[Election-Methods] Fwd: RE : Corrected "strategy in Condorcet" section, Chris

[Kevin Venzke]

Chris,

I didn't check the archives partly because they weren't available the
last time I'd checked, partly because I didn't think it was too likely
that you had pointed out that Diego's method and yours were very similar.
However, I will start checking the archives at least while we're trying
to discuss something.

> > Kevin Venzke wrote:
> >> As for IIB, well, Top-Two Runoff already fails that.
> > Technically, based on "intended rankings", I don't think it does.  
> > Certainly the ranked-ballot one-voting-round
> > automated top-two plurality runoff meets Irrelevant Ballots (IIB).   
> > BTW, I gather that in the same circles where
> > IRV is called the Alternative Vote, that method is called the  
> > "Contingent Vote" (and the ghastly version of that
> > that allows the voter to rank a maximum of two candidates is called  
> > the "Supplementary Vote".)

Ah I see. Even if irrelevant ballots deprive you of your first-round
majority, you still expect to win the second round.

> >> This method is intended to be simple yet still give good results  
> >> in likely scenarios. It's a niche method. The basic idea is to  
> >> handle at least the case that there are three viable candidates,  
> >> with an underlying political spectrum (so that the candidates can  
> >> be called left/right/center). So yes, the ballot is restrictive,  
> >> and yes, if a fourth major candidate attracts votes then you will  
> >> see problems. (But note that the incentives of the method should  
> >> make a fourth viable candidate unlikely, just as FPP makes three  
> >> unlikely.) As for IIB, well, Top-Two Runoff already fails that.  
> >> This is just an improvement of that method.
> >
> > In a scenario like the 2002 French Presidential election (where  
> > there were 12 candidates and the top 3 had
> > a total of  under 53% (19.83,  16.91, 16.14)  and second highest  
> > scoring candidate wasn't expected to be
> > among the top few)  I don't think the improvement would be very great.

Well, keep in mind that it only makes strategic sense to vote against
a candidate that you believe can place in the top two. Since Jospin failed
to do that, a full majority of "against" votes could possibly be wasted.
But on the other hand if a full majority voted against Chirac, then the
second round would have been Jospin vs. Le Pen. I think this functionality
would definitely have been nice.

If neither the left nor the right had a clear frontrunner, I couldn't
expect any improvement, since no one would know how to use their "against"
votes.

> >>>> I am sure that something that uses approval ballots in the first  
> >>>> round could be much better. A while ago I suggested that the two  
> >>>> qualifiers should be the Approval winner and the
> >>> candidate
> >>>> with the most approval opposition to the AW. How do you see your  
> >>>> suggested method as being better than that?
> >>
> >> I don't think your suggestion is too bad. However, I think the  
> >> strategy is harder for the voter to understand. Also, I think  
> >> there is a strategy problem that I tried to avoid in the case that  
> >> your favorite candidate is left and you think he may be able to  
> >> defeat center head-to-head. In my method you most likely vote for  
> >> left and vote against right. (Though if you are confident left can  
> >> at least beat right, you might not do this.) In your method, if  
> >> you approve both left and center, you not only can make center the  
> >> AW, you are also unable to provide any opposition for left against  
> >> center. You could cause the second round to be center vs. right.  
> >> If you bullet vote for left, there is a greater chance that center  
> >> will be shut out of the second round (which is something I, at  
> >> least, want to try to avoid).
> >
> > In my suggested method the voter's strategy problem is more or less  
> > the same as it is in plain Approval,
> > unless the voter is tempted by a risky Pushover strategy of trying  
> > to make a "turkey" the first-round AW.

Yes, I agree. 

> > I think a better method that would achieve everything you are  
> > trying to do with your method (technically
> > if not "psychologically") would be this:
> >
> > "1) Voters indicate one Favourite and also Approve as many  
> > candidates as they like.
> >
> > 2) Any candidate voted as favourite on 50% or more of the ballots  
> > wins.
> >
> > 3) Eliminate any candidate whose max. approval opposition score is  
> > greater than 50%, unless that is all
> > the candidates.  [I'm not sure if that's possible].

Nope, that's not possible. You can only get this score if someone else
has majority approval and you don't. It's an MD filter really.

> > 4) Of the remaining candidates, the two voted as favourite on the  
> > most ballots go to the second round."
> >
> > This uses a more expressive ballot and mainly confines the split- 
> > vote problem to the "top" of the ballot.
> > So the normal recommended strategy in the 3 viable candidates  
> > scenario would be vote the most preferred
> > of the 3 as favourite, and approve all the candidates you prefer to  
> > the least preferred of  the 3.
> >
> > What do you think of that?

I've had this exact thought... I agree that on paper this should be 
similar in effect and better.

I'm a little concerned about approving candidates strategically. If you
have three factions, A B C, with A and B being the frontrunners and C
being an oddball, if both the A and B supporters approve C in attempt
to disqualify their opponent, and C supporters don't approve anyone else,
then C automatically wins.

40 A>C
40 B>C
20 C


> > Subject: Re: [Election-Methods] Another method on approval ballots  
> > (approval-limited minimum opposition)
> >
> > Kevin Venzke wrote:
> >
> >> So this compromise occurred to me:
> >>
> >> "Elect the candidate to whom the greatest opposition is the least  
> >> (breaking ties in favor of greatest approval), whose approval is  
> >> at least
> >> as high as the greatest opposition to him."
> >
> > This didn't interest me much when I first saw it because I can't  
> > see that getting voters to do nothing but fill in
> > approval ballots and then not elect the Approval winner can be  
> > seriously justified.
> >
> > But I think for methods that also collect ranking information it  
> > could be the basis of  a potentially useful set:
> > "the set of candidates whose approval score is higher than  their  
> > maximum approval opposition score".

Interesting idea.

> > If we interpret approval as ranking above bottom or equal-bottom,  
> > then we have a concept that is immune
> > to Irrelevant Ballots and implies Plurality and Minimal Defense.  
> > The set always includes the approval winner
> > and I think also the CW if there is one. (And of course we have a  
> > maybe-useful criterion: "the winner must
> > come from the set.")

Yes, the CW would always be in this set. Otherwise he would necessarily
have a pairwise loss.

> > So one idea for a Condorcet method: "elect the member of the set  
> > that is highest-ordered by MinMax (Margins)".
> > [I'm not sure if we need to do it that way or if we can just first  
> > eliminate (and drop from the ballots) the non-members
> > of the set.]
> > This should lack WV's random-fill incentive, and I think meet mono- 
> > add-top.
> >
> > Another alternative, for a method that hopefully meets FBC, would  
> > be to use MinMax (PO) instead of  MM(M).
> >
> > In the classic  49A, 24B, 27C>B scenario the set is {B}.
> >
> > What  do you think?

I think it's pretty interesting... I'm having trouble thinking through
these particular methods, but as a criterion it seems pretty good. I
note that in the 7 5 8 plurality failure example, again B is required.

It reminds me of "pairwise plurality" (at least, my conception of it),
where a candidate can't win if their worst loss is stronger than their
best win.


Here is something I was considering working into my last mail to Diego,
but thought better of...:

>Maybe three years ago I suggested a rank-ballot, single-round, ranking-
implies-approval method in which the pairwise winner of FPW (first-
preference winner) vs. AW (approval winner) contest was elected, except
that the AW would be elected despite losing to the FPW if the FPW had
a loss to a third candidate that was stronger than the FPW's win over
the AW (measured according to WV). I called this method "NWL" for "...and
has No Worse Losses."

>The point of the NWL rule was to avoid inappropriate FPW wins in a
scenario like this:

>7 A>B
>5 B
>6 C
>2 D>C

>The FPW is A and the AW is B; A defeats B pairwise, but an A win is
deemed inappropriate due to A's loss to C (strength 8 vs. strength 7).
So NWL elects B.

>Anyway, it occurs to me that instead of the NWL rule you could have a
second round between these two candidates. The ballots say that A will
beat B, but there was plenty of reason for other voters not to vote
for B, even if they had a small preference. If they hold a second round
between A and B, and the C and D>C voters truly do not care to express 
a preference between them, then I'm fine with allowing A to be elected.


It occurs to me to paste this here as the purpose of the NWL rule is
to enforce the kind of standard we're talking about...

Kevin Venzke


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