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7min chapter
A very Planet Money Thanksgiving
Planet Money
Thanksgiving Seating Strategies
This chapter humorously explores the complexities of seating arrangements during a Thanksgiving gathering among colleagues. It delves into matching theory in economics, examining how preferences influence social interactions and the challenge of creating optimal guest arrangements. Through a computer simulation and entertaining anecdotes, the speakers highlight the intricacies of achieving happiness and stability at the dinner table.
00:00
Transcript
Episode notes
Speaker 2
So good to see you! Hi! Welcome to Thanksgiving! I'm totally distracted by the view. The view is pretty, pretty awesome. Be careful, there is a hot oven. Our guests are Planet Money colleagues Amanda Aronchek, Mary Childs, Keith Romer, James Snead, Willa Rubin, and former host Robert Smith. They come in and they admire the feast we spent all day making. Oh, it smells good in here. Smells like, oh my gosh, it smells good.
Speaker 1
Oh, guys, you want to see the proteins? Sure.
Speaker 2
Check this out.
Speaker 3
Oh my goodness.
Speaker 1
Holy moly. Everyone is here. We have a table overflowing with food and a problem. Where should each dinner guest sit? Who should sit next to whom?
Speaker 2
This is the final part of our very Planet Money Thanksgiving, a challenge, the seating arrangement. And we didn't want to just throw people together randomly. We wanted to find the optimal seating
Speaker 1
arrangement. And this, this is actually a really tough challenge. It's related to a whole field of economics called matching theory.
Speaker 2
Economics, at its heart, is all about matching people with the things they want. That usually happens through prices. But there are some markets where you can't put a price on things.
Speaker 1
Yeah, maybe you are trying to match kidney donors with people who need kidney transplants. Or you're trying to match medical students to residency programs. Or public school students to high schools in their area. These are all real-world instances where it would be immoral or unethical to use prices to match people. So instead, economists have used matching theory to come up with solutions. Matching theory even won the Nobel Prize in 2012.
Speaker 2
And the way that matching starts is by asking people what their preferences are. So to make our optimal table seating arrangement, several days before our Thanksgiving feast, I called our guests, each one individually. Can you rank from 1 to 10, like one being amazing, great, and ten being like no, terrible, bad, who you want to sit next to? You want me to choose who I want to sit beside? Yeah. Like, rank them. No. That is like the rudest thing ever. I would never. I
Speaker 3
work with these people. This sounds really uncomfortable. Who
Speaker 2
I'd like to sit next to? Yeah. Oh, gosh. And this is recorded for podcast. We are always recording. We are always recording. Yes. A very awkward question to ask your colleagues, but we had to make them do it for the sake of economics. And people started sharing some answers so i'm seeing amanda on
Speaker 1
friday so in terms of scarcity uh that downvotes her but i love her well i can give you a top two no
Speaker 2
no now i'm second thinking i'm second
Speaker 3
guessing it i've never met jeff glow in person so jeff glow is number one okay
Speaker 1
can i revise my list i
Speaker 3
would i would i want to revise my list okay
Speaker 2
revise your list. And
Speaker 1
after we got a sense of people's preferences, that's when we got to work on figuring out how to make this optimal seating arrangement. And economists, they say there are actually two ways to think about what an optimal match
Speaker 2
even means. The first way to make matches is to optimize for overall happiness. In other words, what match will maximize the group's overall
Speaker 1
utility? Another way to make matches is to optimize for stability. Having a stable match means that there isn't any pair or group of people who could make themselves better off by trading seats with each other.
Speaker 2
Economists have found that in a lot of situations, you can't really achieve both goals. You can't maximize utility and have stability. In
Speaker 1
the real world, in a lot of situations, people have chosen to optimize for stability, like for matching medical students with residency programs or public school students with high schools. And the reason they choose stability over maximizing overall utility is, and this is an oversimplification, but because when you maximize the total amount of everyone's happiness, you can end up with situations that feel unfair, where maybe a few people are really unhappy so that they can make the whole group happier.
Speaker 2
Matches that are optimized for stability, they are the ones that tend to feel more fair. So for our Thanksgiving table conundrum, what we decided to do was to optimize the table arrangement for stability. We wanted to create a stable table. Is
Speaker 1
there an appetizer snack? Would you like to eat a whole sweet potato? Yes.
Speaker 2
Mary, here, have a parmesan crisp. Thanks. And this stable table question and questions like it, they're on the frontier of this field of matching theory. Just this year, two new papers have come out about it. And unlike with the matching problem for kidneys, medical residents and for public schools, which can all be solved with a clever algorithm, economists haven't figured out an algorithm to reliably produce stable table arrangements.
Speaker 1
So to solve this problem, the only thing we could do was to use brute force because we only had eight guests and that's only 5,040 possible seating arrangements. For those who remember from math class, that is 7 factorial.
Speaker 2
So we, meaning Jeff, wrote a computer program that simulated every single seating arrangement possible. And
Speaker 1
for each arrangement, it calculated every person's utility by looking at who was sitting on their left and who was sitting on their right and how that matched that person's preferences. And then it checked to see if that person might be happier if they could switch seats with someone else at the table.
Speaker 2
And after looking at all of this, the computer gave us a seating arrangement. A supposedly stable table. And it was time to put this stable table to the test. So Willa, you're going to sit
Speaker 1
here. Next to Willa is going to be, oh, me. I'm going to sit next to you. All right. And then Keith is going to sit to my left. So everyone is in their seats just looking at the heaping plates of food on the table. But before we let anybody touch the food, well, because this is Planet Money, we're going to quantify how good this seating arrangement really was. So everyone's
Speaker 2
going to get a piece of paper. You get a paper.
Speaker 1
You get a paper. We
Speaker 2
had to see if there were any trades that people wanted to make, if someone else's seat might make them happier. So we asked everyone to look around the table. Is
Speaker 1
there anybody's seat you would rather be sitting in right now? Please write down those seats on this piece of paper right now. That was the test. Have we optimized this table for
Speaker 2
stability? We collected all the slips of paper and there were a couple folks who were interested in sitting in a different seat. We won't disclose who. You
Speaker 1
guys know who you are. But
Speaker 2
none of those people who wanted different seats matched up.
Speaker 1
There are no possible trades within this group that would make anybody happier.
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highlights
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highlights
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