By applying whatever claim system to past events and seeing how often the claim system produces the correct answer. You can compare it to marginal or other types of claims.

Edit:

More concretely for tyrants. Get a definition to classify example of who is a tyrant, get a definition to classify who is a democracy. Consistently apply to all historical examples. Given subset before target example evaluate what you expect to happen, compare to what happened. See if there is drift/etc. to be better: look at other confounders, etc.

That's not empirical study, it's statistical analysis of historical data. Which is useful, certainly, but it shouldn't be treated as the same level of certainty as empirical study and it shouldn't be confused for it. The article makes the distinction between the two very, very clear.

Economics loves to play fast and loose with the definition of "empirical" tests, but almost none of the main theories of economics are empirically testable—because we simply cannot create new, controlled economies and run preregistered experiments against them. Instead, we have to make do with the data we have, and we can't generate more, and we have to deal with the amount of uncertainty that the analysis of existing data brings with it.

Im not here to defend economists, but the historian argument is that because they can’t verify if their arguments holds water robustly they instead don’t verify at all. If everything is so subjective as to be unverifiable then why should we care about history at all? I think in reality history is much more tied to present and many claims can be verified to some degree (of not absolute) certainty.

"Instead what he’s actually suggesting isn’t an empirical test at all: it is a quantitative, statistical test of data none of which can be empirically verified because it all happened in the past; only the statistical analysis is subject to empirical verification."

Devereaux points out that that is not empirical verification. Past events cannot be sense-experienced.

He claims that, but it’s not a justified claim. As my edit show you can do this analysis, it’s a lot of work.

Your analysis doesn't involve sense experience of tyrants. Doing the statistics makes it sound empirical, but the choosing of the data will never be empirical.

Presumably sense experience is one of many confounders?