> Condorcet was assumed to be the gold standard for a long time, but then in the year 2000, Warren Smith's Bayesian Regret figures showed that actually Score Voting (aka Range Voting) was better with any mixture of strategic or honest voters.

What such simulations consistently miss is the information problem facing range voting (approval voting has a similar problem; preference systems don't entirely lack information problems but they are much smaller.) And that is that, contrary to simulations where preferences are based on quantified utility and there is a clear and consistent relationship between that and ballot markings on a numerically scored ballots, real world preferences are ordinal preferences which, while they do vary in intensity, are not consistently quantifiable, resulting in radically different score ratings for the same preferences by different voters. (There's quite a lot of research showing that numerical rating systems in all domains have this problem.)

> Approval Voting is extremely competitive in terms of performance, and _dead simple_.

Approval Voting again suffers from an information problem like range voting; there's no consistent mapping from actual preferences to ballot markings. This is easily solved if you are doing open-ballot voting for a group activity—eithet treating “approve” as a binding commitment to participate if the approved action is chosen or “disapprove” as a binding opt-out nearly resolved the information problem. In scenarios like that, Approval is a great system.

Likewise, Range Voting is great in a scenario where your score is a commitment to contribute an amount of resources proportional to the rating if the option is chosen.

But when you are voting with secret ballots in public elections, these information-problem mitigations don't apply.

> No comparison exists between the best PR methods and the best non-PR methods, so it's still very much an open question.

Comparisons in actual government satisfaction between countries do exist and show that proportionality of outcomes is key. See, e.g., Lijphart’s Patterns of Democracy. The absence of flawed, limited, abstract mathematical comparisons that ignore key features of the real world is not particularly a problem.

> And you may have to get Score Voting or Approval Voting to get PR in the USA anyway.

The article making that case considers the federal situation ignoring the possibility of bottom-up reform from the states, which is possible because many states permit the citizenry to bypass the politicians to institute reforms from the ballot box directly. And bottom up reform is desirable anyway.

> A significant fraction of the world's major electoral procedures experts support Approval Voting. E.g. www.electology.org/approval-voting

I don't see any support for that claim on that page.

> I'd be curious to hear your thoughts on the book "Gaming the Vote" by William Poundstone.

I haven't read it, but unless the book's own promotional copy substantially misrepresents the argument it makes, I can't imagine I'm missing much of value. Arguing that US Presidential elections going to a candidate other than the most preferred is due primarily to spoiler effects on simple majority elections and that a solution to that would satisfy both the left in the right ignores completely the existence, original purpose, and continued structural effect of the Electoral College.