Beware unfinished bridges

[Adam Zerner]

This guy don’t wanna battle, he’s shook
’Cause ain’t no such things as halfway crooks

- 8 Mile

There is a commonly cited typology of cyclists where cyclists are divided into four groups:

1. Strong & Fearless (will ride in car lanes)

2. Enthused & Confident (will ride in unprotected bike lanes)

3. Interested but Concerned (will ride in protected bike lanes)

4. No Way No How (will only ride in paths away from cars)

I came across this typology because I’ve been learning about urban design recently, and it’s got me thinking. There’s all sorts of push amongst urban designers for adding more and more bike lanes. But is doing so a good idea?

Maybe. There are a lot factors to consider. But I think that a very important thing to keep in mind are thresholds.

It will take me some time to explain what I mean by that. Let me begin with a concrete example.

I live in northwest Portland. There is a beautiful, protected bike lane alongside Naito Parkway that is pretty close to my apartment.

It basically runs along the west side of the Willamette River.

Which is pretty awesome. I think of it as a “bike highway”.

But I have a problem: like the majority of people, I fall into the “Interested but Concerned” group and am only comfortable riding my bike in protected bike lanes. However, there aren’t any protected bike lanes that will get me from my apartment to Naito Parkway. And there often aren’t any protected bike lanes that will get me from Naito Parkway to my end destination.

In practice I am somewhat flexible and will find ways to get to and from Naito Parkway (sidewalk, riding in the street, streetcar, bus), but for the sake of argument, let’s just assume that there is no flexibility. Let’s assume that as a type III “Interested but Concerned” bicyclist I have zero willingness to be flexible. During a bike trip, I will not mix modes of transportation, and I will never ride my bike in a car lane or in an unprotected bike lane. With this assumption, the beautiful bike lane alongside Naito Parkway provides me with zero value.^[1]

Why zero? Isn’t that a bit extreme? Shouldn’t we avoid black and white thinking? Surely it provides some value, right? No, no, and no.

In our hypothetical situation where I am inflexible, the Naito Parkway bike lane provides me with zero value.

1. I don’t have a way of biking from my apartment to Naito Parkway.

2. I don’t have a way of biking from Naito Parkway to most of my destinations.

If I don’t have a way to get to or from Naito Parkway, I will never actually use it. And if I’m never actually using it, it’s never providing me with any value.

Let’s take this even further. Suppose I start off at point A, Naito Parkway is point E, and my destination is point G. Suppose you built a protected bike lane that got me from point A to point B. In that scenario, the beautiful bike lane alongside Naito Parkway would still provide me with zero value.

Why? I still have no way of accessing it. I can now get from point A to point B, but I still can’t get from point B to point C, point C to point D, D to E, E to F, or F to G. I only receive value once I have a way of moving between each of the six sets of points:

1. A to B

2. B to C

3. C to D

4. D to E

5. E to F

6. F to G

There is a threshold.

• If I can move between zero pairs of those points I receive zero value.

• If I can move between one pair of those points I receive zero value.

• If I can move between two pairs of those points I receive zero value.

• If I can move between three pairs of those points I receive zero value.

• If I can move between four pairs of those points I receive zero value.

• If I can move between five pairs of those points I receive zero value.

• If I can move between six pairs of those points I receive positive value.

I only receive positive value once that threshold is met.

Why does this matter? Well, say that you are the city of Portland and you are deciding whether to add an unprotected bike lane between points A and B. You have to ask yourself in what way you expect this new unprotected bike lane to add value for people.

If you just add that one bike lane and then stop, I don’t see the new bike lane getting many people past a threshold that would yield positive value for them. I think it’d function largely as an unfinished bridge.^[2]

However, if the new bike lane is one step in a larger plan to build a complete bridge, so to speak, then that starts seeming to me like something that might be a good idea. The “larger plan” part is crucial though: you only get value once the bridge is complete, so if you’re going to start building a bridge, you better make sure you have plans to finish it.

1. ^

   Well, I guess I should say zero direct value. It provides me with indirect value in various ways. For example, it might persuade a friend to meet me at a coffee shop.

2. ^

   In addition to making life a little bit better for a few “Strong & Fearless” bicyclists.

[DirectedEvolution]

Literal unfinished bridges provide negative value to all users, and stand as a monument to government incompetence, degrading the will to invest in future infrastructure.

Short bike lanes provide positive value to at least some users. They stand as a monument to the promise of a substantial, interconnected bike grid. They incrementally increase people’s propensity to bike. They push the city toward a new, bike-friendly equilibrium. The same is true for mass transit generally when the components that have been built work well. Portland ought to be thinking about its population-level utility over the long run, not your personal utility now.

As such, I think that “unfinished bridges” is a misleading metaphore for the S-curve phenomenon you are talking about, and “beware” is probably not the right take when it comes to the idea of incrementally moving along S-curves. In fact, when the S-curve is the payoff for incremental steps toward a desired goal, “take heart” seems more correct. Incremental moves along an S-curve bring you closer to saturation faster than it would seem, judging by linear extrapolation of the marginal gains of each incremental step. I added labels to Tiuto’s plot that reflect this change in interpretation.

Edit: There are multiple reasons all the incremental steps toward saturation of the S-curve aren’t always taken at once. In the case of bike lanes, availability of funds, land, and political will are sporadic. Incremental opportunities must be seized where possible over the course of years or decades. In other cases, there may be uncertainty in how to design the buildout to maximize the level of saturation that becomes incrementally resolved over time, such as a startup that’s trying to find product/​market fit or a politician who’s trying to determine what platform would maximize their vote share by gauging the public’s reaction to a sequence of political appearances.

[Adam Zerner]

America’s response to covid seems like one example of this.

If I’m remembering correctly from Zvi’s blog posts, he criticized the US’s policy for being a sort of worst of both worlds middle ground. A strong, decisive requirement to enforce things like masking and distancing might have actually eradicated the virus and thus been worthwhile. But if you’re not going to take an aggressive enough stance, you should just forget it: half-hearted mitigation policies don’t do enough to “complete the bridge” and so aren’t worth the economic and social costs.

It’s not a perfect example. The “unfinished bridge” here provides positive value, not zero value. But I think the amount of positive value is low enough that it would be useful to round it down to zero. The important thing is that you get a big jump in value once you cross some threshold of progress.

I think a lot of philanthropic causes are probably in a similar boat.

When there are lots of small groups spread around making very marginal progress on a bunch of different goals, it’s as if they’re building a bunch of unfinished bridges. This too isn’t a perfect example because the “unfinished bridges” provide some value, but like the covid example, I think the amount of value is small enough that we can just round it to zero.

On the other hand, when people get a little barbaric and rally around a single cause, there might be enough concentration of force to complete the bridge.

[cubefox]

Perhaps more generally: The effectiveness of energy put into an action can easily be a non-linear function. Most gain in value may be achieved at a certain energy level, such that energy differences significantly below or above that level hardly change anything.

In some cases the function may even be non-monotonic, where spending some larger amount of energy is actually worse than spending some smaller amount.

[Adam Zerner]

Yeah. Unfortunately I only learned about them after writing the post, but I think S-curves are the right way to model these situations.

[dr_s]

Well, this is really just networking effects. Also why it’s really hard to break out with your new hot dating app or social media website, no matter how much Tinder or Twitter suck. For your app to provide utility to users, it needs… users. Good luck breaking that stalemate.

Roads, or bike lanes, are a very literal network. Usefulness suddenly undergone a phase transition only when you hit the percolation point.

[Dagon]

This combines well with Robin Hanson’s theory that signaling explains most public choice oddities. Showing that we care about bike riders doesn’t require that we actually make the city work for bike riders.

[ChristianKl]

Bike lanes don’t only exist to get people from point A to point B. They also exist to provide an outlet for biking as a recreational activity.

I would trust decisions based on empiric measurements of usage of the bike lanes a lot over your analysis when it comes to justifying decisions by cities.

[Jackson Wagner]

So, sure, there is a threshold effect in whether you get value from bike lanes on your complex journey from point A to point G. But other people throughout the city have different threshold effects:

• Other people are starting and ending their trips from other points; some people are even starting and ending their trip entirely on Naito Parkway.

• People have a variety of different tolerances for how much they are willing to bike in streets, as you mention.

• Even people who don’t like biking in streets often have some flexibility. You say that you personally are flexible, “but for the sake of argument, let’s just assume that there is no flexibility”. But in real life, even many people who absolutely refuse to bike in traffic might be happy to walk their bike on the sidewalk (or whatever) for a single block, in order to connect two long stretches of beautiful bike path.

When you add together a million different possible journeys across thousands of different people, each with their own threshold effects, the sum of the utility provided by each new bike lane probably ends up looking much more like a smooth continuum of incremental benefits per each new bike lane that is added to a city’s network, with no killer threshold effects. This is very different from a bridge, where indeed half a bridge is not useful to any portion of the city’s residents.

Therefore, I don’t think “if you’re going to start building [a bike lane network], you better m ake sure you have plans to finish it”. Rather, I think adding random pieces of the network piecemeal (as random roads undergo construction work for other reasons, perhaps) is a totally reasonable thing for cities to do.

Another example of individual threshold effects adding up to continuous benefit from the provider’s perspective: suppose I only like listening to thrash-metal songs on Spotify. Whenever Spotify adds a song from a genre I don’t care for—pop, classical, doom-metal, whatever—it provides literally ZERO value to me! There’s a huge threshold effect, where I only care when spotify adds thrash-metal songs! But of course, since everyone has different preferences, the overall effect of adding songs from Spotify’s perspective is to provide an incremental benefit to the quality of their product each time they add a song. (Disclaimer: I am not actually a thrash-metal fanatic.)

[Gordon Seidoh Worley]

Sort of a tangent, but when I ride I technically fall into the “strong & fearless” group, but don’t feel like it.

I’d much prefer protected bike infrastructure, but for a variety of reasons it’s often unavailable. In those cases, at least in an urban setting, I generally prefer to ride in the lane with cars over using an unprotected bike lane. To me this is obvious:

• in the lane the cars will definitely see you

• if you ride far enough into the lane cars can’t pass you by “squeezing by”, getting dangerously close

• less likely to put yourself in precarious situations at intersections

Unprotected bike lanes seem like the worse possible option, and find it strange that anyone falls into the “enthused & confident” category.

[Adam Zerner]

Hm yeah, I feel the same way. Good point.

[Tiuto]

I had been thinking about the exact same topic when I read this article, only I was using bus routes in my analogy. I created a quick program to simulate these dynamics^[1].

It’s very simple, there is a grid of squares, let’s say 100 by 100, each square has some other square randomly assigned as its goal. Then I generate some paths via random walks until some fraction of squares are paths. Then I check what fraction of squares are connected to their goal via a path.

Doing this we get the following s-curve:

The y-axis shows the fraction of squares that are able to reach their goal. The x-axis is what fraction of squares were turned into path squares^[2].

We can see what we probably expected, the first few paths do almost nothing but eventually each additional path has a large payoff.

The path length determines how long each random walk is. Long walks tend to create blobs of path. This is good if there are very few paths, you might get lucky and connect a couple of squares to their goals. But once there are lots of paths just turning random squares into paths is actually better.

To make the situation a bit more realistic I also simulated what happens if all generated paths are straight.

The yellow graph hasn’t changed but the longer paths are now more efficient and are never beaten by the totally random paths. These two maps show the difference, clearly the top approach would work better.

I also have to add that I find the idea that a cyclist wouldn’t cycle on a road absurd. I don’t think I know a single person who wouldn’t do this, presumably a US vs EU thing.

1. ^

   Code is here.

2. ^

   To be connected to its goal a square and its goal don’t have to be paths themselves just directly adjacent to a path connecting both. This is the reason the plots can go above the 45° line.

[Adam Zerner]

Cool simulation!

I also have to add that I find the idea that a cyclist wouldn’t cycle on a road absurd. I don’t think I know a single person who wouldn’t do this, presumably a US vs EU thing.

You mean the “No Way No How” group? If so, yeah, it feels implausible to me as well. I have a feeling that for people who were surveyed and said this, it wouldn’t match their actual behavior if they were able to experience an area with genuinely calm roads.

[Adam Zerner]

Related: this video shows an example of a bike lane that just randomly ends. It’s main point is that the city should put up signs to warn you that it will end so you don’t head down it if you don’t want to, but I think that it also kinda illustrates the idea that as an “unfinished bridge”, it doesn’t really provide much value (it probably provides negative value).

[R S]

I didn’t even realize there was such a categorization of bikers

Years ago I tried doing it a couple times and stopped because I fall into group 3

I tried being group one and an ambulance honked at me because I took a left turn in front of it (sirens were not going off)

And I just never did it again

I figured most bikers were group one

[Adam Zerner]

Yeah I think those experiences are pretty common. I was the same until I started going to some local bike meetups. I would see these intense looking bikers on their road bikes riding amongst fast, aggressive traffic and thought that’s what you need to do if you’re a biker, and that I just lacked the skills. I would stick to sidewalks and off-road paths.

Well, I guess in places without good bike infrastructure there’s a lot of truth to my assumptions actually. But the important thing to realize is that, although hard to find, some places do exist that are actually decent for those of us in group three.

[Trashmanbenny]

Well I understand that you are talking about how people in the interested but concerned group are affected by the “unfinished bridge”, we should note that there are still 13% of people who would use an unprotected bike lane.

Further, the unfinished bridge helps build up to addressing the network problem, with less investment than a protected bike lane, we can move from 7% of cyclists using the system to 13%.

Finally, this is a chicken and egg sort of problem. People need to cycle to make the bike lanes worth it, but no one will start cycling without any bike lanes. If society deems more cyclists to be a social good, we need finished bridges, but unfinished bridges are still better than no bridges.