MitD XIII: Learning is happening

[Grey_Wolf_c]

That's kind of what I said (or at least, was attempting to say) in the bulleted list: If option B is removed, "A+B" cannot be met, so the entire "A+B" combination is removed from the ballots.

Again, that feels wrong to me. If there is a majority of people who only want A and B when they go together, but don't want either individually, then converting their vote to an option they didn't want feels wrong. Now, in practice, from what I remember, anyone that wanted A+B last time (for any value of A, B) did tend to then vote for them individually. But it is not a given. Voters may not want B individually, they may want B and A together or not at all, so I shouldn't convert their A&B to A simply because B got voted out - I should allow that B individually might be unwanted, but A&B together exactly what a majority feels should be done.

If an option on over 50% of the ballots nevertheless has the smallest number at the top line (perhaps a very popular second-place choice, with one first-place supporter), it will be removed from the ballots. This is why IRV fails the monotonicity criterion: the option was removed because it had first-place supporters instead of second-place supporters, so rating their first choice higher was responsible for its loss. (A ballot with all its options removed will mean the entire ballot is removed, lowered the number needed for a majority of ballots; so IRV will still come up with a winner).

Aaaah. Yes, you are correct. Damn. Fair enough, I'll be more careful with ballot resolution.

Oh...so !A would be like antimatter A votes? You subtract them the count of votes in favor of A?

No, I don't subtract a vote. Instead, at resolution, !A does become equivalent to Any(B, C, D...). A vote for !A is a vote for any extant combination that doesn't include A - i.e. it's "Anything but A". Admittedly, I think mathematically the result is the same, but I do the latter and not the former.

Grey Wolf