# [EM] Another three-slot method

Kevin Venzke stepjak at yahoo.fr
Sat Nov 8 12:32:02 PST 2003

```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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