[EM] Re: Contd, method proposals

[MIKE OSSIPOFF]

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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