> when you construct a measure designed around their shared features

dragonwriter thinks the metric being used in the article linked here was cherry-picked because it favours particular voting systems that the author likes for other reasons.

(I do not believe this, nor do I believe the similar allegation made by vintermann in a top-level comment that's currently the highest rated. Neither offered any actual evidence, and the metric used here seems obviously reasonable to me. What I could believe is if someone thinks that VSE / Bayesian regret captures the essence of what matters in a voting system, then they are likely to prefer systems like approval voting or range voting or STAR. I don't see anything wrong with that.)

> while ignoring the cultural variation in honest ballot marking for these methods

dragonwriter thinks that different voting systems, implemented in different cultures, will exhibit strategic ("dishonest") voting to different extents and in different ways, and thinks this is a problem not addressed in the OP.

(The linked article does consider strategic voting, of various different kinds, but it's certainly possible that it isn't realistic enough about what real voters might do. It would be easier to tell whether dragonwriter has found a real problem here, if dragonwriter had given some examples of variation in strategic voting that are important but neglected in the OP.)

> resulting from the fact that the ballots for them ask a question that doesn't have an objective relationship to preferences.

dragonwriter thinks that what voters primarily have is preferences: candidate A is better than candidate B who is better than candidate C. This is what an IRV ballot asks for. STAR or approval-voting ballots ask different questions (please give a score for how much you like each candidate / please say for each candidate whether you would find them acceptable); dragonwriter finds that unsatisfactory on the basis that voters will have to translate their preferences into answers to those questions, and there is no One True Way to do that.

(I disagree with dragonwriter about what's in voters' brains. At any rate, looking within myself, it is very common that I have a better idea of some candidates' acceptability to me than I do of their relative ranking. E.g., maybe there's the Nice Party, which I like a lot, the Mean Party, which I don't like much but concede has some competence, the Evil Party, which I really don't like but again concede has some competence, and a bunch of Crazy Fringe Parties, none of which I know enough about to rate them relative to one another, but all of which I consider obviously unfit to rule. With a range/STAR system, I might rate Nice at 100, Mean at 30, Evil at 10, and the Crazies at 0. Or I might rate Nice at 100, Mean at 70, Evil at 10, and the Crazies at 0. These are importantly different opinions I might have. A preference-ordering system like IRV doesn't let me express the difference between those, but would really like me to say exactly what my order of preference between the Crazies is. For me, range/STAR does the best job of matching the actual kinds of opinions I have about candidates; 3-2-1 is also pretty good; approval and preference-ordering are similar to one another and distinctly worse than those two; and of course plurality/first-past-the-post is hopeless.)