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Advanced Fairness At The Marathon

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You have been running this marathon for a long time.


MALONE: Oh, wait; that's confusing.

CAPIRASO: Yeah, 'cause people often say, you run the marathon.

MALONE: And you're like, I do run the marathon.

CAPIRASO: I do, yes.

MALONE: Michael Capiraso is the president and CEO of the New York Road Runners, the organization that, 50 years ago exactly, created the New York City Marathon.

CAPIRASO: If you talk about Year 1 - right? - 1970...


CAPIRASO: ...They came up with this idea to run a marathon all in Central Park - 26 miles. And to get some people to run a marathon in Central Park seemed crazy at the time.

MALONE: For the very first New York City Marathon, there were just 127 runners. But then, in the late 1970s, 1980s, there was this huge change.


MIKE WATERS: That's becoming a familiar sound along America's highways and byways.

MALONE: This audio you're hearing - it is from a 1979 NPR special - an hourlong special - about this jogging thing and the millions and millions of people suddenly taking this up.


WATERS: A look at jogging produced by David Sullivan (ph). David, where are all these people running to?

DAVID SULLIVAN: Well, Michael, they're not really running anywhere, although they seem to be everywhere.

MALONE: This is what's now known as the running boom. And by the end of the running boom, the New York City Marathon had more people who wanted to run the race than it had space for. Today's New York City Marathon can handle about 53,000 runners - more slots than any other marathon in the world. And yet, Michael Capiraso told me they still have to turn away around a hundred thousand people.

Do you ever run into people getting upset that they couldn't get into your race?

CAPIRASO: I have had some people say that they've had challenges, but...

MALONE: Do you ever get anybody - like, has the mayor ever called you up to be like, I need - I got - I need a slot for my son-in-law, or something like that?

CAPIRASO: The mayor's never called me up and asked for a spot for his son-in-law.


The New York City Marathon is dealing with literally the Cliffs Notes definition of economics. Reading from Cliffs Notes here, quote, "the study of economics is the study of how society allocates scarce resources and goods." But as we all know, allocating scarce resources in a fair way is incredibly difficult. Just take the marathon. Who exactly would this be fair for? Would it be fair for everyone who kind of wants to run the marathon? What about people who want to run the race more than the average person? What about those elite, world-class runners who need a spot in the marathon in order to set a new world record?

This is the kind of complicated and sticky scarce resource problem that is dealt with all over the world. Who gets to study at our top colleges? Who gets to live in affordable housing? These are high-stakes problems with no clear answers. And yet, the system the New York City Marathon has come up with is so clever that we thought it deserved an entire episode.


MALONE: Hello, and welcome to PLANET MONEY. I'm Kenny Malone. Today on the show, what the New York City Marathon can teach us about allocating a scarce resource as fairly as possible. After all, it requires advanced fairness methodology to keep tens of thousands of Type A marathoners all happy - or at least, you know, not angry.


MALONE: Check one, two.

Watching the New York City Marathon is a blast. For one, you are reminded how great it feels to not be running a marathon.

I see a lot of people grimacing. They look pretty tired.

But also, it is the one day New Yorkers realize that it is sort of fun to be nice to strangers.

UNIDENTIFIED PERSON #1: All right. Let's go, runners. You look good. You look good.

MALONE: This person apparently brought their own bullhorn for cheering people on.

UNIDENTIFIED PERSON #1: Everybody say woo.

MALONE: The marathon has expanded beyond Central Park. It now goes through all five boroughs in New York City, and it takes the entire day from sunup to sundown to get all 53,000 runners through that course. Just watching it, there really does not seem to be much more room, which is why the marathon has had to develop a system to decide who gets a running spot and who does not.

But the genius of the New York City Marathon is that instead of trying to pick a single fairest method to allocate slots, it has split up that pool of 53,000 slots into four chunks, essentially. Each chunk uses a different fair division solution, each with its own idea for what fair could or should mean. And so we are also going to break this show up into four chunks, four ministories that will explain how the New York City Marathon became a master class in fairly allocating a scarce resource.

CAPIRASO: Well, look; again, I've been fortunate along the way to kind of keep running it in spite of...

MALONE: This is, again, Michael Capiraso, the New York Road Runners CEO. He runs the marathon. But before that job, about 30 years ago, he decided that he did, in fact, actually want to run the New York City Marathon.

CAPIRASO: It's a story that I often tell. I got dumped by my girlfriend and said, I will run the New York City Marathon and show her, and she'll take me back. I've never seen her since, and I've run the marathon every year since 1991.

MALONE: Whoa. That is a good origin story.

Michael has now run 28 straight New York City Marathons. But what's worth noting here is how he got into the race back in 1991.

CAPIRASO: Back then, I think we had to go to the post office and put your name on a postcard and get it in by a certain time in order to get selected.

MALONE: And what was the application?

CAPIRASO: It was just - yeah, it was just a postcard or a letter.

MALONE: But, like, you didn't have to write, like - I don't know - I'm not just sending you a postcard; this is because I want to run the race.

CAPIRASO: No, no. I think it was pretty basic.

MALONE: So all these people would send in their postcards. The marathon would then randomly select some of those postcards, and those were the people who got spots in the marathon. It was a lottery. And that is our first method of fairly allocating a scarce resource - a lottery.

And you can still get into the New York City Marathon through a lottery. Of course, there are no more postcards. It's all digitized. You get one entry per person, which makes the marathon a special kind of lottery, a uniform lottery. Unlike, say, the Powerball lottery, where you technically could increase your odds by buying more and more tickets, a uniform lottery gives every single person the same odds of winning. It is the most egalitarian way to give something away, which is why you will often see uniform lotteries used to give away undesirable things. Think about the Army draft or jury duty. It is hard to argue with the outcome of a uniform lottery because everybody had the same odds. You're just lucky or unlucky enough to have your number come up.

This year, the New York City Marathon gave away about 20% of its slots through their lottery. And any given runner had about a 1 in 10 chance of getting picked. You get an email saying, hey, you made it. Better start training. Of course, back in Michael's day when he was applying through the postcard lottery, you had to wait by the mailbox for an actual letter.

Do you remember getting that letter?

CAPIRASO: I do. I probably still have it, too.

MALONE: Really?

CAPIRASO: My wife probably isn't happy about that, but I'm sure I still have it.

MALONE: Oh, because it's tied to the ex-girlfriend.

CAPIRASO: Well, along with a lot of the other things I've saved from the 27 years.

MALONE: I see. So it's more about the clutter than it is the emotional baggage.

CAPIRASO: I think it is.

MALONE: Now, it is possible that a uniform lottery is the easiest, cheapest way to give out all of the marathon slots. However, Michael would end up with a low-performing marathon since most of us are not very good at marathons and the lottery's randomly pulling from a giant pool of people, which brings us to method No. 2 for allocating a scarce resource, merit-based allocation.

Were you a runner? Like, did you run competitively at some point in your life?



CALGARO: I actually started running late. I was a dancer. I always loved running.

MALONE: Kristen Calgaro has become a very talented runner, and she decided to try and get into the New York City Marathon as a time qualifier. New York and lots of other marathons will set aside some spots for people who go off and run a different marathon under a certain time. And as Kristen learned, there's so much demand for New York that it has some of the hardest qualifying standards.

CALGARO: For a woman of my age, I need to run a sub - a 3:15:00 or lower.

MALONE: 3:15:00 or lower.


MALONE: So on average, what is a mile then?

CALGARO: A 7:25 pace.

MALONE: That's really fast.

CALGARO: Yeah, not so bad if you're just running a mile, but I guess over 26.2, it adds up.

MALONE: I mean, I think it's pretty fast for just one mile, honestly. But, yes, fair enough.

We see versions of, quote-unquote, "merit-based systems" everywhere. You want to get into the best colleges, ace the SAT. Want to be a Navy SEAL? There is an insanely hard physical fitness test. Even aspiring diplomats have to take a foreign service exam.

Merit-based systems only really work when the thing you want to test for is actually testable and predictive of success. The simpler and more objective the skill is, the better your merit-based system will be. And running a marathon in 3 hours and 15 minutes, or not - that is a pretty objective skill.

But even within those parameters, Kristen Calgaro realized there is a little room for strategy on top of skill. That is why she very carefully chose which other marathon she was going to run to try and qualify for New York.

CALGARO: So it was a small marathon in Pennsylvania called the Pocono Mountain Run for the Red. It sounds like it's really hard, right?

MALONE: It's mountains. I'm hearing mountains, yes.

CALGARO: The thing about this race - it's considered potentially a fast course, which is why I chose it because it's net downhill.

MALONE: As in it was more downhill than uphill, which is genius. Unfortunately, on the day of the race, there was 100% humidity. Kristen did finish the race. She needed medical attention. And then when she finally managed to hobble over to, like, the posted finish times, she's looking for her name, hoping she ran this thing in 3:15:00.

CALGARO: It said Kristen Calgaro - 3:14:55.

MALONE: 3:14:55.

CALGARO: Yes. I made it with a five-second margin.

MALONE: Oh, my God. Can you imagine if you had missed the other way?

CALGARO: Yeah. I mean, it would have been a bummer. But, you know, at that point, I just was glad that I finished.

MALONE: All right. I'm just past Mile 19 now. Let's see if we can spot Kristen.

Kristen was one of just a few thousand runners who managed to get into the New York City Marathon through time qualification.

Here comes Kristen. Here comes Kristen. (Shouting) Kristen, Kristen.

CALGARO: Hey. How you doing, Kenny?

MALONE: Good. Keep going. Kristen is blowing kisses to everybody. That is super fast. Kristen is in her 20th mile and is still running faster than if I were just running one mile.

And by the way, the really fast runners who win the New York City Marathon - they have a slightly different merit-based path into the race. They're so good that they're just recruited to show up and run the race in, like, 2 hours and 30 minutes.

You are Greek.


MALONE: Where the marathon is from.

DASKALAKIS: That's right.

MALONE: You don't feel any extra obligation to run a marathon because you are Greek.


MALONE: All right. That's fair.

DASKALAKIS: No, I do not.

MALONE: This is Costis Daskalakis. You may remember his voice from an earlier episode where he was helping us allocate limited spots on a boat dock. He actually kind of inspired this entire episode.

And how do we describe what you do? You're an expert in - well, you're a computer - you're a computer scientist.

DASKALAKIS: I'm a computer science professor at MIT, and my research is studying the theory of computation and how that interacts with game theory, economics, probability theory and machine learning.

MALONE: Yeah, that's, like, just everything, so everything. You study everything.

Costis studies, among many, many other things, mechanism design. This is an economics, game theory field where you start with a desired outcome or objective and then design a system to make that work. So let's say you have a marathon and a limited number of slots, and you're trying to do this as fairly as possible. That is a mechanism design challenge. And so uniform lottery, merit-based allocation - those are two mechanisms for allocating a scarce resource, but they boil down to basically, like, are you fast? Are you lucky? Costis says there are far more interesting ways to think about who should get a scarce thing.

DASKALAKIS: So you would like to give, for example, some resource to whoever would value it the most.

MALONE: Right.

DASKALAKIS: However, you cannot just go to people and ask them, hey, how much you value this? Because they may say, oh, I value it infinity much.

MALONE: Yeah. That's the problem, yeah.

DASKALAKIS: And you're left without any input because if I get a bunch of infinities, I have no idea who values it the most.

MALONE: And this is where mechanism design gets fun and big and important, honestly, because if we can just figure out who values something the most, who will get the most out of that thing, then this would open up a whole new way of allocating things fairly. The challenge is finding a useful proxy for value. And, of course, most of the world does use a default proxy for value - money.

DASKALAKIS: Quote-unquote, "you put your money where your mouth is," or you put your mouth where your money is.

MALONE: I think it's money where your mouth is. I think if you put your mouth where your money is, then that's unsanitary.


MALONE: This brings us to method No. 3 for getting into the New York City Marathon - money. Now, the marathon isn't auctioning off slots to the highest bidder, but they do offer runners two ways to put their money where their mouth is and show financially that they really want to run this race. The first method is through charity. The marathon has set aside about 10,000 racing slots for select charities, and then those charities can give you a marathon slot if you raise money for them. Usually, you need to come up with a little over $2,500.

The second way you can kind of buy your way in is if you are an international runner. If you live overseas, you can go to specific travel agencies and book a marathon package that would include flights, hotel and a marathon slot. There's no set price for this, but you could imagine this would cost at least a couple thousand dollars. Not necessarily profit-maximizing ways of letting people buy into the marathon, but two ways that let people show that they want in through money.

Of course, using money as a proxy for value has some pretty obvious problems. For one, if I were up against Bill Gates for a slot in the marathon, I do not value a dollar the same way Bill Gates values that dollar. So how can we figure that out? There must be a better measure of value than money, which brings us to our final and, honestly, most brilliant way of allocating a scarce resource.

Why don't you just start by telling me your name and who you are?

DAWN PAPACENA: OK. Hi, everyone. (Laughter) My name is Dawn. I'm from Brooklyn, born and raised. We're here in Brooklyn right now. And, yeah, that's about it.

MALONE: Dawn Papacena and I are sitting on a bench in Prospect Park. She's a social worker, and her marathon story starts four years ago. She says she'd reached a point in her adult life where everyone around her - all of her friends and family - they just - they all seemed to be doing something.

PAPACENA: Marriage, babies, new careers, moving, houses, buying things. And I'm just like, I'm just, you know, living in Brooklyn, working.

MALONE: One of her friends was like, you know, Dawn, I'm going to run the New York City Marathon. Maybe you should also do that.

PAPACENA: I was like, I don't think I could do that because that's - I don't even run for the bus. Like, I still don't run for the bus or the train because of the MTA. But that's a whole other podcast, a whole other story.

MALONE: But she decides, you know what? Maybe that is what I need. And quite frankly, the New York City Marathon needs Dawn. If there is not a spot for a New York City-native social worker looking to start a healthy new chapter in her life, then what kind of hometown marathon would this be? The problem, though, is that those classic entry methods are not going to be a good fit for Dawn. The lottery - too uncertain.

PAPACENA: Right. I want to do it. I want a guarantee.

MALONE: There was, of course, the money option - raising thousands of dollars for charity.

PAPACENA: All my friends work in social services, which we do not get paid that much in New York City, FYI.

MALONE: And then, you know, you've got merit-based - time qualification.

PAPACENA: Which - ha-ha - no. My qualifying time would have to be in the three-hour range, and I am not a three-hour runner.

MALONE: How...

PAPACENA: I am closer to six-hour runner.

MALONE: Which I think is great.


MALONE: But it is not going to get you in the race.

PAPACENA: It's not going to get us in the race.

MALONE: And for most of the marathon's history, somebody like Dawn would have just been out of luck. But in 2002, the race added our fourth and final method, and we're going to call it effort as a proxy for value. Technically, this is called 9+1, as in you can guarantee yourself a spot in the marathon, but first, you need to go out there and run nine other races. Finishing time doesn't matter. Just show that you're committed to this.

Do you remember which races you ran?

PAPACENA: Yes. This year I ran...

MALONE: To qualify...

PAPACENA: Yes. I ran the New York City Half, the Queens 10K, the Bronx 10-Mile Race, the Staten Island Half, the Brooklyn...

MALONE: All of these races are organized by the New York Road Runners, which puts on the marathon. And you do have to pay them for each race, but you can run nine races for as cheap as $200. That is, like, a tenth the cost of buying your way in through charity. There are about 10,000 spots for the 9+1 runners, and this is particularly useful for getting actual New Yorkers into the New York Marathon because if you think about it, you need to be around the city for a lot of weekends to pull this off.

Dawn, by the way, has become a total marathon junkie. She's run almost 10 marathons now, including the Chicago Marathon, Paris, even Berlin.


MALONE: When I was talking to that MIT professor, Costis Daskalakis, about mechanism design, he told me that you always have to think about how somebody is going to game your system. And the best designed mechanisms - they take that into account and still manage to get the result they want.

That is part of why I love the New York City Marathon, because here you've got these four different avenues to get in, and it seems like because of that, you don't need to try and game this system. Let's say you're a really rich person. Sure, you could go pay, like, a body double to go run nine races on your behalf and save you the time. But why would you do that? There already is a method for you to buy your way in through charity or international travel. And so it seems like each of these different methods of fair allocation - they sort of work in balance with the other ones, and they relieve some kind of corruptible pressure created by any given method. It is somehow this clunky but really quite elegant design.

And by the way, in case you're wondering about the plus-one of the 9+1...

Is anybody volunteering as part of 9+1 to, like, run the marathon next year?

...You have to run nine races plus volunteer at one qualifying race. This is how I met Myve Newin (ph).

MYVE NEWIN: We're at the fluid station at Mile 22 just handing out water and some bananas to the runners.

MALONE: Can we hand water out to people? Like, would that...

NEWIN: Sure.

MALONE: Can we do that?

NEWIN: Yeah.

MALONE: And I will say I've never really dreamed of running 26.2 miles, but it has always looked super fun to be one of those people participating in the flyby water-cupping.

All right. What's the technique here?

NEWIN: You just want to make sure you go - I don't know. There's not too much technique. You want to make sure the runners have access to it. You want to make sure you're holding it in a way that they can grab it since most of them are sprinting by.

MALONE: Yes, they are going very fast.

NEWIN: Yeah.

MALONE: I want to get sound of people dropping them.


MALONE: Oh, man. We're in, like, the splash zone. I got totally splashed.

NEWIN: That's why we have these ponchos.

MALONE: Oh, that's why you have the ponchos.

After the break...


WATERS: David, where are all these people running to?

MALONE: ...Assorted highlights from NPR's special hour where they discovered jogging.


MALONE: If you would like to run the New York City Marathon, you should know that there is a small window for which you can apply to the lottery. It opens on January 30, and then it closes about two weeks later. So if you are into that, get on it - no postcards.

As always, we love to hear from you. Maybe you know another single event that helps explain an area of research. Email that to us at We're also on Instagram, Facebook and Twitter. Generally, we are @planetmoney.

Today's show was produced by Darian Woods and engineered by Isaac Rodrigues. Alex Goldmark is our supervising producer. And Bryant Urstadt edits the show. I'm Kenny Malone.


WATERS: And this is NPR, National Public Radio.

MALONE: Thanks for listening.


WATERS: You've been listening to jogging.

UNIDENTIFIED PERSON #2: The first part of the run is always kind of an adventure. It's about 20 degrees right now, and I'm warm. In fact, I'm starting to sweat. My legs are a little chilly. I'm wearing running shorts. The rest of me is nice and warm. Feels good.

WATERS: The following is an interview with an imaginary physician, Dr. O. Elmer Merkley (ph). In a few words, Dr. Merkley, what exactly are you advocating?

UNIDENTIFIED ACTOR: (As Dr. Merkley) Not running.

WATERS: Are you seriously suggesting we can achieve mental clarity and spiritual awareness merely by not running?

UNIDENTIFIED ACTOR: (As Dr. Merkley) No. Not running has to be approached consciously and with dedication. I recommend a gradual program of not running until one has reached a quite vigorous level of dynamic inactivity.

WATERS: What do you say to the current contention that regular running is good for the heart, the lungs and the general physical condition?

UNIDENTIFIED ACTOR: (As Dr. Merkley) Well, that's right, of course. I will confess I often run a few miles for the good of my body. And every time, it makes me feel wholesomely tired and ridiculously noble, wise and self-important.

UNIDENTIFIED PERSON #2: You should always run at a pace where you're able to carry on a conversation. Trouble is there's nobody to talk back to me.

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