[EM] Tiebreaking in STV: Lundell-LastDifference

[John]

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Jonathan Lundell proposed a rule for tiebreaking in STV:

http://www.votingmatters.org.uk/ISSUE22/I22P1.pdf

1. Find the first mention of any member of the tied set of candidates on
each ballot, and calculate the total such mentions for each of the
candidates, using the transferable weight of each ballot. Ignore ballots
that do not mention at least one tied candidate.

2. If all n candidates are still tied, exclude one tied candidate at
random; finis.

3. Otherwise, remove from consideration for exclusion the candidate (or a
random choice from the tied set of candidates) with the highest score from
step 1.

4. If only one candidate remains, exclude that candidate; finis.

5. Otherwise, n is now the remaining number of tied candidates (that is,
less the reprieved candidates from step 3); continue at step 1.

Basically, when you're trying to exclude candidates in STV and you have
multiple with the same last-place vote count, use the transfer weights of
each ballot to perform instant runoff voting between these candidates and
eliminate the winner from consideration; repeat until you have one
candidate left.  Eliminate THAT candidate from your STV election.

Lundell cites exclusion of a random candidate in the event of a tie in this
algorithm.  I propose using the Last Difference method, by Lundell's own
arguments, and only falling back to random exclusion if that fails.

Lundell's argument for his proposed method is that prior-round tiebreaking
encourages insincerity, and that Last Difference is superior to First
Difference by O'Neill's arguments, therefor current-round information is
even better.

I observe that Lundell's tiebreaker will run first, and so will dominate
over the fallback.  If strategically targeting Last Difference sacrifices
Lundell's runoff method, then it will cause losses, and so the strategy is
unviable; yet Last Difference, when it produces a break, is better than a
random tiebreaker.  The final fallback would be random.

Last Difference is equivalent to First Difference if the immediate prior
round was the first difference.

Thoughts?

—John
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