer it to their other offers.) The algorithm ends when no offer is rejected, so that no firm wants to make any additional offers. At that point, each applicant and employer is (finally) matched by having each applicant accept whatever offer he or she had most recently tentatively accepted. That is, all acceptances are deferred until the end, when no more offers are forthcoming.

Deferred Acceptance Algorithm

“the Iron Law of Marriage,” which says that you can’t be happier than your spouse.

as long as the Match had to produce a stable outcome — we couldn’t send more doctors to rural hospitals than wanted to go. Otherwise there would be some doctor at a rural hospital who was part of a blocking pair with another hospital that he preferred, and it would be more than a market could do to keep him there.

A democracy that makes education both free and compulsory has an enormous collective responsibility to provide its youngest citizens with a top-quality education.

The multiple offers were gumming up the system and making it congested.

markets can be dramatically improved when their design encourages people to communicate essential information they might otherwise have kept to themselves.

as communication gets easier and cheaper, it sometimes also gets less informative.

It will give us an idea of how easier communication can lead to congestion, and why signals of interest are important.

It’s easy for students to apply to many more colleges than they used to — and they do. This in turn makes it hard for colleges to assess just how interested a given applicant actually is. So colleges look for other signals.

If students fill application once via central website, a la linkedin job applications

while the very top schools can do what they like, all the others must face the fact that the Common App has become a very thick marketplace. It attracts so many applicants that a college that now insists on individual applications might not get enough applicants, since many students are drawn to the convenience of using the Common App.

So the Common App makes it easier to apply to multiple colleges, but it also contributes to a vicious circle in which applicants need to apply to more colleges than before.

That’s one reason so many jobs demand a college degree, even if the job itself has little to do with what is taught in college. Going to college and doing well signals not only what the job applicant may have learned but also that he or she is good at learning things. That’s a valuable skill in itself for just about any demanding job.

For the sake of the signals the degree gives

Economists call such superficial messages “cheap talk.” When talk is cheap, it doesn’t reliably signal anything.

turned out that proposals with roses attached were 20 percent more likely to be accepted.

(Evolutionary biologists refer to the “four Fs” of natural selection: feeding, fighting, fleeing, and, um, reproduction. A large tail is a “handicap” in the first three categories, which sends a signal about his underlying fitness, and that increases his opportunities in the fourth.)

An impressive lobby was their peacock tail: a less well-funded bank couldn’t afford to build such an expensive building, or might have built a building that could be more easily turned into a restaurant in case the bank failed.

it helps to be able to signal not only how desirable you are but also how interested.

arranging a date on the Internet, which makes the dating market thicker by making initial contacts easier, also makes it harder to send credible signals to cut through the congestion.

So a scarce signal isn’t cheap talk; it comes with an opportunity cost — you could have sent that signal to someone else instead.

So the seller in a first-price auction receives the amount of the highest bid, which is, however, less than the true value of the highest bidder. By comparison, in a second-price auction, the seller receives only the second-highest bid, but the bids are higher. That is, when the rules of the auction change, the bids change, too. In fact, there are reasons to think that these two effects balance out.

Experts can estimate the value of that Rembrandt painting, for example, but its true value is unknown until the bidding stops.

So it isn’t the case that as we get all modern, we just abandon old repugnances. Sometimes we revisit them — or develop new ones.

Near the beginning of his long essay The Protestant Ethic and the Spirit of Capitalism, Max Weber quotes Benjamin Franklin on the virtues of responsible lending and borrowing.

Loans, adoption of children, and love are widely regarded as good things when offered freely, even when their commercial counterparts are regarded negatively.

It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own interest.”

For example, the concern that only the rich could afford kidneys might be addressed by amending the current outright ban on purchases to allow purchases only by a single authorized government buyer, with the obtained kidneys then being allocated according to the rules that today govern the allocation of deceased-donor organs.

That doesn’t mean we shouldn’t disapprove of some behaviors and try to moderate them, but sometimes we will more nearly achieve our goals if we try to channel behavior or offer alternatives, rather than institute a ban.

While all those restaurants are attracted to their thick marketplaces in similar ways, different kinds of restaurants deal differently with congestion. If we’re going to eat at a popular time, we’ll probably have to wait. And when I tell you how each restaurant deals with congestion — where and when we’ll wait — you may be surprised at how many other things that detail will tell you about the restaurant.

Some restaurants have learned to use reservations to slow the flow of customers to cope with congestion in the kitchen, much as kidney exchange networks figured out how to organize nonsimultaneous chains to avoid operating room congestion. Mid-priced restaurants handle dining room congestion with waiting lines, and fast-food restaurants are fast not only because they prepare the food continuously, but also because they reduce each customer’s transaction to a single encounter, at the cash register.

To give an analogy from biological evolution, walking erect gives us humans many advantages, but we’re not well designed for it; we suffer back problems and flat feet because we’re made of parts that were largely shaped before we walked the way we do now.

In chapter 1, I made the analogy between a free market with effective rules and a wheel that can rotate freely because it has an axle and well-oiled bearings. I could have been paraphrasing the iconic free-market economist Friedrich Hayek, who in his 1944 free-market manifesto The Road to Serfdom wrote, “There is, in particular, all the difference between deliberately creating a system within which competition will work as beneficially as possible and passively accepting institutions as they are.”