James--
You posted an example in which, in wv, offensive order-reversal took victory from the CW, and elected the offensive strategists' candidate contrary to majority wishes, as I define that term.
Then you said:
IRV will pick A either way, and in general IRV will not be vulnerable to manipulation in this example.
I reply:
It's common knowledge that IRV isn't vulnerable to manipulation. As I've been trying to get through to you, you're barking up the wrong tree when you talk about vulnerability to mainiulation.
I've told you why that is, in recent postings.
You continue:
So, if the strategy is successful, it causes a problem that is not found in IRV.
I reply:
No, not really. That problem is found in IRV. IRV will often fail to elect a CW, and/or violate majorilty wishes. So then, how are IRV and wv different? Two ways:
1. In IRV that happens automatically, easily, without anyone using offensive strategy. In wv, it can only happen when someone uses risky offensive order-reversal.
2. In IRV, preventing that result requires defensivse order-reversal, often favorite-burial. In wv, even when someone is trying offensive order-reversal, it can be thwarted, and the problem thereby avoided, by mere equal-ranking. In fact, tuncation can be used as a deterrent that will prevent the offensive strategy from even being tried.
You continue:
Which is to say that the burying-vulnerable methods contain at least the _possibility_ of a type of problem occurring that cannot occur in IRV.
I reply:
Wrong. The type of problem consisting of failing to elect a CW, or violation of majorilty wishes is a type of problem that will often happen in IRV. In fact, with IRV that problem will happen without any offensive strategy being used by anyone, and, and it will require favorite-burial to protect against that result.
Now, does it always happen with IRV in the same examples as in wv? Of course not. They're different methods. Different methods give different results with the same ballots. That's why they're called different methods. If you're saying that you expected different methods to have their problems in the same examples, then let me be the first to tell you that different methods often have their problems in different examples.
How often will it happen in IRV? For simplicity, let's consider 3-candidate examples. It will happen when the middle CW's favoriteness support is less than the difference between the favoriteness support of the two non-middle candidates.
A sufficient, but not necessary, condition for that, when there's a middle CW, is for the favoriteness support of all the candidates to be within a factor of 2 of eachother.
How likely is the possibility? That is another, much more complicated discussion.
What does it take for that to happen in wv?
You already know part of the answer to that:
1. The A voters must be willing to attempt risky offensive strategy.
2. No one must use any counterstrategy. That would be odd, for the A voters to organize their offensive order-reversal, without tipping the B voters off about it. Having heard about the A voters' plans, the B voters wouln't rank A. When refusing to rank A, the B voters would publicize that refusal in advance.
And that would make it distinctly inadvisable for the A voters to attempt their offensive strategy.
3. A would have to be certain to pair-beat C. Otherwise the offensive order-reversal would make C into the BeatsAll winner, cause C to win as would a CW.
4. The B voters must prefer A to C, and rank A, in keeping with 2 above. But it's worth adding that this means that, in wv, you can only steal the election from voters who are trying to help you. Congratulations, you must be proud of yourself.
And don't expect another opportunity to do that. Don't expect anyone to trust you again. That's it.
5. Of course A's defeat in the resulting strategic circular tie would have to be the smallest of the three. And, at the very least, to avoid giving the election to C, it's necessary that C not have the smallest defeat. Could you predict those things? But you think the A voters could?
For the offensive strategy to succeed, in addition to no counterstrategy being used, and in addition to A pairwise beating C, in addition to the B voters preferring A to C, it's also necessary that A be the sincere Plurality winner. That isn't necessary for IRV to have its problem.
Mike Ossipoff
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