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.

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.  

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.

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. 

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.

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.)

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).

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.