[EM] A better 2-round method that uses approval ballots

[Kristofer Munsterhjelm]

On 06/14/2013 09:06 PM, Abd ul-Rahman Lomax wrote:
> At 12:44 AM 6/14/2013, Chris Benham wrote:

>> My suggested 2-round method using Approval ballots is to elect the
>> most approved first-round candidate A if A is approved on more than
>> half the ballots, otherwise elect the winner of a runoff between A and
>> the candidate that is most approved on ballots that don't show
>> approval for A.
>
> Yeah. My general position is that runoff voting can be *vastly improved*
> by some fairly simple tweaks, or by using an advanced voting system, in
> the primary and maybe in the runoff. Approval is an advanced voting
> system *and* a tweak on Plurality.

> Parties fielding 2 candidates is a disempowering move, in general,
> weakening campaigning. I'm generally opposed to "open primaries" in
> partisan elections. A unified primary makes sense in a non-partisan
> election.

Couldn't open primaries weaken party leadership and so encourage the 
transition from Duverger-style two party rule into multipartyism? As 
long as the primary/runoff method can handle multiple candidates, that 
is. Or do you think the leadership would instead say that "we need to 
stick together or the other party, that keeps party discipline, will 
divide and conquer us with much stronger focused campaigning"?

> And we need to understand something about nonpartisan elections. They
> are *very different* as to voter behavior from partisan elections. What
> seems to be, from the behavior of nonpartisan IRV, is that voters vote
> on name recognition and affect. It is the kind of thing that is heavily
> influenced by public exposure of the candidates, and it has little to do
> with "political position" on a spectrum. Voters do not appear to be
> voting as if there is this spectrum, with second preferences then being
> predictable from spectrum position of the candidates and the voter.

It'd be interesting to run some kind of SVD on cardinal polls in such 
elections to confirm whether that's the case, but I trust you :-) You 
certainly know more about non-partisan elections than I do, since pretty 
much every election here is partisan. It's a consequence of the party 
list method we use.

(However, I do note that in one of the few cities that have direct 
mayoral elections, a candidate from a very left-wing party was elected. 
This party has about 2-3% national support, and I get the impression he 
was elected on "nonpartisan" grounds - by character and quality rather 
than by political affiliation.)

> I would conceptualize Chris's system this way. It's a 2-winner approval
> method, designed to maximize *representation* on the runoff ballot.
> Voters who approve A are already represented, so, it makes sense to only
> consider ballots not approving of A in determining the other runoff
> candidate.

Yes, and it probably does so to a greater degree than a PR method would. 
Consider a case where we have a candidate that's preferred nearly 
unanimously, and then another candidate preferred by the slight minority 
that remains. Assuming Chris's method doesn't have a threshold similar 
to the "greater than majority support and he wins" threshold of TTR, the 
method would pick both candidates mentioned above for the runoff. On the 
other hand, if the majority is sufficiently large, a PR method could 
pick two candidates preferred by the near-unanimous majority.

I don't think that would make much of a difference in a runoff, though. 
If candidate A is preferred (approved) by a near-unanimous group, 
meaning that candidate is considered to be vastly superior to everybody 
else, then that group will have the power to make him win in the runoff. 
The issue is more whether a runoff should aim towards maximizing 
representation (as Chris's method, as well as minmax Approval, tries to 
do), common center focus (as top-n Approval would do absent deliberate 
clones) or some combination of both (as PR methods would do).

> However, limiting the runoff or general election ballot to two
> candidates is an unnecessary restriction. It is only a false majority
> that is created when candidates are eliminated, and, as we know, the
> pathologies of elimination systems are rooted in that elimination.
>
> As a compromise, up to three candidates can be permitted on the runoff
> ballot, using an advanced voting system that can handle three candidates
> well, and the selection can include much better criteria that mere top
> two. If a ranked ballot with sufficient ranks is used, condorect winners
> can be identified and placed in the runoff, thus making the overall
> method condorcet compliant, i.e., a persistent Condorcet winner would be
> identified as such -- publically known -- and would win *unless voter
> preferences change or turnout shows that the condorcet preference
> strength is low.*

One possible way of doing that would be to use a combinatorial PR method 
where you force-include the winner from the other type of system. For 
instance, you might render cardinal ballots into ordinal ballots and 
then run Schulze STV on them - but force the inclusion of the Range (or 
MJ or whatnot) winner in the outcome. If the Range/etc winner would 
appear in the winning Schulze STV outcome, you don't lose anything; if 
it wouldn't, you've ensured the representation of both 
strength-of-preference winners and ordinal winners.

It's probably way too complex, though, but it shows that making such 
"combination slates" is indeed possible; and if the basis method is PR, 
then it degrades gracefully - e.g. if the election is partisan and the 
cardinal winner leans left, then that won't bias the list of candidates 
leftward because the PR method will compensate for the fixed winner that 
has to be included.

> Another approach with a fixed general election and the primary not being
> the election, but a determination of ballot position, would be to run
> the primary as three-winner STV, with an advanced method in the runoff
> (not STV, single winner STV is atrocious.)

In an attempt to find a PR method that passed weak monotonicity, I made 
one that is based on Bucklin. It reduces to Bucklin in the n=1 case 
while passing the Droop proportionality criterion for n>1. I *think* it 
also passes weak monotonicity, but I'm not sure of this: all I have is 
lack of evidence to the contrary, not a mathematical proof.

(Here, for multiwinner methods, weak monotonicity means that if the 
outcome includes X, then raising X can't push X off. It's not "strong", 
because if the outcome includes X and Y, raising X could push Y off and 
vice versa.)

Anyway, the reason I mention it is because it reduces to Bucklin. So 
using that method would mean that you don't have to use a different 
method in the single-winner and multiwinner case, or in the different 
rounds of the runoff. It is limited, though: It doesn't support the kind 
of skipped-ranks feature some Bucklin methods do.