[EM] Another three-slot method

Forest Simmons fsimmons at pcc.edu
Wed Nov 12 14:56:13 PST 2003

Kevin, this looks promising.  Could you expand your explanation of why
some of the first slot candidates are not to be counted in the contest
between the AW and the FPW?

Perhaps an example with two candidates in the first slot would help.


On Sat, 8 Nov 2003, [iso-8859-1] Kevin Venzke wrote:

> After sitting on MCA (with only one candidate permitted in the first slot) for
> awhile, I thought of another idea, a kind of compromise between MCA (any number
> in the first slot) and Conditional Approval (a method I described months ago).
> It seems like a better attempt at getting Condorcet-like behavior without using a
> pairwise matrix:
> The voter places any number of candidates in the first, second, or third slot.  If
> it would be more politically acceptable, the number of first preferences could be
> limited to one.
> 1. Count how many first and second preferences each candidate gets.  The candidate
> with the most first preferences is the "FPW" (first-preference winner).  The
> candidate with the most first+second preferences is the "AW" (approval winner).
> 2. Count the ballots again, with either a first or second preference counting as
> a vote for a candidate, EXCEPT: Ballots which placed the FPW in the first
> slot are counted as bullet voting for the FPW.  (They bullet vote even if they had
> additional first preferences: This is necessary to ensure the method elects a
> majority favorite when there is more than one.)
> 3. If the FPW wins in this second count, he wins; otherwise the AW wins.
> Here are a few examples:
> 5 A>B>C
> 4 B>C>A
> 3 C>A>B
> The FPW is A.  Thus the 5 voters (and only they) have the option of truncating.  If
> they do, A is the winner (A 8, B 4, C 7); if they don't, B would win (with 9).
> (This latter means that B is the AW.)  A is elected.  (Same as RP or Schulze.)
> Change the 3 voters to C>>AB:
> FPW is still A, and the AW is still B.  This time if A truncates, C will win.
> If they don't truncate, B wins.  Because A cannot win through truncation, the AW
> B wins, as in WV.
> 49 A>>BC
> 24 B>>AC
> 27 C>B>A
> The FPW is A, and the AW is B.  But A truncating doesn't make A win (it doesn't
> even make any difference), so B wins, as in WV.
> 8 A>B>C
> 5 B>>AC
> 7 C>>AB
> A is the FPW; B is the AW.  If A truncates, A wins, so A (the CW) is elected.
> But add two C>>AB voters: C is the FPW, and B is still the AW.  C truncating doesn't
> make C win, so B wins.  This is also the WV result.
> I like that this method meets Majority Favorite without any reference to the
> term "majority."  In the situations above, MCA (and most methods I've suggested)
> always pick the AW.  By giving the plurality winner a "privilege," a weaker
> pairwise victory may be respected, and the method also gains a touch of later-no-harm.
> I also like that this seems less likely than Approval to turn front-runner predictions
> into self-fulfilling prophecies.  That is, the potential in Approval for a
> prediction of A and B being the front-runners, to result in every voter approving
> one of them.  If a third candidate C manages to be the first-preference winner, in
> this method, they stand a good chance of winning instead of giving the election away
> to their second preference.  (If C turns out to be a dog, the worst they've done
> is to keep Compromise from being the FPW, which is far from fatal.)
> I believe this method is monotonic (unlike Conditional Approval).  I can tell it
> doesn't meet Participation or weak FBC, but I have yet to come up with the situation
> where it fails them.  Not sure if it meets later-no-help.  It clearly meets
> Plurality.
> Kevin Venzke
> stepjak at yahoo.fr
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