[EM] Proportional election method needed for the Czech Green party - Council elections

[Abd ul-Rahman Lomax]

At 08:59 AM 4/29/2010, Jameson Quinn wrote:
[quoting Juho]
>One problem with Approval (that was not mentioned yet) is the 
>limited expressive power of the Approval vote and resulting problems 
>in choosing the right strategy, e.g. when there are three leading 
>candidates and one should approve either one or two of them. That is 
>problematic e.g when left wing has 2 candidates and is is bigger 
>than right wing that has 1 candidate. (In Approval voters are 
>generally assumed to vote strategically and not just sincerely list 
>candidates that they consider "approvable".)
>
>
>This is exactly the problem that Bucklin is intended to solve. 
>Bucklin is essentially multi-round approval using one ballot. It's 
>not as theoretically clean as many methods, so there are some 
>desirable criteria that it doesn't strictly satisfy; but it's a 
>simple, practical method, both for voting and for counting. (Of 
>course, as always, I'm referring to the equal-rankings-allowed 
>versions of Bucklin.)

All the known implementations of Bucklin (all in the United States, 
eighty to ninety years ago) did not allow equal ranking in the top 
two ranks. I'm not sure of all the variations that were used. 
However, the versions I'm familiar with did allow equal ranking in 
the third rank. With what we know now, there is no harm in allowing 
equal ranking in all ranks. The reason that would be advanced to 
prohibit it is to disallow the Majority Criterion failure that can 
happen when voters vote for more than one in first rank. Because 
there is very little strategic reason for them to do that, if any, 
unless they really do have only a negligible preference -- in their 
judgment! -- this MC failure is technical, not substantive. It's also 
not very likely to happen unless the jurisdiction is blessed with 
more than one widely pleasing candidate.

(If the conditions of the majority criterion are set up, the majority 
preference must be elected in the first round, unless some of the 
majority also votes for another candidate. The Condorcet Criterion, 
which Bucklin also technically fails, for the same reasons, occurs if 
the ranking is limited. That is not intrinsic to Bucklin; a Bucklin 
ballot could allow full ranking and could consider it if deterministic.)

It's important to separate ballot design from counting method. Just 
as IRV can be run as 3-rank or with full ranking (and some 
implementations that FairVote touts as "IRV" only allow two explicit 
ranks), so too Bucklin could be run with as little as two approved 
ranks or with a full Range ballot that has, effectively, say, 100 
ratings. As long as there are as many ratings as ranks, the voters 
can decide to fully rank the candidates, but the key difference with 
equal-ranking methods is that they have the *option* of equal 
ranking. If there are not enough ranks to fully rank the candidates, 
we must notice, all methods require equal ranking, but usually just 
at the bottom!

Mr. Quinn has correctly described Bucklin as "multi-round approval." 
That is, if we imagine that a series of approval elections are held, 
with a majority being required for election. At the beginning, voters 
vote conservatively, i.e., the easiest way for them to vote, 
particularly if they don't yet know the preferences of the other 
voters, is simply to vote for their own preferred candidate. They 
will only equal-rank if they have no strong preference; allowing 
equal ranking makes the voters' decision easier. If it's hard to 
decide, you really don't have a strong preference! But if you have 
some nagging doubt when you decide to equal rank, which one do you 
prefer? In the end, the decision that most matters, in Bucklin, is 
whether or not you'd be pleased to see the outcome be a particular 
candidate, or at least not displeased. If so, then probably you 
should vote for the candidate, and then the voting problem reduces to 
ranking these candidates. Which can be done as pure ranks or as ratings.

One device that is used by Borda Count, which is a related method, is 
to have as many ranks as candidates. While I generally favor this (it 
allows voters to use their ability to compare preferences to generate 
a rank order), it may be collecting noise, if there are a lot of 
candidates. My sense is that 3-rank Bucklin (which means 3 approved 
ranks), with an added rank within the disapproved set, is enough for 
most purposes, but some studies should be done with simulations to 
determine how much results are improved with additional ranks.

Bucklin addresses the major concern of most voters when they hear 
about Approval: why can't I vote for my favorite, to give my favorite 
a chance to win, before my additional approvals are considered?

It should also be understood that, like any good method, Bucklin 
doesn't force voters to approve any additional candidates at all. If 
Bucklin is used in a runoff system, this is a perfectly sane vote 
under some circumstances. It all depends on how strong the preference 
is! Often voting system analysts deprecate "bullet votes" as if they 
were morally reprehensible. In fact, they are simply expressions of 
strong preference. And to reduce the damage, the loss of information, 
I've suggested that additional informational but non-election ranks 
be added, so that voters *may* rank unapproved candidates. This is 
all new, it has never been tried.

In the end, only a Range ballot collects critical preference strength 
information, if the voters choose to disclose it. We have to 
understand that many voters don't have any information other than the 
knowledge of their favorite. (If they have no knowledge at all, they 
should be encouraged to abstain!) What Bucklin does, in effect, is to 
interface a kind of Range ballot to a majority-seeking election 
system. In my view, done properly, particularly in the context of a 
runoff system, this will encourage fuller disclosure of preference 
strength information. It will very likely find a majority in the 
first ballot; historically, it did this well in seriously contested 
elections. Bucklin cannot fail to be better than plurality, because 
it defaults to Plurality if voters elect not to add additional 
approvals. But because it collects more information, potentially, and 
because we know that some voters will definitely add those approvals, 
it can make a better choice than plurality, it will not make a worse 
choice (except under unusual situations where it is arguable that the 
majority criterion has failed -- but only in order to elect a more 
widely-approved candidate, which is arguably a better choice), and it 
can definitely make a better choice of candidates to go into a runoff.

IRV encouraged, we saw in Burlington, Vermont, voters to add ranked 
votes for candidates they probably did not like at all; this is 
because it allowed full ranking; I forget the exact numbers, but if 
there were six candidates on the ballot, there were six ranks, and 
some voters filled out all of them. But they did not realize, I'm 
guessing, that there were really seven ranks, so by filling out all 
the six, they were voting against any possible write-in candidate. 
There were, I'm again guessing, six explicit ranks to allow any voter 
to vote for a write-in and then vote for all but one of the remaining 
candidates.

I.e., these voters were voting For their most-disliked candidate.

In Bucklin, in a primary, one would never compromise like that. A 
vote on a Bucklin ballot, except within the disapproved ranks I've 
mentioned as a possibility, is a vote for the candidate, and if it's 
a primary, this can elect the candidate if enough other voters do the same.

Bucklin is very easy to understand and vote. Natural voting 
tendencies are sound strategy!

>Of course, the issue with Bucklin is that it uses a different 
>(simpler) balloting style than STV or Condorcet.

It can use the same ballot, the same set of preferences. A Range 
ballot can be used for STV or Condorcet analysis. That the ballot is 
simpler is not exactly correct. A three-rank ballot looks the same as 
a three-rank STV (IRV) ballot. It's counted differently in Bucklin.

>  So if you used Bucklin for the single-winner method, you'd either 
> need to take two ballots, take a combined ballot (with some 
> ficticious "cutoff" candidates - possibly hard to understand), or 
> use a proportional method like RBV which is based on Bucklin ballots.

No, you could use a Range ballot for both; all that is needed is to 
distinguish between approved and non-approved ratings, and the 
easiest way to do this, and quite justifiable from a theoretical 
point of view, is to use mid-range. That's why I've studied 3-rank 
Bucklin ballots as Range 4 ballots with the rating of "1" missing. 
Only approved ranks are listed, and the rating of 0 is expressed by 
not voting for a candidate. Add that rating and you have the capacity 
of ranking four candidates plus lumping everyone else in bottom rank, 
if you want. Or you can use multiple approvals at some rank and rank 
even more candidates. If you want full flexibility, you need as many 
ranks as candidates.... but how much more utility you get from it is 
questionable.

So: you would use the ballots as, say, STV, using a good proportional 
method, to determine representation, and you would analyze the 
ballots as Bucklin to find the optimal single-winner positions of 
President and Vice-President.

(Elect the President, then re-analyze with the President eliminated 
to find the Vice-President.) Allow the Board elected to remove the 
officers if needed, if Asset is used in conjunction with the STV 
method, then voters who simply vote for one candidate are still fully 
represented in the process, and it's safe to allow an Asset-elected 
board the right to change officers when needed. The Board, if the 
election is Asset/STV represents all the members, some directly 
through their ranked votes and effective direct votes, some 
indirectly through vote transfers by candidates holding the "assets.")

Notice that elimination of the President incentivizes the addition of 
a preference, but Asset still allows voters to vote for one if that's 
the information they have.

I highly recommend that you come up with a preliminary conclusion, 
lay it out in detail, and then bring it back here again for critique; 
then compile the information and criticisms and take it back to your members.