Which is all well and good, so I start reading this fairly detailed white papper explaining how things go. And immediately, that table at the start looks a lot like the sort of biased table a manufacturer would produce; did they really need 5 different variations of the thing which only they have? Well, ok, it's technical, so they were refining things, so I could bear with that. But then it turns out the '?' for the one spot in the table is really just a '-', they say "the probability is small" but hey, the probability of some of these other entries is probably small too.
So one of the criteria they offer is the "Strategy-Free Criteria", which is a good idea, but they formulate it as:
If an ideal Democratic Winner (IDW) exists, and if a majority prefers the IDW to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies any preferences.
An IDW is somebody who beats ever other candidate in the simple test described in the first paragraph. The idea of this criterion is great: does this voting system discourage "strategic voting", where you don't accurately express your preferences, hoping to improve your top choice's result? The problem is that they observe that the majority can achieve their victor by just voting sincerely and no other voter falsifies any preferences. So this criterion says "the majority-favored candidate will win as long as those opposed don't vote strategically"! So they're just encouraged to vote strategically. They explain this in the notes as requiring "risky offensive strategy" rather than defensive strategy, and hence less of a big deal, but I dunno, that sort of attempt at classifying just seems like hedging to make their favored scheme seem better, especially given that probability comment about the Favorite Betrayal Criterion mentioned above.
In fact, they like to stress that the Condorcet Criterion (the basis for the method) is common-sensical, but the example they give for it for why IRV fails that criteriont is, I think fairly a conundrum:
so when they write "B is preferred to A by 12 votes to 8, and B is preferred to C by 13 to 7, hence B is preferred to both A and C. So according to common sense and the Condorcet criteria, B should win," they overstate what commen sense suggests in this case: B is preferred to A by 12 votes to 8 but it is only in second place on most of those votes (with A 3rd place); so when you see the actual votes, at least for me, common sense is kind of stumped.
There was another weirdness somewhere in there that I forget now.
Anyway, it seems like a weird thing for people to use wacky tactics to convince people about, especially as it's not like it's their idea.