Kevin--
You said:
Well, if Random Ballot is then used, then at least the CW has some probability.
I reply:
Sure, but if wv is used, then the CW has a stronger probabilty.
RB favors the Plurality winner over the CW when they differ. RB (used by itself) does terribly by SU.
You said:
The point isn't to punish A voters for truncating. The point is to never punish for *not* truncating.
I reply:
That's LNH, right? But is that compatible with the desiderata that are important to me? SFC and GSFC describe plausible conditions under which, with complying methods, a majority don't need to truncate or do anything other than rank all the candidates sincerely. WV only guarantees that under those conditions, while LNH methods always guarantee no gain from truncation, right? But what good does that do if defensive favorite-burial is needed, or if defensive equal ranking is needed where it wouldn't be needed in wv?
What's the best LNH-complying method? Which one does best by the majority defensive strategy criteria? Obviously there's a price for LNH compliance, and I suspect that it's always too high, as judged by me, by the defensive strategy criteria.
You'd said:
I don't understand why you say "halfway" if you're not referring to the "price" of indecisiveness and poorer Condorcet efficiency.
I'd replied:
I meant that there's a 50% chance of the truncation being regretted in that defection. But, of course, if it isn't regretted, that's because the CW wins, and that isn't bad.
You reply:
Are you saying that this method only "halfway" solves the defection problem, because the A voters may regret truncating? Even though they will never regret *not* truncating?
I reply:
It's true that, with your Simpson-Kramer version (I'll just abbreviate it "SK") they won't regret not truncating in my 40,25,35 example, with B as CW, and that they can't gain by truncation. But in that example they can't gain by truncation in wv either. With either method, in that example, the truncation-defection problem is avoided. But, by electing {B,C} instead of {B}, SK is less Condorcet efficient, lowering SU.
I'm talking about these examples without having them in front of me, and I hope that that laziness or sloppiness doesn't result in mis-statements about what the methods will do. I'm going by what it seems to me the methods did when I checked the examples out.
Now I don't know why I said that SK only halfway solves the defection problem. Maybe in your other example, where truncation is by B voters, and C is the CW, the truncation elected {A,C} with your method, where, in wv with ATLO, it would have fullly penalized the truncation by electing {A}. Of course if it was impossible for the truncation to gain anything with SK in your example, then I realize that it doesn't matter how well-penalized the truncation is, and that, in that case, SK completely solves the truncation-defection problem in that example.
We haven't discussed order-reversal defection with SK. ATLO wv avoids it just as it avoids the truncation-defection problem, in those defection examples where, say, the B & C voters all prefer B and C to A.
I'd said:
If CDTT,RB can do so [solve the defection dilemma] without some high price, that's desirable.
You replied:
The price is indecision, failing Condorcet and Smith, and failing the Plurality
criterion (which, for the scenario at the top, says that C must be elected
with no more probability than A). (WV methods except for Raynaud do satisfy
Plurality.)
I reply:
That sounds a bit steep. Might ATLO wv be a more reasonably-priced solution?
I'd said:
But when the defection succeeds in wv, isn't that in a cycle, rather than with one candidate beating everyone?
You reply:
Yes. I think you and I look at this situation from different perspectives.
You see the B voters as benefiting from defection. I see the B voters as being
punished for listing an additional preference.
I reply:
In your defection example where C is the CW and B voters defect by truncation, it's more reasonable to say that the B voters are getting away with something if they elect B by the defection. I wouldn't say they're punished by a result that elects the CW.
You continued:
So, using MinMax(PO) or a CDTT method, neither the B nor C faction can benefit
from defection (in the scenario we were talking about before), period, regardless
of what the other faction chooses to do.
I reply:
Does that apply to defection by order-reversal as well as by truncation? If so, it sounds good. But, for CDTT, you stated the price, and it sounded like a lot. If SK has no defection problem, by truncation or order-reversal, in those examples where B & C voters all prefer B & C to A, and if the price is lower, than SK may be looking good in comparison to PC. But there's still the tradeoff of lower Condorcet efficiency in other kinds of examples, such as my 40,25,35 example with truncation.
Mike Ossipoff
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