[EM] Re: A Condorcet-like method that satisfies FBC (I believe)

[Kevin Venzke]

Ted,

--- Araucaria Araucana <araucaria.araucana at gmail.com> a écrit:
> On 18 May 2005 at 15:14 UTC-0700, Kevin Venzke wrote:
> > For clarity, here is a brief definition of the method I'm suggesting:
> >
> > The voter places each candidate into one of three slots.
> > v[x,y] is the number of voters voting X over Y.
> > t[xy] is the number of voters ranking X and Y together in the top slot.
> > Define a set S containing every candidate Z for whom there is no other 
> > candidate W such that v[z,w]+t[zw]<v[w,z].
> > If S is empty, then S contains all the candidates.
> > Elect the member of S who is in the first or second slot on the most 
> > ballots.
> 
> Hi Kevin,
> 
> This is a very interesting idea.  But I don't see any reason why it
> couldn't be applied to a 'standard' approval cutoff ranked ballot.

You could. I have two comments on doing this:

1. I suggest that t[xy] should still only refer to the number of voters
ranking X and Y together in the top spot. You could alternatively define
t[xy] to be the number of abstentions from the X:Y contest, in which 
case all sub-majority-strength wins wouldn't count. But it's not clear
that the voter would want this behavior: Suppose the vote is A>B=C>D
and this is counted towards t[bc]. It could well be the case that this
causes B or C to win when otherwise A would have won.

Further, generally increasing t[xy] will make it more likely that
candidates will not suffer "strong defeats," meaning it will be more
likely that more than one candidate will be a first-round winner.
I want to avoid this when possible since using approval to pick from
a set of candidates (when the voters do not know which candidates will
be in the set) is kind of dissatisfying.

2. Ranking below the cutoff should be disallowed. If it's permitted, then
it is almost risk-free to bury your main opposition candidate under
turkeys that you don't intend to support in later round(s). The only case
where it wouldn't be risk-free is if other voters try to do the same
thing, turning a turkey candidate into a CW.

> Your question is what do to on subsequent rounds, and you choose to
> pick the approval winner among the remaining candidates.  I think this
> might actually fail FBC because a lower-ranked candidate could have
> higher approval.

I don't follow what your doubt is here. I don't see how lowering a
candidate from the top slot could cause a below-top-slot candidate to
become a first-round loser.

> Here's another idea:  combine this with something sort of like Bucklin:

Yeah, I suggested this idea to Chris Benham, calling it "Condorcet Bucklin."
I have the same gripe with it as with ordinary Bucklin: Deciding at which
rounds you will make additional compromises is a silly game of chicken.
Also, burial would become more effective; in the method I've suggested
burial strategy is far too risky to try.

> Round 5:  Elect DMC winner among remaining candidates.
> 
> No candidate is eliminated until it is strongly defeated by another
> candidate, according to the strong defeat measure in the round.  So if
> X and Y are not strongly defeated by Z, but one of them strongly
> defeats Z, Z can be eliminated and then the preference between X and Y
> is considered.

I have to doubt that FBC can survive more than one elimination, although
that's just a hunch.

Kevin Venzke



	

	
		
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