One question posed by Jason Brennan's Against Democracy is: who should be the epistocrats?

Ideally, of course, they would be informed and rational. But these are two different things. Which means we have four categories of people* as my diagram summarizes.

In the top left we have the informed and rational. These are proper experts (who might, of course, be only a subset of those who appear to be expert). But here's a problem: there are no general purpose experts. Some of you might think I'm tolerably rational and informed about a few economic issues, but I'm ignorant about foreign and legal affairs - just as experts on those might know little about economics. This is a problem, as people who are rational and informed on some matters can be as daft as a brush in other contexts.

In the opposite corner we have the ignorant and irrational. Perhaps the most dangerous of these are those prone to the Dunning-Kruger effect: those who don't realize that they are ignorant.

It is, however, the other corners that interest me. In the top-right we have the informed but irrational. These include some people whose perhaps genuine expertise in one field emboldens them to consider themselves more general experts; think of dinner party bores and some guests on the BBC's moron-yak shows.

But there's another group in this category: people who are befuddled by their own knowledge. Take two examples from investing. Even financially literate and intelligent retail investors make expensive mistakes, such as trading too much or investing in poorly-performing high-charging funds. And even quite short runs of good returns can make investors "dizzy with success": their good performance emboldens them to take too much risk. In such cases, moderate knowledge creates an illusion of knowledge and overconfidence.

This can happen in politics. Thatcher's successes (by her own lights) in the 80s led her to introduce the poll tax, which destroyed the Tories in Scotland for a generation and contributed to her losing her job. And Blair's successful interventions in Kosovo and Sierra Leone led him to think he could repeat the trick in Iraq.

In the opposite corner from these, we have those who are rational but ignorant. Exemplars of this include Charlie Munger and Warren Buffett. One of their strengths is that they know their "circle of competence" and try not to stray outside it. This means they avoid lots of businesses which they don't understand but stick to principles they know that work - namely, using (pdf) their insurance float to take cheap geared positions in defensive stocks, a trick retail investors can only half-emulate.

Another example of rationality and ignorance is the Brainard principle - the idea that, faced with uncertainty one should do less than one otherwise would. Although this is associated with monetary policy it has wider relevance. For example, if I were conducting foreign policy I would set an extremely high bar for engaging in military action. Such a rule would risk not intervening in cases where one could do good. But it would avoid catastrophic engagements.

The general idea here is that the rational but ignorant stick to rules which require inaction in many circumstances.

This brings me to a problem with epistocracy: what if true experts are scarce? One danger is that if you call some people "epistocrats" they'll believe they are experts when they are not and so commit the errors that arise from overconfidence.

Personally - given the choice in a second-best world - I'd prefer rulers to be rational but ignorant than informed but irrational. But this poses the question: do we have the rules and institutions that best mitigate the problems that arise when informed rationality is absent?

* Of course, there isn't a sharp divide between rational and irrational or between the informed and ignorant: we lie on a spectrum between the two. I'm simplifying.