[EM] Re: Contd, method proposals

[Kevin Venzke]

Mike,

 --- MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit : 
> 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?

LNHarm might be compatible with SFC. I don't believe it's compatible with
SDSC. So, I feel CDTT,RB is better than SK because it satisfies SDSC, even
though it can fail LNHarm with 4+ candidates.

SFC seems to be:
>If a Condorcet candidate exists, and if a majority prefers this candidate to 
>another candidate, then the other candidate should not win if that majority 
>votes sincerely and no other voter falsifies any preferences.

If there's a sincere CW and no one uses order reversal, then no candidate will
have a majority-strength beatpath to the CW. If a majority prefer the CW
to another candidate, then the CW will have a majority-strength beatpath to him,
so that under CDTT he can't win (no path back).

If no one uses order reversal, then the CW's maximum opposition from another
candidate will be <50%. If a majority prefer the CW to another candidate, then
the other candidate will have maximum opposition >50%. So this other candidate
can't be an MMPO slash SK winner.

Unless you see a mistake, I think LNHarm is compatible with SFC.

> 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.

I think the best method that *strictly* satisfies LNHarm is MMPO/SK. I believe
this is just as bad as PC by the defensive strategy criteria.

Otherwise I suggest CDTT,RB or CDTT,MMPO,RB.

> 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.

In the scenario where B voters do not vote for C (the sincere CW), both
MMPO and CDTT elect {B,C}, and both give that same result when B voters do
vote for C. (I wouldn't consider it acceptable for A to be a potential
winner in either case.)

So the B voters aren't penalized (that is, unless C voters truncate as well),
they just can't gain.

> 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.

Do you mean, when B voters insincerely vote B>A>C?

> 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?

It might be, although I'm not convinced that the voters wanting to use ATLO
have the upper hand in the game of chicken with the defectors.

One mitigating factor I want to note: If voters take to heart the fact that
listing additional preferences in CDTT,RB can only very rarely harm an earlier
preference, then voters should truncate less often. And if it happened to be
the case that no voter truncated, then CDTT,RB would be equivalent to
Schwartz//RB, and it wouldn't be possible to fail the Plurality criterion.

> 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.

But it takes a Condorcet-centric perspective to say that the B voters are
"getting away with something." I doubt B voters will appreciate this perspective
if it seems that their choices are to 1) give the election away or 2) "get away
with something."

If you insist on electing the CW, then I agree that you have no choice but to
elect somebody awful when the B voters defect.

> 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.

I think that when you say "defection by order-reversal" you're talking about
the offensive order-reversal which in WV can be countered by defensive truncation.
CDTT and MMPO/SK have the same scenarios and solutions. One difference is that
with CDTT,RB, the defection can't succeed without giving some probability of
election to the candidate insincerely raised above the sincere CW.

Condorcet inefficiency doesn't in itself bother me. I see the point of Condorcet
largely to be to minimize voter regret. That's also the point of LNHarm. So when
the two bump heads, it's not crystal clear to me which trumps the other.

I consider SDSC to be far more important than Condorcet.

Kevin Venzke



	

	
		
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