How I Cross Streets
There are subtleties beyond "don't die."
A few years into knowing me, my now-spouse told me she had a question. She phrased it something like “What’s going on with the weird way you cross a street?” She’d worked out what I was doing, but not why. And it is a little unusual, the way I cross, but not in any blatant way—this was a perceptive question. So yeah, I fell in love with her a little more, which is probably why I remember the moment.
This post is literally about how I cross streets.
The Strategy
If I, or someone I’m with, cares about time: I carefully look both ways while pretending not to, then cross the street at a brisk walk, remaining alert but trying to look as distracted as possible.
If I’m mostly just walking for the sake of walking: I check whether there are any cars coming. If there aren’t, I cross. If there are, I stay on the sidewalk, turn to face the oncoming traffic, and, if there’s sidewalk in that direction, start walking.
The Why
Scenario 1: I, or someone I’m with, cares about time.
I cross streets in two different styles, depending on circumstances. This approach is for when I’m walking from point A to point B as the main goal of the walk.
Everywhere I’ve lived, when crossing a street as a pedestrian, I’ve had to worry about getting hit by a car. The drivers of cars are also worried about hitting pedestrians. So in that respect, our interests are aligned. But drivers are also trying to get from point A to point B, so all else being equal, they would rather I wait for them rather than they wait for me. And I’d rather the reverse. So our interests are only partially aligned.
This is where the work of Thomas Schelling, a 20th-century game theorist, comes in handy. Now, “game theory” is a phrase that sounds like it should mean “theory of games.” But it’s actually much more abstract, and therefore more widely useful. In game theory, we’d model a typical street crossing—one pedestrian who probably technically has the right of way, one driver who doesn’t care—like this:
The numbers in parentheses are the points each player gets from each of the four possible outcomes, starting with the Pedestrian’s points. This 2x2 grid translates to “It’s a two-player game. We both make our choices at the same time. If we make different choices, whoever chose to go gets 2 points (they’re happy to get to their destination a few seconds faster), while the other one gets a point because they’re closer to being able to go. If we both wait for the other, nobody gets any points, because nothing happens. If we both go at the same time, something moderately-to-extremely bad happens, so we each lose a thousand points.”
You may have heard the terms “zero sum” and “nonzero sum.” That comes directly from this kind of modeling. If the numbers in each of the parentheses sum to zero, the game is zero-sum—every point I get is a point you lose. In this one, some of the parentheses don’t sum to zero (all but the top left), so this game is non-zero sum. The prisoner’s dilemma is another example of a non-zero-sum game. I think the technical term for this one is even more famous, though—“chicken.” (There might be a more precise name for this variant that I’ve forgotten.)
The common-sense analysis here works pretty well, just not quite optimally. The points we lose from a car accident, or even a scary near-miss, are so much higher than the points we gain from crossing first, that if we prioritize making absolutely sure no accident occurs, our average score is close to the highest possible. But not the highest. The value of your time, relative to the risk of a car accident, is not negligible. That is, after all, why we drive cars at all.
If you choose to wait until you’re absolutely sure no cars are coming, some drivers will be jerks and ignore your legal or informal right-of-way. Even if you start crossing, some drivers will be mega-jerks and cut you off. In both cases, this is because a fixed strategy is an exploitable strategy. If the pedestrian is definitely going to avoid risking an accident, the driver can grab some free points at their expense.
In conventional game theory, the solution to this is a mixed strategy—i.e. one that involves randomly selecting one of the two options, not necessarily with equal probability. Suppose pedestrians crossed the street recklessly every one time in a thousand. Drivers then have to choose between letting the pedestrian go first, thereby foregoing a point, or going first, with a one in a thousand chance of losing a thousand points. The two considerations approximately balance each other out. If pedestrians crossed recklessly a little more often than one in a thousand, they’d give drivers a clear incentive to let them cross.
As with most Econ 101 models, if you try to actually apply this logic, people will die. Drivers and pedestrians come in a wide variety. We’re not always playing exactly the same game, and we don’t always have a good read on each other. Some drivers have a different payoff ratio—either they’re in a big hurry, or they place an unusually low value on human life. Also, some drivers are simply bad drivers, and others are just now discovering that their brakes are broke.
Schelling-type analysis, as first laid out in his 1960 book The Strategy of Conflict, is more respectful of the rich diversity of human experience. For Schelling, in situations like this, you should always be thinking about the limited information your counterpart has about your mental state, as well as where your interests do and don’t align. I don’t actually know how Schelling crossed streets, but he won a Nobel Prize for economics and more importantly lived to the age of 95, so he was probably pretty good at it (unlike Albert Einstein, whom someone I know almost vehicular-manslaughtered once while driving through Princeton. Not to name-drop or anything).
Schelling pointed out that interactions like this tend to work out better when we control what is and isn’t ambiguous about our behavior. In this case, I benefit as a pedestrian from making it ambiguous how careful I’m being. Unless they’re as thoughtful and perceptive as the love of my life, they aren’t going to be totally confident that I checked for oncoming traffic, and they aren’t going to be totally confident that if they tried to cut me off, I wouldn’t obliviously jog into them. So this has the same effect in reality as the randomization strategy does in idealized perfect-information world. It’s better, because it fails more gracefully in cases where the model doesn’t apply—I still see the out-of-control car coming and dodge it (source: am alive).
By default, drivers already benefit from ambiguity—pedestrians usually can’t see their faces or body language until they’re really close, by which point it’s often too late. Drivers who cut you off are exploiting this asymmetry. So really I’m just leveling the playing field. This saves a few seconds, partially offsetting all the time I spend overthinking trivial decisions.
To do this correctly:
Make sure you have good peripheral vision. I have long unruly hair sometimes, and when I do I tuck it behind my ears before crossing the street.
Check for incoming traffic right before stepping onto the street, as quickly as you safely can, minimizing the side-to-side motion of your head. Like most animals that evolved in places with lions, humans tend to be quite good at this.
Cross at the highest speed that you can without significant risk of stumbling.
While crossing, look in the direction of various landmarks just off the street to your left and right. This lets you keep checking for oncoming traffic, while looking like you might be doing that, or might be noticing an attractive storefront or unusually athletic squirrel.
If you’re in the middle of the street and a fast-moving car shows no signs of stopping, take evasive action. If they’re still willing to play chicken when you’re being ambiguous, you should let them win, because it looks like one of the assumptions under which you have a chance of winning doesn’t apply.
Like most street-crossing strategies, this all becomes automatic after you do it for a bit. It’s just crossing the street.
Scenario 2: It’s a lovely day.
I like to walk. I do it a lot, often without having a destination in mind. Even when I do, I often don’t care about when I’m going to get there, give or take a few minutes.
Unfortunately, cars. Cars everywhere. I can’t help but end up with a street to cross. But now, my payoffs look different—I care just as much about avoiding an accident, but don’t gain or lose points in any other scenario.
Some pedestrians in this situation will still cross when they have the right of way. This, however, is imposing a cost on drivers to no benefit to yourself. I probably don’t have to explain why that’s bad, but for the sake of parallelism with the previous section…
Pareto optimality is the term for when there is no change that could benefit someone without doing harm to anyone else. This is a very weak condition. For example, if we’re discussing how to divide $100 between two people, every possible distribution is Pareto-optimal. And in our messy, densely interconnected reality, almost anything worth doing is going to harm someone. At its worst, this concept is sometimes used to justify entrenched inequalities—they’re Pareto-optimal, so they’re still the best of all possible worlds! This is rarely actually true in the long run, in any practical sense, because extreme enough inequality will create economic inefficiencies.
But the flip side is that when you see an actual Pareto improvement, you should grab it with both hands. If you know you’re not in a hurry, and you don’t know whether someone else (or the person behind them) is in a hurry, you should let them go first. The only cost to you is the one-time, up-front cost of changing a habit, and you can recoup those lost points in feelings of moral self-complacency.
Now, some people will try to accomplish this good deed by waving the other party ahead. DO NOT DO THIS. It’s an example of what some people call the Wave of Death. Worst case, some people will misinterpret your wave as meaning “go ahead, I’ve checked for all possible hazards in all directions!” and literally die. The much more common failure mode is that they don’t see your wave, do see some other reason not to go, or wave back “no no, you go” forgetting that the light is wrong for you to see their wave. You don’t know why they’re not going. Maybe they’re distracted and about to go, maybe they’re willing to sit there forever and starve to death out of politeness. I hate this. Better to just cross than to wave.
The trick here is the opposite of the one above—your interests are fully aligned, so you want your intentions to be unambiguous. Turn and face to the side. Don’t put your back to the street, because that can look to a driver like maybe you’re about to walk backwards out into the street, probably while saying goodbye to someone. Turn to the side. Drivers are hopefully aware of the rich diversity of human behavior, but even still, they’re going to be confident you don’t plan to crab-scuttle across the street sideways.
If you can, ideally you now start walking in the new direction. This reduces ambiguity still further, keeps your heart rate elevated, and has a 50/50 chance of getting you closer to your intended destination. If you walk antiparallel to the traffic (I never get to use that word!), you can more easily see if and when all the cars are gone. If that happens before you reach the next intersection, you may have the option of crossing after all.
Thank You For Coming To My Ted Talk
Did I get this all right? For me, at least? You, or your local norms, might be different enough that this logic doesn’t apply. But am I crossing the street in an optimal way, or have I missed a trick? I’m not sure, and would welcome feedback.
Bonus: Trivia
“This saves a few seconds, partially offsetting all the time I spend overthinking trivial decisions.” I wrote this joke above, and then realized it was also kind of a pun. The word trivial derives from an ancient Roman word for intersection. Specifically it’s for a three-way intersection (hence the tri), which hurts the pun a little, but you do still sometimes need to cross a T-intersection on foot. So they are trivial decisions in (*coughs importantly*) the classical sense.
Intersections are natural public gathering places. The modern meaning of trivia descends from a kind of sneer: the common people, loitering in intersections, chattering about things that couldn’t possibly be important. But there’s no such thing as an unambiguously unimportant fact. Connections are everywhere.
Intersections were also dangerous in those times, but for a different reason. Julius Caesar was assassinated at, or near, a trivium. It’s where the conspirators felt most confident they could slow him down.