[EM] Better runoffs

[Peter Zbornik]

Dear all,

A simple extention of IRV to two rounds IRV would be the following:
1. In the first round have no quota (i.e. no transfer of surpluses).
2. The two candidates who are eliminated last go to the second round
3. In the second round the two candidates meet in a normal IRV election.

Question: Will this method always generate the same winner as one-round
IRV, in the case that the preference orderings of the voters are the same
in both rounds?
I believe yes and it seems trivial, but cannot prove it just like that.

I am considering proposing this method for use among the Czech Greens as an
improved IRV and a natural two-round alternative to the Run-off elections
we use today.

Example:
10 A D C
20 B C
25 C A
15 D C

70 votes, no quota
In the 1st round A is eliminated first, his votes goes to D who gets 25
votes.
Then B is eliminated with his 20 votes.
Thus D and C go to the second round, where C wins.

Thanks for some help.

Otherwise, we will use STV in our party, and we are working with the
details.
More info coming in a month or two.

Best regards
Peter Zborník

2012/7/10 Kristofer Munsterhjelm <km_elmet at lavabit.com>

> When runoffs are subjected to criterion analysis, one usually considers
> voters to vote in the same order in each round. If they prefer A to B in
> the first round, and A and B remain in the second round, they'll vote A
> over B in the second round.
>
> This may not necessarily fit reality. Voters may leave or join depending
> on whether the second round is "important" or not, and the same for later
> rounds in exhaustive runoff. But let's consider top-two runoffs and, to
> begin with, that the voters will stay consistent.
>
> The kind of criterion analysis performed on top-two then says that top-two
> Plurality runoff is not monotone. Furthermore, it is worse than IRV (i.e.
> fails participation, consistency, and so on, but also things IRV passes
> like MDT and mutual majority).
>
> If we want to have a method that does better, what would we need?
>
> Some methods (like Ranked Pairs or Kemeny) pass what is called local IIA.
> Local IIA says that if you eliminate all candidates but a contiguous subset
> (according to the output ranking), then the order of those candidates
> shouldn't change. If you eliminate all candidates but the ones that
> finished third and fourth and rerun the election, then the candidate that
> finished third should win. More specifically, for runoff purposes: if you
> pick the two first candidates to the runoff, and voters are perfectly
> consistent, then the order doesn't change.
>
> Thus, all that you really need to make a runoff that isn't worse than its
> base method is that the method passes LIIA. Use Ranked Pairs for both
> stages and there you go -- if the voters change their minds between rounds,
> conventional criterion analysis doesn't apply, and if they don't change
> their minds, you don't lose compliance of any criteria.
>
> However, such runoffs could become quite boring in practice. Say that
> there are a number of moderates in the first round and people prefer
> moderates to the rest. After the first round is done, two moderates are
> retained and run in the second round. What does it matter which moderate
> wins? The closer they are to being clones, the less interesting the runoff
> becomes.
>
> More formally, it seems that the whole voting population is not being
> properly represented. Two candidates represent the middle but nobody
> represents either side. That might be okay if voters are normally
> distributed around the candidate, but if they are, you wouldn't need the
> runoff to begin with.
>
> If that's correct, then it'd be better to have a proportional ordering.
> That proportional ordering should still put one of the moderates first
> (assuming he'd be the winner had there been only one round), but also admit
> one of the side candidates. But here's the tricky part. That proportional
> ordering method should also pass LIIA, so that all the criterion
> compliances held by the base method are retained. It's thus necessary that
> the winner of the base method comes first. Beyond that, however, I have
> little idea how the method might be constructed, or if it's even possible
> to have both a proportionality criterion and LIIA.
>
> Finally, if such a method were to be found, one could possibly have more
> than two candidates in the runoff. The runoff would serve as a way of the
> method to say "hey, look at these candidates more closely", where their
> positions could then be compared and voters possibly change their minds. If
> the method passes LIIA, it doesn't matter how many (or few) candidates you
> put in the second round - the method acts like the one-round method if all
> the voters remain perfectly consistent. Practically, also, if there are
> only two candidates and one is a moderate, the "other" wing not represented
> might feel cheated out of a chance if only one of the wings are
> represented. If the centrist and the leftist goes to the second round, the
> right-wingers may complain that their candidate is not represented, whereas
> ordinary top-two runoff would have no such problem because both the
> right-wing and left-wing candidate would be represented at the cost of the
> centrist.
>
> ----
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>
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