[EM] Compromise/Composite of votes &margins for Schulze Method

[Stephanie Finney]

Hello all,

I've been trying to catch up on the highlights of controversies past in
regard to voting methods.  I personally find the Condorcet methods
attractive, and have been persuaded by my reading online that Schulze Method
is the best for my interests.  However, I have seen good arguments both for
and against votes against and margins as standards for measuring beatpath
strengths.  I will note here that I am tentatively in favor of allowing ties
and truncations, as well as allowing each voter to indicate whether they
wish any particular tie to count as 0 or 0.5 votes.  But here is my
fundamental question.  Is there some way to combine the strengths of these
two methods of measuring victories/defeats?
One simple method (perhaps too simple?) which occurs to me would be to
analyze the ballots by Schulze both with margins and with votes against, and
when they both choose the same winner, you'd be finished, but where they
choose different winners, choose the candidate who won the original pairwise
comparison between them.  How often would either Schulze Method variation
choose more than one winner in the absence of a numerical tie?  Most of the
time it would appear that Schulze is fairly decisive, so I think this as a
fairly reliable way to choose a winner.
Another thought I've been playing with is a way of combining the votes
against with the margin to express a composite value.  The first way I
thought of was to simply add the margin and votes against together.  This
would give you a value that is heavily weighted by the votes given to the
victor, yet also takes into account the margin of the pairwise matching.  I
had problems with seeing a result of 51:49 as equal to either 51:1 or to
3:1, not to mention all the possibilities between.  And as the election
considered grows in voters, the extreme possibilities grow too (although, I
have to wonder, just how disproportionate can the votes get and still have
the candidates all in the Smith set?).  If, however, we were to add the
votes, then you narrow the range of equivalent votes by almost half for
competitions were some voters truncate the two candidates in pairwise
competition (for example, for 51:49 the most extreme equivalent is 27:1
since 51+(51-49)S and 27+(27-1)S.  All other comparisons fall between these
ranges of votes against and margins.  Of course, if we say this is a
possible alternative to margins or votes against, it can in some instances
choose a winner in a cycle who is different from both the votes against and
margins winner.
After thinking about this combo measure for a little while, I found that
another idea kept intrusively popping to mind.  Another way to positively
combine the measures would be multiplication.  Wouldn't the large elections
be fun to calculate (Oh look, A's beatpath to B is only a trillion, guess B
wins that one...).  Actually, the math is simplistic, it's just the numbers
that are large.  Multiplication of margins by votes against tends to really
spread out the results, keeping much lower the number of beatpaths of equal
value, and has the nice effect that margins have of automatically giving
ties a beat value of 0.  I haven't looked too deeply at this multiplicative
option yet (as I tend to think of these things on the commute to and from
work, the multiplication begins to get a little distracting when I go above
10 voter examples (20 is not too bad, but still...).
My purpose in proposing these combinational ideas is to try to give value to
the two concepts of what constitutes the strength of a pairwise result.  I
think both have merit, and information about voter choices that's worth
preserving.  I would greatly appreciate commentary from all about the
possible strengths and weaknesses of these proposed measures.  If these
ideas have been suggested in the past, I apologize for re-inventing them and
ask if someone could point me towards the discussion on them.  As far as I
have been able to find in my short time looking into condorcet methods, they
have not been proposed before quite like this.  I would like to thank all
the contributors to this list from 1998 on for posting their thoughts,
ideas, and debates, from which I have learned and leaned upon in trying to
figure this stuff.
Glen Finney



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