Transitive Tolerance Means Intolerance

Our society is pretty messed up around arguments of whose ideas we should and shouldn’t tolerate. Some of this is inevitable: even without censorship, there are cases where group X can choose to actively show respect to person Y, and members of X will argue about that, and people with any influence over members of X may try and sway the decision too.

Of course, the actual kinds of conflicts in our world are… less tame than the above example. Troublingly, people lose jobs* for saying things that a supermajority of Americans find inoffensive, both on the left and the right.

You don’t need me to tell you that things are bad. I do think I can point out how some of this is a consequence of the natural impulse to judge people by their friends, turned corrosive by the property of transitivity.

Transitivity is the property where if A relates in a certain way to B, and B relates in that same way to C, then A relates in that same way to C. For instance, if Alex is shorter than Beth, and Beth is shorter than Chris, then Alex is shorter than Chris.

Not all relations are transitive. If Alex is Beth’s cousin, and Beth is Chris’s cousin, it doesn’t follow that Alex and Chris are cousins: Beth could share one set of grandparents with Alex, and the other set with Chris.

Pivoting back to toleration, we begin with the idea of guilt by association, which we rightly exclude from legal consideration, but which is still pretty good Bayesian evidence. A person who chums around with the Mafia might not be a mafioso themselves, but they’re more likely to be one than a random person is.

Similarly for people who proclaim ideas: a person who associates with an X-sayer is more likely to believe X than a random person.

Where this goes horribly wrong is when toleration is assumed to be transitive.

In reality, if X associates with Y who associates with Z, that doesn’t mean X associates with Z, or knows of/​cares about/​approves of Z. Y could be in a D&D group with X while volunteering with Z, or whatever.

But if our social rules treat toleration as fully transitive, then as soon as Z says something awful, X is contaminated by it. In fact, X needs to quickly ditch/​denounce Y in order to avoid the contagion, and sometimes even that won’t work.

(I may be getting the details wrong, but I recall a case where A was denounced for saying nice things about B… who had once appeared on C’s podcast… which also had D on at some point… who years after that podcast had started saying absolutely reprehensible things.)

At its most extreme level, this contagion spreads to all of society except for the few people who agree completely with you (or are scared enough to tell you they agree completely). Anyone who defends a witch must themselves be a witch, and by the transitive property, everyone else is a witch. The principle of assumed transitive toleration has left you in a bitter, disconnected molecule drifting in a sea of total intolerance.

Now, there is some level of Bayesian evidence you get from multi-step toleration. But it reduces sharply, the further out you get.

If X explicitly talks about wanting the USA to be invaded and taken over by Canada, and Y tolerates X, then Y is probably at least a Canada-conquest sympathizer/​apologist. But if Z tolerates Y, then I wouldn’t be as sure about Z’s politics. I find it unlikely that Z has a high opinion of American self-rule (why would they then tolerate Y?), but it’s not that likely that they’re as enthusiastic about Alberta-annexation as X. And so on.

In a healthy society there’s a six-degrees-of-toleration connection between people with very different politics. I worry that these chains have been growing longer and more fragile, for many reasons. This strains the bonds of liberalism, which (contra Hobbes) has been our best tool at averting the worst forms of violence humanity has to offer.

And the assumed transitivity of tolerance is perhaps both a cause and a symptom of that.

* I’m not giving my examples because I don’t want to start a political row, but yes it’s both. More of it happens behind closed doors than publicly on Twitter, although the latter does have a chilling effect. Please don’t focus on this.