[EM] Could a single specially-crafted new vote resolve all ties in a Shulze election?

[Scott Ritchie]

Hi, I serve on Ubuntu's community council and we've been discussing our
election method lately.

We currently use the CIVS service for our elections (voting for various
councils/boards is available to official Ubuntu members), however we
never actually formally picked an algorithm.  CIVS tallies the votes
using 4 different algorithms, and all 4 have so far agreed on every
single election, so it was a bit of a moot point.

However, somewhat recently we had an election where there was a tie
between the 2nd and 3rd place candidates for an election where the top
two won.  We had no procedure in place for dealing with this, and 3/4 of
the CIVS methods produced a tie, but one (CIVS-IRV) produced a winner,
so we just sort of went with that one without much thought (this was
before I was on the CC).


Anyway, I'd like to prevent problems in the future, so:
1) Endorse an algorithm.  I've already decided on Shulze, since that's
what Debian uses and they're our sister project.
2) Create a formal tie-breaking rule.  My intuition says that we can
give Mark Shuttleworth (who already has special privileges) a second
vote that he only uses in the case of a tie, add that vote to the box,
and then rerun the election.

However, I'm not 100% sure that a regular vote cast in the CIVS sense
will actually resolve ties cleanly.  So, I'm asking the list:

Suppose we have a tie among {A,B} for the marginal seat in an election.
 Would a vote for A > B that expressed no other preferences always
result in an identical overall ranking except with a resolved tie?

If the tie is larger (or number of marginal seats larger), could he
similarly vote {A>B=C} or {A=B>C} to resolve them?

Could either vote affect the non-marginal seat order?  Shuffling the
above winners, provided they all still win, isn't much of a problem,
however shuffling the losers might be an issue since we use the list
order for replacement candidates when someone steps down mid-term.

Could this limited vote produce new ties further down the line?

Thank you muchly.  :)


Thanks,
Scott Ritchie