Game, Set, Match: The Designer’s Economist on Matching Market Design

Photo Credit: pexels.com/@ann-h-45017

By Eric Schultz

How are UX design and economics similar? No, this is not a joke. The two disciplines have quite a bit in common. As my recent piece on the surprising links between design and economics shows, both seek to understand why people do what they do, then use what they learn to make those experiences better.

So yep, design and economics have the potential to become BFFs. And sure, I hear you saying, “But those other guys are so boring. All they talk about is math.”

I get it; numbers can be scary for many design types. But the concepts behind those numbers can be fascinating. And when we put them in the brains, and hands, of folks with a design perspective, they have the potential to make many more people a lot better off.

Markets Beyond Money

Markets are human artifacts, not natural phenomena.
— Alvin Roth, “Who Gets What and Why”

Economic markets are human constructs — and as such, they can be designed to work well, or work poorly, or to have no design at all. In this article, I’d like to focus on a concept called matching market design. A few definitions:

• Market design seeks to identify and implement rules that produce desired behaviors in market participants.
• Matching is the area of economics that focuses on the question of who gets what and how, particularly when the goods to be allocated are scarce (not enough to go around), heterogeneous (not identical), and indivisible (not able to be split among two or more parties).

Matching design tends to focus on situations where money cannot be used. A lot of thinking about economics forgets this fact, but much of our lives are spent interacting with other people without involving money — and anything that counters the notion that economics is synonymous with money is good in my book. Crucially, much of the discipline focuses on improving experiences in our lives and with the current state of the world, matching people to people or resources is more important than ever. Once you understand the basics, you’ll start to see matching design all around you — and even more important, areas of life where it could help make people’s lives better. For example, matching design has been used or suggested for:

• Matching donor kidneys to people who need them
• Matching for fellowship interviews
• Matching students to available campus housing
• Matching student tenants to empty nesters with rooms to rent
• Matching students to schools for school choice
• Matching refugees to locations in host countries
• Matching dogs to animal shelters
• Matching vacationers to timeshares
• Matching employees to projects and managers in Google’s internal labor market
• Matching Uber drivers to routes that bring them closer to home at the end of the day

To illustrate a variety of concepts in matching design, I’m going to cover five different but relatable scenarios, and we’ll look at what happens in each.

• Book Swap: What happens if we just expect a market to work on its own?
• Book Club: What common but ineffective ways are matching designs implemented?
• Book Cycle: What does it look like if we apply right-from-the-textbook matching designs?
• Book Summaries: What can happen if we apply the concepts in a unique way?
• Feedback Chain: What if we expand a bit more and consider something else, like people instead of books?

Ready to go? You are, trust me.

Book Swap

I read books. My colleagues read books. I have some I wouldn’t mind trading for new ones, and it would be great to have a virtual book swap where:

• Folks can post what books they have
• Folks can post what books they want

This leads us to our first and most basic conceptual building block: Someone has both wants and willingness to give something up.

Someone may also be willing to give something up with nothing expected in return.

Launch this market as is, with everyone free to “figure it out,” and it will more than likely dissolve as it struggles with the coincidence of wants — I want what you have, and you want what I have — aka bartering. You might have used this technique when you were a kid, trading a yo-yo for some Pokemon cards. You may have even felt like you made a good trade. But for adults, such one-off negotiations are incredibly time-consuming, with a whole lot of friction. How can we make this “market” better for everyone?

Book Club

OK, so that whole swap thing didn’t work out. Let’s say instead we created several book clubs, each with a limited set of spots; each person can belong to only one club. (Yeah, it’s contrived, but there’s a point here. Go with it.)

The design works like this:

• Each club member lists first, second, third ( …nth) book preferences.
• We randomly assign priority numbers.
• We go through the list in priority order and assign each person their first choice.
• After that, if a group still has open slots, we go to the second choice, third choice, etc., until everyone is assigned to a club.

You probably see where this is going. Folks with lower priority numbers don’t get into the more popular clubs. And if they list a more popular club as a first choice, they put themselves in the risky position of not getting their first choice — but also not getting their second, third, and so on.

That brings us to our second conceptual building block: each person has a list of preferences. Each wants some things on that list more than, and some less than, the thing they currently have.

A poorly designed matching market leads to scenarios where people say a thing like “Maybe we should put School B as our first choice, since we have a better chance of getting in there, instead of School A, which we really prefer.” In scenarios like this, people start “working the system” so much so that it seems normal to do so — which makes the system worse for more participants.

Does this scenario sound farfetched? Alas, many school systems used it for assigning students to magnet, charter, or focus option programs (and some still do). In many, strategizing was so ingrained that districts recommended that students not list their first choice as, uh, first.

There are many signs that both the school district and families are aware that students may not always want to rank schools truthfully. The BPS school guide [2004, p3] explicitly advises parents to strategize when submitting their preferences (quotes in original) : For a better chance of your “first choice” school … consider choosing less popular schools. Ask Family Resource Center staff for information on “underchosen” schools.
— Changing the Boston School Choice Mechanism: Strategy-Proofness as Equal Access

Even worse, when fairer systems are proposed, some parents and committees fear that those systems will be to their disadvantage. Now isn’t that a profound lack of trust?

I’m troubled that you’re considering a system that takes away the little power that parents have to prioritize. . . you call this strategizing as if strategizing is a dirty word. . . (Recording from Public Hearing by the School Committee, 05/11/2004).
— The “Boston” School-Choice Mechanism

Ideally, of course, such a system should be designed to work for participants, so less effort is spent on strategizing and enough trust is established that people can safely share their real preferences. A system that doesn’t penalize participants who don’t strategize (or don’t strategize well) creates more equal opportunity and therefore better outcomes.

Economic design principle: Make telling the truth the best option. Design a system so people want to tell the truth — and are not penalized for doing so. A system where truth-telling is the dominant strategy makes it easier to find the most efficient solution, inspires participants to trust the system, and creates a simpler — that is, better — user experience.

Book Cycle

So swaps and clubs haven’t worked out so well. Ready for a design that will work? The rules start like this:

• Each person posts the books they are willing to give up.
• From the books posted, each person lists the books they want, in order of preference.

Imagine that you can link one person’s wants to another and another, and so on. When we find a cycle, we can issue these trades in a trading cycle. Issuing trades on chains is even possible if someone is willing to kick it off without expecting anything in return.

What makes this design so special in the vernacular of economics, it is:

• individually rational: We shouldn’t assume folks will choose something that will make them worse off. In this case, no one is made worse off by participating.
• Pareto efficient: We can’t make any one individual better off without making at least one individual worse off.
• strategyproof: A participant cannot achieve a better result by misrepresenting their preferences (i.e., it’s safe to say that my first choice is my first choice).

Let’s step through how this design works.

Imagine that we have nine participants, each with one book to trade. Each has an ordered list of preferences of the other books up for trade. With this information, the algorithm can iterate step by step, finding any cycles, until each person has a match to the best option available to them.

Step 1: Draw each person’s first preference to the person with the book they want. Notice how many people want Leo’s book, Trailblazer.

Step 2: Find any cycles and issue those trades. Now, since Trailblazer is no longer available, we go to Tyrone’s and Ethel’s next preferred book. But Tyrone wanted only Trailblazer and nothing else. He keeps what he has and leaves the market until a later time.

Step 3: Draw Ethel’s preference for the person with the book she wants instead of Trailblazer. Find any cycles and issue those trades.

Notice how each person keeps their own book if they don’t get any trades due to cycles? Drumroll, please:

Economic design principle: Make it so no one is worse off by participating. Participants may keep what they have now or get something better — but never something worse. If this is not the case, people are likely to opt-out for fear of losing what they have now. When we reach a point where no other allocation can make at least one person better off without making someone else worse off, we call that efficient.

Here’s a video where I show how trading cycles could be implemented in Salesforce:

While this is just a simple book swap, this system could apply to anything from schools to kidneys to housing to projects to virtual networking events. For example, the New Orleans school district used this method to improve its enrollment system. And this isn’t the only way to do matching design (one alternative is deferred acceptance, which favors fairness over efficiency, and tends to be a bit easier to explain).

One big caveat that, I confess, I’ve been putting off mentioning: We can design markets to be rational, efficient, strategyproof, and fair. But they cannot be all of these things at once, because some aspects of these goals are at odds with each other. One mechanism may be highly efficient but only moderately fair, while another is the epitome of fairness but not nearly as efficient.

Economic design principle: Every design has trade-offs. Consider what’s important to the folks using the system. Is fairness or efficiency more important? You’re not going to get everything you want.

Book Summaries

We now have a functional book trading system. But even if I get exactly the books I want, there’s no way I’ll have time to read them all. What if each participant could write up a summary of the main points of each book read, to share with their team and support collaboration?

Does this scenario sound familiar? “Hey, have you read that book by Brené Brown?” “Yeah, it was great. We should use some of those ideas.” “For sure.” Yet for all your good intentions, those ideas are unlikely to get beyond your initial conversation. Yes, Salesforce has great collaboration tools, like Quip, but for this purpose, we also need a matching design that gives folks incentives to write, share, and collaborate on all the great books they’ve read.

Let’s take our matching design from the Book Cycle and add these components:

• Let people post the book summaries they want
• Let people post preferences for the book summaries they’re willing to write
• Find cycles and chains of trades

Now because this is a digital good, once it’s produced, anyone can consume it. We want to discourage consuming but not contributing, even if for good reasons (“I meant to write a summary, but I was too busy.”). But because this is a digital good, we also have quite a bit of flexibility.

Here’s one of the potentially many solutions:

• All summaries are released only once all participants in a cycle have completed their part.
• We nag participants who are holding back trades.
• If we don’t get everyone in a cycle to contribute a summary after some period of time, we release everything back into the market and try again.
• Participants who have not yet contributed their summaries can see sneak peeks, but not entire summaries.

Feedback Chain

Another area I’ve been thinking about is feedback within an organization. Sharing feedback is incredibly important, but even though there are people who want feedback and those willing to get the ball rolling by offering it, it can be hard to create a sustainable feedback culture.

To address this problem, let’s use some of the concepts and principles we’ve been discussing:

• Chains of trades
• Volunteers
• Preferences
• No one is worse off by participating

Let’s say we’re trying to start chains of feedback, originating from someone who donates feedback. Imagine a design like this.

• A user sends feedback to a receiver.
• Receivers are notified of feedback, but cannot view it until they send another user feedback.
• Sending feedback unlocks the feedback you’ve received.
• Users can set preferences (e.g., “I welcome all feedback, but could really use feedback on my presentation skills”).

Here’s another video where I show how this could be easily implemented in Salesforce:

The Takeaway

Even if you never find yourself designing with a common matching mechanism, the concepts and principles these scenarios represent can shape your user experience design for the better.

Markets are evolving human artifacts, and we can learn from both their failures and the designs that make them succeed. To hone your design skills, and maybe even make the world a bit better in the process:

• Look for ways to match people to things, institutions, or other people to make them better off
• Make telling the truth the best option
• Make no one worse off by participating
• Ask yourself what’s more important in each scenario, fairness or efficiency

Combine design and economics in this way, and we can all be winners.

This is the second article of The Designer’s Economist, a series about Design and Economics. If you enjoyed this, consider reading the introduction to the series An Economist’s Perspective on User Experience Design.

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🙌

Special thanks to my wife, Karen Kahn, and Alexandra Laxmi Iyer for so much encouragement and Lisa Gluskin Stonestreet for the amazing edits.

Also, thank you Lana Herrera and Alan Weibel for helping to make this happen.