Thread by @natematias

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Today I realized hermit crabs are the *cutest* illustration for the Threshold Model of Collective Behavior, described by Mark Granovetter in 1978. First, the crabs

Granovetter argued that if you want to explain behavior, you need an understanding of individual psychology combined with "a model of how these individual preferences interact and aggregate"

Writing about diffusion of innovation, rumors, strikes, voting, riots, & other phenomena, he imagined people who each have a personal "threshold" for acting before doing so. One person needs to see 2 people vote before they will; someone else needs to see 10

In the threshold model, if enough low-threshold people don't vote, then high-threshold people won't either.

🦀 What does this have to do with hermit crabs again? 🦀

As hermit crabs grow larger, they need to change shells. When new shells wash up on the beach, it's a new opportunity! But the shell is too large. For this crab to get a new shell, other, larger crabs need to abandon their former home for this one

What to do? As other crabs arrive, they sort themselves in a sequence from smallest to largest, with the goal of creating an unbroken chain from large to small, where every crab upgrades their shells

In a sequence of 12 crabs, the smallest one needs 11 others to act before it can upgrade too. That's its threshold, in Granovetter's . The largest crab has a threshold of 0. If the middle-sized crab is missing, only half of them get a new home 🦀🐚

When hermit crabs form conga lines to find a new shell, it's what sociologists call a "vacancy chain" and it often happens in the housing market too annualreviews.org/doi/abs/10.114…

Vacancy chains can be imagined as a simple structure where N hermit crabs each have increasing integer thresholds. As each one takes action, the next is also able to take action. But Granovetter was primarily interested in how behaviors spread & grow in crowds & networks

Since hermit crab house size is so one-dimensional, there are far richer ways to illustrate and debate the complex stuctures of behavior explained by Granovetter's threshold model

🦀🐚But I still think this is the cutest 🦀🐚

Oh, and here's a link to Granovetter's "Threshold Models of Collective Behavior," published by the American Journal of Sociology in 1978

sociology.stanford.edu/publications/t…