Is Uber fare splitting fair?
By: Ry Sullivan
Tags: Shapley Values, Uber, Game Theory, Curiosity, Fairness

Is Uber fare splitting fair?

Human behavior and game theory collide in the world of ride-sharing with friends. Ry Sullivan Apr 20·9 min read

Am I about to make ride-sharing less fun? Probably. Party on!

In my last blog post I combined two well known game theory exercises (the Unscrupulous Diner’s Dilemma and the Pirate game) into a new puzzle: the Pirate’s Diner Dilemma. The aim of the problem was to illustrate how the rationally optimal outcome differs from the solution expected from social norms.

Many friends questioned whether they wanted to dine with me again (I hope jokingly!). Others asked whether there was any practical use to the thought experiment. Wouldn’t all diners end up behaving based on emotion, psychology, and culture (i.e. splitting a check evenly) versus trying to be strategic and sneaky like pirates? What social activity will you ruin next, Ry?

These were good questions. The thought process that goes into dividing things amongst people raises a tension between what is rational and what people actually do in the world. Or more philosophically: What is fairness? Why do we think some things are fair and others aren’t? How does fairness change as we reimagine situations?

Rather than explore a theoretical and artificial game, I decided to seek a real-world example to understand fairness dynamics in the wild. I found one in a situation I face regularly but rarely think about while traveling around San Francisco (at least pre-COVID): Is Uber fare splitting fair? Time to ruin another social activity with math!

The Airport Problem

Before answering this question, I think it’s useful to take a step back and explore a well-known game theory thought experiment that deals with splitting costs: the Airport Problem.

Imagine three companies own and operate airlines. They decide to collectively build an airport with a runway that will support all of their different needs. Company A operates only small single-propeller planes and needs a short runway whose length costs $100 to build. Company B owns mid-sized jets that require a longer runway costing $200. Company C flies jumbo jets that need the longest runway costing $300 to build.

How should the airlines split the cost of building a single runway that they can all use?

The Airport Problem: How should airlines with different runway length needs divide the costs of a runway that they can all use?

If they all decide to split the total $300 cost evenly, Company A feels put out. If Companies B and C are willing to pay for the $100 of the short runway as part of their own cost, why should Company A pay $100 for this length? If Company A is asked to pay $100, why not just go build their own runway and not deal with Company B and Company C at all?

If Company A and Company B ask Company C to cover all the costs — e.g. “You were already going to build a $300 runway, so what’s the difference to you?” — Company C feels put out. Why coordinate on this project if Company A and Company B are going to freeload? Company C is better served by building their own airport runway.

Fairness in this case feels like it should exist somewhere between these extremes with each Company paying less than if they did things on their own. But what should the split be? The game theoretical mathematician Lloyd Shapley derived an answer to problems like these — earning him the 2012 Nobel Memorial Prize in Economic Sciences. The Shapley value for this problem is achieved as each company splits the cost of the parts of the runway they benefit from using.

For the first $100 section of runway, all three companies benefit so each pays a third: $33.33 each. For the next $100 section of runway, only Company B and Company C benefit — so they split the cost: $50 each. For the final section of runway, only Company C benefits so they pay the full $100. Overall Company A pays $33.33, Company B pays $83.33, and Company C pays $183.33. All benefit from working together and pay their “fair” share of the runway length they need. Note this is one way (among many!) to divide the cost of the runway — but one that mathematically approaches fairness.

The Shapley value solution to the Airport Problem.

Non-linear Airport Problems

The Airport Problem works out nicely, partly because there’s overlap between what the airline companies need when building runways. The runway needed by Company A is part of the runways needed by Company B and Company C. In the real-world, things get complicated when things don’t line up so nicely. An example of this is available from Yale on Coursera which I’ve recreated below.

Imagine three friends (Rider A, Rider B, and Rider C) want to share a taxi home but who all live in different parts of town. If each took a cab home separately they’d spend a total of $32 dollars as illustrated below:

All riders live in different parts of town and could travel to their respective destinations solo.

However, if the friends share a single ride, they can collectively reduce the amount to $18 with each leg of the journey adding $6 to the trip. How should the friends divide the total fare. Or, put differently, how should the friends divide the $14 in collective savings amongst themselves? Should they split the fare at $6-$6-$6 or something else? If they do an even split, why would Rider A not just choose their own cab?

The optimal path for splitting a ride between the three destinations.

To answer that question, we’d need more information including the costs of taking alternate routes between the destinations. Using GPS and taxi fare predictions, we could draw the following payment map:

The routes and fares between all rider destinations.

With this information we can apply the Shapley value once again to find what each rider should “fairly” pay. The Shapley value for this scenario produces the following result: Rider A pays $2.83, Rider B pays $5.33, and Rider C pays $9.83, for a total of $18.00. Similar to our airport problem, each rider benefits versus taking their own ride. And the riders who live closest (Rider A) or provide the most route continuity advantages (Rider B) pay slightly less than under the scenario where the total fare is split evenly.

If you want a full explanation of the math and reasoning — which involves probabilities and logic (fun!) — you can find it here.

What happens in the real world? Enter: Uber.

Calculating fares down to the penny is awkward and tedious for riders. Asking them to make a rational decision by calculating the optimal path versus multiple alternate routes to produce a Shapley value is difficult and (dare I say) a little weird. I’ve certainly never seen that happen in real life. And I have nerdy friends.

But what if you’re a software company like Uber that can do those calculations as fast as riders enter in their destinations and doesn’t have to ask riders about their sense of fairness? What do you do? Do you split the fare evenly amongst riders or do you adjust the fares based on the destinations of the riders including distance and how much contributes to collective gains (e.g. a destination on the route of two other riders)?

Uber’s fare split feature as rolled out in 2013. Photo from Techcrunch.

According to Uber’s help website, they opt for the even-split option. Every rider who joins a fare split ride pays the same amount. They also add a +$0.25 cost per rider, which seems unnecessary in my opinion.

Screenshot from Uber’s website.

This is probably what most people expected. And while I’d love to imagine the Uber R&D and business teams asking profound questions about human behavior, rationality, and fairness I expect the reasons are simpler. Occam’s Razor suggests that the following explanations are more likely:

It’s easier to code dividing the fare by the total number of riders than doing a complex Shapley value calculation. I imagine the original pull request by Uber’s engineers focused on getting a solution into the market quickly versus spending time finding a more complicated optimized solution.

If fares aren’t split evenly, Uber would probably get support tickets and complaints from confused riders. For the riders in our example $6-$6-$6 makes sense, whereas $2.83-$5.33-$9.83 is confusing. Support tickets cost money and confusing/losing riders is bad. Uber is a business after all.

Uber can’t match specific riders to specific locations (assuming they’re not tracking the GPS movements of our phones that closely…). Either they would have to do something creepy (like GPS tracking) or ask riders to input this information. This extra rider friction isn’t worth the effort, and it might dissuade use of the feature.

Trying to cleverly calculate payments exposes Uber to all sorts of edge cases. For example, what if riders stop at a destination to drop something off, but don’t actually get out there and continue on?

But what happens if one rider lives really far away?

In the prior example, I believe most people would agree that splitting an $18 Uber fare evenly amongst riders is reasonable. It feels fair — and behavior usually trumps game theory rationality. Like I said, I’ve never even checked how Uber calculated fare splits until writing this blog.

But what happens if Rider C lives 2 hours away? Now the total cost amongst riders is $212 assuming the first legs of the journey remain the same and the last costs $200. The new journey is shown below:

The problem earlier — except now one rider lives quite far away.

Does an even split where each rider pays $70⅔ still feel fair? Probably not. Yet, if you chose the split fare option on Uber, that’s how things would be divided: $70.66-$70.66-$70.67 (Now that I think of it, I wonder who Uber decides to give the extra penny to…).

What I imagine happens in this situation is that Rider C simply offers to pay for the whole trip, allowing Rider A and Rider B to tag along for free. Maybe they strike an off-app bargain where they agree to buy Rider C a drink the next time they hand out. That’s what would happen with my friends anyway.

In other words, people will naturally self-select into the fare-split option when they think doing so makes sense. In extreme cases, they won’t. Imagine what would happen if Rider C suggested the fare split option in this case. You can play this awkward conversation out in your head.

Lingering questions

I’m now left with new interesting questions to ponder. For the Uber fare splitting case, at what point do people stop offering to fare split? Is it when Rider C’s additional leg is $10? $20? $50? Do decisions change if people think in terms of distance versus dollars? What if the ratios of the problem were the same but the split was for something bigger like a large development project in the millions of dollars: would $6m-$6m-$6m be preferable to $2.83m-$5.33m-$9.83m or is fairness also based on size? Who most often suggests to split the fare in real life— Rider A, B, or C? Why?

I bet there’s some interesting behavioral insights to uncover — and I’m betting they’re not rational. If anyone has seen studies like these, I’d love to read them. If not, I tried polling my friends on Twitter. So far I’ve just learned that they’re good people… 😂

Additional Reading