Everyone has beliefs about how they should behave. But people differ in their beliefs. They also differ in their tolerance of others’ beliefs. These differences affect who become friends. Some people “stick to their guns” and befriend only those who agree. Others are more tolerant and befriend others who disagree. Such people are more willing to compromise, changing their behavior to accommodate friends’ beliefs.

Genicot (2022) studies tolerance and compromise in social networks. She describes a finite population of agents with different “ideal” actions. Agents prefer taking their ideal actions. They also prefer friends who take their ideal actions. An agent’s “tolerance” is the largest deviation from their ideal they can accept in a friend’s action.

Agents take actions before making friends. An agent “compromises” if they take an action different than their ideal. Compromise is costly but may lead to beneficial friendships. Agents weigh these costs and benefits when taking actions. Genicot studies the equilibrium in which no-one wants to change their action.

If everyone has the same tolerance then no-one compromises. The reason is as follows: No-one wants to compromise more than is necessary for their friends’ acceptance. Thus, anyone who compromises must do so “minimally” for at least one friend. This friend must also compromise because tolerances are equal. In fact, they must compromise more to make the friendship net beneficial. But then they must have another friend who compromises even more. We can keep applying this argument to find agents who compromise more and more, which is impossible because the population is finite.

Compromise thus depends on differences in tolerance. Agents compromise by deviating from their ideals towards the ideals of relatively intolerant friends. Some compromises are one-sided, where the intolerant friend stands their ground. Other compromises are two-sided. Two-sided compromises rely on intolerant “bridge” agents, who bring their tolerant friends’ actions close enough together to be mutually acceptable.

Compromise also depends on how tolerances and ideals covary. If agents with “extreme” ideals are less tolerant then two-sided compromise is impossible. This is because agents compromise towards intolerant extremists. Consequently, actions tend to be more polarized than ideals. In contrast, if extremists are more tolerant then agents compromise towards the median. This makes the population more connected.

Genicot interprets these results in light of recent political trends. She cites evidence of intolerance among liberals and conservatives, and of rising polarization in the United States. These patterns are consistent with Genicot’s model. If people want to make friends, but making friends requires compromise towards extremes, then people will behave more extremely.

Genicot closes with guidance on finding tolerant people:

Looking at the identity of the members of a person’s social network may overestimate the tolerance exhibited by the person. The distance between a person’s identity and her friends’ behaviors would likely tell us more about her tolerance.

Tolerance isn’t about having diverse friends; it’s about not forcing friends to accommodate your beliefs.