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

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sun Jun 16 10:16:23 PDT 2013

At 07:36 AM 6/16/2013, Kristofer Munsterhjelm wrote:
>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
>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"?

Open primaries attack the underlying principle of parties as 
voluntary organizations. The first chip in this principle occurred 
when major political parties allowed their nomination process to be 
handled at public expense, instead of organizing it independently.

Open primaries allow candidates to declare as affiliated with a party 
without *any* recognition from the party. And how would a party 
designated a candidate for an open primary? That would require their 
own selection process!

When a political party has a leadership that is not responsive to the 
membership, that party can be predicted, long-term, to lose support. 
And that's exactly how it should be.

I don't know what the effect will be of open primaries. However, if 
you want to look at a pathological example, look at Lizard v. Wizard. 
That was an open primary.

The *biggest* problem with open primaries is when they are 
vote-for-one. This, then, can easily lead to serious vote-splitting, 
with the true most-widely-supported candidate losing. And in those 
primaries, the party stands by, helpless, it might seem, because 
candidates simply claim to be affiliated with the party. If it's a 
*party primary,* that's different. *Hosts* of problems arise, though, 
when there are *public elections* that create binding results for 
party nominations. Bottom line, they are no longer party nominations. 
They are something else. A majority of party members may be against 
them. Tough.

>>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.

Right. With party list you are voting for the party. Short of Asset, 
great system. The place to look for nonpartisan elections in such a 
system is in how the parties themselves determine their party list. 
Is that list determined democratically by party members? If it is, 
that's a nonpartisan election. If it is determined by "leadership," 
it may be something else. How does the leadership make decisions?

>(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.)

That happens, even in partisan elections. Was his party listed on the 
ballot? If so, that was what we call a "partisan election."

Open primaries here follow a fairly new innovation: party name on the 
ballot *without any approval from the party.* Yet candidates are only 
allowed to use a "recognized party name." Specifically, this is a 
party with ballot recognition. All others are "unaffiliated" or the like.

>>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
>Yes, and it probably does so to a greater degree than a PR method would.

It could. It radically deprecates the "party" of the leader for the 
second choice. I can see this, in a primary, being used to select 
*three* candidates for the runoff. (And then a decent method is used 
for the runoff. Approval is a tad too unselective. Bucklin, in fact, 
could be close to perfect. Instant runoff Approval. That's if we want 
to limit runoffs to a single poll. Multiple polls could use Approval, 
i.e, one could go to three polls with only two allowed to advance.

This keeps the terminally simple Approval ballot. Bucklin is *close* to that.

>  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.

Right. Now, is that bad? I see advantages to each.

>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.

And then the question is why we are going to the expense and bother 
of a runoff? If the primary is merely a nominating system, that would 
explain it. Low-participation primary, generally, picking candidates 
for a general election that gives the voters a significant choice, at 
the most convenient election for them to vote in.

>  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).

Asset, of course, totally sidesteps all these issues, by shoving 
elections into deliberative process. However, short of that, I'm 
liking the simplicity of Chris's method. Very simple to canvass:

1. total all votes. Single majority? Done, unless a runoff is *mandatory*.
2. If no majority, candidate with the most votes goes into the runoff.
3. Pull all ballots with a vote for that candidate. Retotal remaining votes.
4. Candidate with the most votes wins the second runoff position.
5. (repeat if needed for more candidates).

>>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.

It's fairly obvious that the future of voting systems is toward hybrid methods.

>>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.

Simplicity and ease of understanding are important values.

>(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.)

Well, yes.

>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.

It's very strange to me that Bucklin seems to be the poor stepsister 
of voting systems, when I started learning about this field. FairVote 
was writing pieces about the history that radically distorted it. I 
made up the name "Instant runoff approval," because that's what it 
was. Then I noticed that the ballot was actually a Range ballot, 
i.e., sane strategy indicated voting as if it were a Range ballot 
covering the approved range (default vote, unapproved.) Jameson has 
been running with this, pointing out that Bucklin is median range.

This leads to the idea of using a fuller Range ballot for Bucklin. If 
that's done, we would be, for the first time, collecting real Range 
data in public elections.

Bucklin was *really* rejected because it worked. That's my brief 
summary of the history. However, it was also true that it did not 
eliminate bullet voting, and in some elections, bullet voting is how 
most voters will vote; essentially, they don't have the information 
to do more than that, neither about the candidates, nor, more subtly, 
about the position of the rest of the electorate. So the 
last-standing Bucklin implementations were for party primary 
elections. Those are nonpartisan elections, and as a first poll, 
bullet voting should be quite common. Bucklin was replaced with 
top-two runoff, vote for one. What would have been a deeper solution 
was missed: Bucklin/runoff.

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