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

[Abd ul-Rahman Lomax]

At 03:39 PM 4/26/2010, Peter Zbornik wrote:
>The best PR system in terms of producing decent factional 
>representation is STV-PR, and others can explain how to do it. There 
>are programs that exist. But with 400 ballots, counting ballots is trivial.
>
>Has it occurred to you to wonder why, with 2000 "members," you only 
>get 400 ballots? I can tell you, it's pretty simple.
>
>We have 400 ballots because the local organizations elect their 
>delegats to the natonal rally, where the national council is 
>elected. The election of these delegates have its own irks and 
>quirks, this is another scenario, which I would like to discuss separately.

So you have "delegates" at the "national rally"? If you have 2000 
members and 400 delegates, that's one delegate for five members, 
that's extremely low. However, an average of five might work, if 
delegates are chosen, not elected. Elections on a small scale create 
warped representation, if the elections are majoritarian. If you have 
a local group with, say, 20 members, and they are electing four 
delegates, Asset could be used, it can do amalgamation on that scale 
(ESF proved it). But it would be much simpler to use proxy voting or 
delegable proxy. There are hosts of issues involved. Are delegate 
expenses paid? How? If they are paid centrally, that then creates a 
dependence of the members on the party, when it should be the other 
way around....


>If you are going to hold a single-winner election, I highly 
>recommend Bucklin-ER with runoff if there is no election in the 
>first round. And, in fact, if you are doing elections at a meeting, 
>Bucklin simply is more efficient, and you can hold all the rounds you need.
>
>Could you please send a description of this method?

A number of variations on Bucklin were used in the United States in 
roughly 1915-1920. Political scientists were enthused. And then it 
disappeared, almost without a whimper, and I haven't been able to 
figure out what happened. The reports of elections were that it 
worked, and it worked well. People liked it. But, I suspect, there 
were powerful forces that didn't want improved voting systems.

I'll describe two variation. The first is what was actually used in 
Duluth, Minnesota, it is described in detail in the Minnesota Supreme 
Court decision that outlawed it based on a rather strange 
interpretation of one-person, one-vote that was not confirmed 
anywhere else, and the Court knew that it was defying the precedent 
of other states.

The ballot has three ranks. A form that could be used would be a list 
of candidates. Next to each candidate are three check boxes. You may 
check only one candidate in first rank, one candidate in second rank, 
and as many candidates as you like in third rank. You may check no 
candidates in any or all ranks (you may skip a rank and, say, approve 
a candidate in first rank, none in second rank, and others in third 
rank). If you check no candidates in all ranks (and don't write in a 
candidate in a space provided), your ballot is invalid and is not 
counted in the basis for a majority. But if you write in a name, it's 
a valid ballot (-- according to Robert's Rules, any mark that might 
possibly be a vote makes it a ballot for the purposes of determining 
a majority.)

The first rank votes are counted. A majority is more than half of all 
ballots cast.  If a candidate has a first rank vote on half of the 
ballots, that candidate wins. If no candidate has a majority, the 
second rank votes are counted and added to the first rank votes. If 
any candidate has a vote on a majority of ballots, considering the 
first and second rank votes, that candidate wins. Otherwise the third 
rank is counted.

If this is a final poll, and there is no majority required, the 
winner is the candidate with the most votes. Ties can be decided by 
backing up and comparing the tied candidates with the third rank 
votes struck, then second. The candidate with more votes in 1st and 
2nd rank would then win, or if that is also a tie, then in 1st rank 
only. If still tied, it's decided by chance.

However, if a majority is required, then the election must be 
repeated. In pure deliberative process, the repeated election is not 
restricted, candidates are not eliminated, but some might withdraw. 
It gets simpler if it is Bucklin-ER, which I'll describe next.

For Bucklin-ER, it's the same except that the voter may vote for more 
than one candidate in each rank. It's simpler because there is no 
need to eominate candidates in order to "make room" for additional 
votes at a higher rank. What is needed for an election to complete is 
for voters to make a compromise, to start adding additional approved 
candidates, candidates who are ranked in at least the third rank.

Now, for a more sophisticated version, the ballot is a Range ballot. 
For equivalence with Bucklin-ER, it can be a Range 4 ballot; there 
is, in addition to the 3 Bucklin ranks -- which are now considered 
"ratings" -- and the no-vote rating of zero, a "disapproved" rating 
of 1. So the possible ratings are 4, 3, 2, 1, 0, instead of what 
Bucklin effectively does, 4, 3, 2, 0. Midrange functions as an 
"approval cutoff." In straight Bucklin, by voting for a candidate at 
any rank, you are voting for the candidate, at least as an additional 
approval.

This would be counted exactly the same as Bucklin-ER, and the 
counting would stop at 2, as far as determining a winner would be, 
except possibly with a tie (then the disapproved ratings would also 
be counted, i.e., one would elect the less-disapproved of the tied 
candidates, assuming that both got a majority.)

Note, some like to think of this kind of ballot as positive/negative, 
so the ratings are +2, +1, 0, -1, -2. "0" is the neutral vote, 
midrange, "average expected result." -2 is the default vote. 
(Sometimes in a system like this, 0 is the default vote, it's 
interesting, but it is very much not traditional.) For the Bucklin 
counting, a vote is a full vote, no matter what rank it's in. For 
Range analysis, though, the ratings would be used, and they could be 
considered as fractional votes. I.e., 1 vote, 3/4 vote, 1/2 vote, and 
0 vote in straight Bucklin, and 1/4 vote is the additioal disaproved 
rank. Or one could think of them as +1 vote, 1/2 vote, 0, -1/2 vote, -1 vote.

Why use this more sophisticated ballot? The method is Bucklin, which 
incentivizes sincere voting. (Remember, a bullet vote, just for the 
favorite, is a sincere vote, it means that the voter is not ready to 
support anyone but the favorite. The cost of this, though, is that 
the election may not complete, so, next round, the voter might add a 
candidate in third rank..... etc.

Because the ratings are sincere, Range can be used to estimate 
overall satisfaction for each possible winner, and also to look to 
see if there is a Condorcet winner, a beats-all winner by ranking. In 
my view, that should not be enough to determine a winner without a 
majority approval, but it can suggest compromises or possible 
desirable outcomes. To give an example, someone who would bullet vote 
with pure Bucklin, without that disapproved rank, can safely indicate 
if there is a disapproved candidate who is better than the others, by 
voting that disapproval rating, it's higher than the default of no-vote.

Range data, if it can be obtained, is highly useful, it presents a 
more accurate picture of preferences than is available with pure 
ranking, because it allows the estimation of preference strengths. 
The system describe allows four different strengths of preference.

The same system could be used with more Range resolution. The 
counting would proceed, down the ratings, just as Bucklin did, 
seeking a majority. For repeated ballot, it would terminate at 
mid-range except to do deeper analysis.

What a voter does in voting Bucklin-ER is to categorize candidates 
into classes: Favorite, Good, Okay (or Neutral), and Unacceptable. A 
Not-Good but Better than the Worst is that additional rating, if used.

This is closer to how people actually think than pure ranking. It's 
pretty easy to vote if you know about the candidates....

This is a single-winner method, as described, but it could be used 
for multiwinner elections.

The best way would be analgous to STV. But I won't describe it, 
because there should be some attention to detail. This is new theory.

Bucklin has been used for single-winner, it works. The criticism has 
been that voters frequently don't add additional preferences, but 
that's what happens with any voting system, unless somehow deep 
ranking is encouraged. Majority failure is common with IRV, for example.


>What Bucklin does in simulating multiple rounds of approval is to 
>lower the approval cutoff. The input ballot is really a kind of 
>Range ballot, and you can allow the approval cutoff to slide down as 
>low as you want. With standard Bucklin, the lowest rank is "bare 
>approval," more or less "I don't mind rating, I'm (minimally) 
>willing to accept this result." On a pure Range ballot, you'd want 
>to set an explicit approval cutoff, which I recommend as mid-range. 
>The ballot, then, allows determination of majority approval, and 
>ratings below a majority are used when needed to assess how far 
>short of approval some candidates are, when compromises must be made 
>to complete the election.
>
>You can do anything you want if a ratification vote is held and 
>passes by a majority. I.e., you could use, even, Plurality and then 
>someone could move the election of the leader, and if a majority 
>accept that, it can be considered done. But I've mentined the risks.
>
>You can use a Range ballot in the same way.
>
>
>It sounds intersting to me, but I really need to understand the 
>basics of approval voting and Bucklin and the combination with a 
>range vote, and how this will achieve proportionality. The method 
>seems to be really complex and untried.

Bucklin is very simple. Adding some Range sophistication to the 
ballot, for informational purposes, doesn't actually complicate the 
method. I was describing how to use a higher resolution Range ballot 
instead of the three-rank Bucklin ballot. But what's been done is 
three-rank, with equal ranking allowed in third rank. Allowing it in 
all ranks is a very simple change, and the practical effect, mostly, 
is that there are fewer spoiled ballots.

(By the way, the contingency that the voter votes for the same 
candidate in more than one rank must be addressed. There are three 
ways to handle it: Count the vote only at the highest rank, count it 
only at the lowest rank, or count it in the middle. (If this latter 
option is used, it's actually quite interesting. Counting the first 
rank votes for a candidate, you would not count a ballot with a vote 
for a candidate in the first and second rank. You would count those 
separately. If no majority was found in the first rank, then you 
would add in these "double rank votes," and if no majority, then the 
second rank votes.

Thus while the ballot only shows three ranks, among the approved 
candidates, one can actually vote five.

If 1st rank has a value of 4, and second rank has a value of 3, and 
third rank a value of 2 (and no vote a value of 0), then a vote of 
(rank numbers)

12 has a value of 3.5
_23 has a value of 2.5

It's not that voter will necesarily need this, but the question must 
be asked how to evaluate the "voting error," and, since it turns out 
to have an interesting meaning, why not use it?

It's like the "voting error" of voting for more than one candidate in 
first rank. It's quite useful to simply count all the votes! It makes 
a Plurality ballot into a far more sophisticated system, Approval Voting.

So with a single three-rank ballot, one can express, in a way easy to 
undertand, five ranks.

But, I'll say it once again, straight three-rank Bucklin has been 
done. One election, one of the earliest, handled about ninety 
candidates. When it was realized that the voting system could handle 
a lot of candidates without damage, almost a hundred people in the 
town (was this Grand Junction?) registered as candidates.... Of 
course, many people added approvals in the lowest rank for a 
frontrunner, at least, so the great pile of candidates did no 
harm.... And people got to see just how popular they were!

[...]
>Using a sophisticated voting system to try to amalgamate some ideal 
>representation from an instant set of ballots misses the opportunity 
>for the election process to be a broad discussion involving all the 
>members, so that those elected do know the views and opinions of the 
>entire membership. The model, then, becomes, in effect, if you just 
>elect by rapid amalgamation, is the strong-leader model, which will 
>create the sheep you described.
>
>
>I can aggree with the discussion being an integral part of the 
>election, and I guess this could be addressed too. But that is an 
>other discussion.

The basic issue is "How can large numbers of people communicate, 
coordinate, and cooperate?" If you just look at the voting system, 
you won't get a deep answer.