Who will shovel the snow? This weird math puzzle can help

Who will shovel the snow? This weird math puzzle can help

By Joseph Howlett edited by Clara Moskowitz

A snowstorm is a real test of the social contract. Nature dumps 12 to 18 inches of nuisance evenly over an entire community and leaves it to you and your neighbors to clean up the mess. Who cleans the streets or sidewalks? How about “sneckdowns”?! Each storm leaves a maze of shared responsibilities for us to resolve and not always without conflict.

It is still largely an open mystery why and how social creatures like ourselves choose to cooperate. Game theorists, computer scientists, anthropologists and behavioral economists have all approached the problem from different angles. There is even a scientific version of the blizzard called the “snow drift problem”.

It is a variant of the prisoner’s dilemma, where two accomplices in a robbery are separated and asked to sneak up on each other. Each of them must decide whether to betray their partner to go free or to stay quiet in the hope that both can escape. (If both sneak, both go to jail.) The snow drift problem poses a related question: Who should shovel in a selfish world?

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Imagine waking up in the middle of a snowstorm and having to get to work. You manage to dig out the car and make it halfway until a massive snowdrift blocks the way. There’s another car coming from the other direction that’s also stuck, and you both have a shovel.

Both drivers must choose whether they want to cooperate or not. The game awards points to each of the four possible outcomes. You win the most points if you can convince the other person to do all the work. The payoff is moderate if both agree to shovel – everyone gets to their job with minimal delay. And even if your opponent chooses to stay warm in the car, it’s better to shovel. It’s not fair, but at least you’ll (eventually) get where you’re going.

Game theorists typically break the decision down into several rounds, as if the two drivers renegotiate after a few minutes of sparring. Compared to the apparent consequences of the prisoner’s dilemma, being skinned in the snowdrift problem scenario is not quite so catastrophic. (Any amount of lateness to work beats years in prison.) But in both games, theorists argue, it’s generally better to cheat your opponent if you can. This result raises a question: Why do humans cooperate as much as we do?

Studies show that the blizzard version of the game leads to more cooperation than the prisoner’s dilemma. And many sociologists believe the former is a better proxy for cooperation challenges in the real world, where betrayal often hurts oneself as well as others.

The snowdrift problem and its variants are still active areas of study. Recently, researchers used graph theory to evaluate a new strategy, which they call “poor-defective-rich cooperation.” Roughly speaking, this means the following advice: check if your neighbors are cooperating; if their driveways look clear, you should decide to pitch in too.

Scientists turn to these highly simplified models because cooperation is a true wonder of the natural world. Natural selection seems to prescribe selfishness in most situations, and yet, across the animal kingdom, we see the fruits of cooperation. Games like the Snowflake Problem are a way to explore this puzzle using simple math, with the aim of figuring out how a bunch of selfish individuals add up to a cohesive society.

Now stop procrastinating and go shovel the walkway.

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