[EM] Re: Contd, comments on your methods

Fri Apr 22 21:54:44 PDT 2005

Mike,

 --- MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit : 
> I'd said:
> 
> >Consider any standard wv truncation example:
> >
> >40: A (B>C preference truncated)
> >25: B
> >35: CB
> >
> >Maybe you might want to consider your best proposal?
> 
> You replied:
> 
> ...Why on earth would the A voters truncate the B>C preference?
> This causes C to obtain a great chance of winning when otherwise it is
> a decisive B win.
> 
> I reply:
> 
> Truncation isn't always strategic. Maybe the ballot is very long, and some 
> people are in a hurry to finish voting and do other things. Maybe someone is 
> lazy. Maybe someone doesn't know much about some of the candidates. Maybe 
> someone is refusing, on principle, to vote for someone.
> 
> Those don't sound to me like good reasons to not elect the CW. If someone 
> refuses to vote for a candidate out of principle, that could make that 
> candidate lose with any method. No method can always undo the result of not 
> helping one's best compromise. But wv sometimes can, when the result is a 
> cycle. WV can still elect the CW under those conditions, and that seems a 
> good thing. Even though I myself would truncate on prinicple in every 
> election.
> 
> Besides, what about the people who truncated for those other nonstrategic 
> reasons. It's good that wv will sometimes not fail to elect the CW as a 
> result.

I see what you're saying, but as before, it seems to me impossible to elect
B (100% of the time) on the above ballots without inviting a defection dilemma.

I hope, perhaps unrealistically, that the A voters might list a second
preference, since under this method, it cannot hurt A.

> I'd said:
> 
> >Your method has a truncation  CW failure that PC doesn't have.
> 
> Well, the scenario above shows that if voters truncate the CW, they can
> get someone they like less. That isn't your point, I'm sure.
> 
> I reply:
> 
> But if they're truncating for one of those nonstrategic reasons that I 
> named, then it isn't necessary to teach them a lesson for offensive 
> strategy, and it's best to elect the CW, as wv will often do, in spite of 
> truncation, when the Simpson-Kramer version you propose wouldn't.

Well, if Random Ballot is then used, then at least the CW has some probability.

The point isn't to punish A voters for truncating. The point is to never
punish for *not* truncating.

> You said:
> 
> I don't understand why you say "halfway" if you're not referring to the
> "price" of indecisiveness and poorer Condorcet efficiency.
> 
> 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.

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 don't have serious objection to that Simpson-Kramer version. It's largely 
> a subjective matter of opinion which is better, that or PC. I myself prefer 
> PC, but I don't strongly object to that  Simpson-Kramer version.

Ok, I'm pleased to hear that.

> You said:
> 
> I don't propose BP in this case because part of the point of CDTT,RB is to
> address the defection problem. When only majority-strength defeats are
> regarded, then adding a preference can create a defeat, but it can't reverse
> the direction of one. That means voters don't need to worry that adding a
> new preference could turn that candidate into the CW (who would 
> automatically
> have to win, in a Condorcet method).
> 
> I reply:
> 
> Ok, I hadn't considered new methods or variations, other than ATLO, to get 
> rid of the defection problem. If CDTT,RB can do so without some high price, 
> that's desirable.

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.)

> But when the defection succeeds in wv, isn't that in a cycle, rather than 
> with one candidate beating everyone?

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.

In a Condorcet method, adding a preference for X over Y can only create an
obstacle to Y winning if it also removes an obstacle to X winning. So when
you add a preference, you have to worry that you might be turning that candidate
into the CW, when perhaps a higher preference of yours could have won the cycle-
breaker (especially, in a WV method, if your higher preference is expected to
get a lot of votes, and thus have stronger wins).

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.

> You said:
> 
> A big reason I don't mind the indecisiveness, is that the voters have the
> power to avoid indecision: They can vote non-cyclic majority-strength wins.
> 
> I reply:
> 
> But indecisiveness would likely adversely affect a method's chance of 
> acceptance by the public.

Yes, that's a shame. But I wonder if it would be worse to elect C with 100%
probability in the top scenario; that is an option.

> You said:
> 
> Maybe I should note that I want to use Markus' BC with Random Ballot
> 
> You mean the winners, before RB, are the candidates who don't have a 
> majority beatpath to them that isn't in a cycle of majority defeats? Then 
> apply RB to the winners?

Yes, that's what I mean by "CDTT,RB." I didn't mean this to be new information,
but to note that Markus' criterion is more suitable than Steve's.

> You continued:
> 
> , because
> using Steve's BC is not monotonic. I can give an example if desired.
> 
> I reply:
> 
> Steve mentioned a Beatpath Criterion Method based on BC. If I remember 
> correctly, it would elect the candidates who could be elected without 
> violating  BC. Then, if (and for as long as) that results in a tie, the same 
> method would be re-applied to the tie. It was shown to be nonmonotonic.

That's interesting; although, even if you don't reapply the method in a
tie, and just go to Random Ballot, it's still not monotonic.

Suppose pairwise wins A>B>C>A and D>B. D ties with A and C. The potential
winners should be {a,c,d}. Now suppose A gets raised on some ballots so that
now A beats D pairwise. Then the potential winners are {a,b,c,d}.

If these are majority-strength wins, then CDTT,RB elects {d} in the first
situation, and {a,b,c,d} in the second, avoiding the monotonicity problem.

Kevin Venzke

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