How to illustrate that society is mostly irrational, and how rationality would be beneficial

Society is made up of individuals. If you can demonstrate that individuals are irrational, then you have a better chance at claiming that the society is too. Yudkowsky wrote about the sanity waterline rather late when he had already covered a lot of other topics and I think this was intentional.

You can't just start from the assumption that society would be more rational if rationality was taught at school. You'd also need evidence that rationality can be taught to a lot of average people. I don't think such evidence exists. Whatever taken out from the curriculum might be replaced by something completely ineffective.

Of course, if changing the curriculum would make some of the smarter individuals more rational, and leave the average student with nothing, the result might still be a net positive. This argument wouldn't convince anyone professing egalitarianism however.

Individual benefits are far easier to sell than societal benefits. They're easier to imagine, examples are available, they're near rather than far, self interest is inherently motivating, and your reader won't be mindkilled by politics. If you can get the reader to accept the individual benefits, then you might be able to extrapolate a bit from there.

The title of this post is misleading, since you're not illustrating anything but asking for advice.

You might start by tabooing rationality.

The proxy we used in the last LW survey for rationality was whether people are well calibrated in their uncertainty. It might be a lot easier to write an article about how calibrating your uncertainty is beneficial than writing it about an abstract phrase like "rationality".

I'm writing an essay about how to improve education, and one of my proposals is that a core part of the curriculum should be rationality.

Again what do you mean with rationality. Medical doctors are already taught bayes rule somewhere in their statistics course. They just don't learn it in a way that allows them to actually use it later when they practice medicine.

The problem is that we don't have any evidence that we can effectively teach bayes rule to those kinds of people even if we make space in the curriculum.

That makes your proposal for putting rationality into the school curriculum an advocacy of a non evidence-based intervention. That might or might brother you, but it's something to keep in mind when writing an article and maybe even worth explicitly addressing.

Your question rings alarm bells for me.

A commonly circulated article in the business world is The case for behavioral strategy.

On the relevance to GCRs, there's Cognitive biases potentially affecting judgment of global risks.

Assuming that rationality can be taught at school to everyone, is there even a connection between more rational individuals and a more rational society?

The problem I see here is that rationality is already very weakly defined for individuals and I know of no definitions in the context of society. A society can't even think (or can it?), how can it be rational?

Many decision processes of society are not based on rationality at all and I see no reason why the tried ways of winning (i.e. corruption) should be replaced by others assuming as the only change slightly more rational agents. Elections produces an average of opinions, this average may not change at all given more rational voters.

You will have to cover a lot of inference steps just to show that society as a whole will become more rational. Rationality isn't the only attribute of a "good" society and there might be ugly trade-offs. Whether a more rational society will have any "huge benefits" is just the last question in a chain that will surely be too much for a single article or a few sentences.

Have a look at Kathryn Schultz's writing. She focuses on a single key piece of rationality - the necessity and desirability of changing one's mind - and writes about it in a fashion that I assume suits your project very well.

Dan Ariely's books offer some good examples of organizations leaving metaphorical hundred dollar bills lying on the ground, and refusing to pick them up even when they're pointed out, apparently out of sheer inertia habit. I'd be more specific, but it's been more than a year since I read any of them, so I've forgotten most of the details. I'd suggest checking out Predictably Irrational and The Honest Truth about Dishonesty for some good examples.

society is generally irrational

Do you mean that people are generally irrational, or that the people could change their relations to each other so as to better achieve their ends?

What you wrote seems to me an anthropomorphism of society.

Society is irrational enough that degrees with a large rationality training component (MBA, Finance, maybe CS somewhat?) make the individual who acquires them very valuable.

Something about the War On Drugs maybe? Or even better, something which happened in the past and is now clearly absurd, such as the Dutch Tulip Bubble, or the threat to racial purity in america posed by the Irish.

Part of the problem is that rationality is a threat to many groups, and they have a tendency to consider rationality to be an ideology, equivocate between "ideology" and "religion", and then pretend that teaching rationality in public school constitutes an establishment of religion. People define their identity in terms of irrational belief systems tend to not like the idea of the next generation being raised to be rational.

And of course, things like the Prisoner's Dilemma show that individual rationality doesn't necessarily translate to group rationality, while the Efficient Market Hypothesis posits that the aggregate can be treated as being rational in the absence of individual rationality.

I think that one idea that should be discussed in schools is making intuitive reasoning explicit. For instance, I think that everyone engages in a version of Bayesian reasoning, but most people just have a vague, intuitive sense of it that is very buggy and susceptible to manipulation, like affirming the consequent ( if ((A -> B) and B), then that can be evidence for A, but is not proof). Unfortunately, in the cases where students do get lessons on rhetoric, the focus is often on constructing arguments that are persuasive, rather than on constructing arguments that are valid.

If you're arguing on the basis of the benefit to society, one point to bring up is that people should be able to debate issues constructively. That means articulating their thinking (and this in turn means being conscious of what that thinking is, which is often not a trivial issue), understanding what the thinking behind the opposing point of view is, how to clarify issues and identify the main issue of contention, etc.