[EM] A four bit (sixteen slot) range style ballot

[Abd ul-Rahman Lomax]

At 06:22 PM 6/10/2010, fsimmons at pcc.edu wrote:
>Here's a possible format for a sixteen slot range style ballot that 
>(for range purposes) can be counted
>with standard talleying equipment:

Funny, I was just discussing this on the range voting list.... I 
really don't like the idea that a voter has to mark four times to 
give a bullet vote! Kinda defeats half the purpose of it (simple).

probably the most that is needed for an election is as many options 
as candidates. The fact that voters can equal rate will allow more 
flexibility, more candidates than ratings can generally be handled 
with little loss in effective voting precision.

I was thinking about a Bucklin ballot. I've been writing about how a 
Bucklin ballot, optimally voted, would be a Range ballot; in original 
Bucklin, with three ranks, it was a Range 4 ballot, with approval 
cutoff at rating 2, and rating 1 amalgamated with 0, both as 
disapproved ratings.

I've also been working on the concept of using a full range ballot 
for Bucklin. While one could continue the rounds down below 50%, I'm 
more interested in keeping symmetry and of seeking a majority, so 
what I'm suggesting is using Bucklin as a crackerjack primary method 
in a runoff system, and then using more sophisticated analysis than 
"top two" to pick up to three runoff candidates. For this, it would 
be better if it is a full Range ballot, but it may not be necessary 
that it be high-resolution.

The three obvious candidates for a runoff would be, given the full 
Range ballot, if no candidate gains majority approval after all the 
rounds have been collapsed into pure approval (50% rating or higher), are

Approval winner
Condorcet winner
Range winner.

One of the common complaints about Bucklin is that it can fail the 
Majority Criterion, but this only happens if more than one candidate 
gains a majority. Note that critics of Bucklin, when they point this 
out, move on to criticize it because supposedly Later No Harm failure 
will cause bullet voting, so there won't be *one* majority, much less two.

They kind of get you coming and going, eh?

Anyway, original Bucklin effectively had three approved ratings, so 
counting proceeded in three rounds. The number of votes added in the 
third round, where multipple approvals were allowed, tended to be 
spread out, making it more likely to find a multiple majority if the 
election was close. Using a higher-resolution Range ballot, the 
"approved half," if we can think of it that way, would make multiple 
majorities substantially more unlikely. Not that I really mind 
multiple majorities....

An argument I have used for allowing equal ranking in all ratings, 
instead of just the lowest, has been that voters will do it anyway, 
spoiling ballots that otherwise have a perfectly obvious meaning. It 
has always been a bit crazy to toss overvoted ballots. Consider the 
possible cases with two votes: Election with frontrunners A and B, 
and two minor candidates C and D.

Categorize the overvote separately if number of votes received is 
important for things like ballot position and campaign funding. For 
those purposes, the votes should be considered fractionally. I.e., if 
a voter voted for two candidates, it's 1/2 vote for each. But not for 
purposes of finding the winner.

These are the combinations and the consequence of just counting the 
votes instead of eliminating the ballot.

Voter intends to vote for A and accidentally votes for B, so voter 
then marks A additionally.

If both votes are counted, they effectively cancel each other out. No harm.

Voter intends to vote for A and accidentally votes for C or D, then A.

If both votes are counted, unless this really does turn into a 
three-way race, the C or D vote is harmless.

Voter intends to vote for C or D and accidentally votes for A, then C 
or D. This is the only somewhat harmful vote, but it would be unusual 
since, by definition, most voters intend to vote for a frontrunner.

And then the other situations are symmetrical.

But there is also another situation: the voter intends to vote for A 
and C, say. That is only an error because the rules say it's an 
error. It's circular. In fact, allowing this implements Approval 
voting, a voting efficiency enhancer that was somehow overlooked for 
years. In repeated ballot, it makes a practically ideal voting 
system, where voters would gradually lower their approval cutoff, 
being aware of the results of the prevous rounds. And then Bucklin, 
of course, simulates a series of such rounds. It is so simple that I 
wonder that it wasn't done before. But, of course, it *was* done 
before, and not only by James Bucklin, but, apparently, the method 
was invented in round outlines by the Marquis de Condorcet, and it's 
said that it was used in Geneva, all around 1800.

With what we know now, we would naturally feed the Bucklin counting 
method with a Range ballot, which is the "program" for a voting robot 
that takes the voter's instructions and votes through a series of 
rounds, lowering the approval cutoff in a fixed way, and the ballot 
allows the voter to specific exactly where to start voting for a 
candidate, and how long to wait, which clearly is a measure of or is 
strategically controlled by preference strength. It is a sincere Range ballot!

The nature of the "sincere" expression becomes clear if Bucklin is 
being used in a runoff system. If a majority is being sought, and if 
the voter prefers the election of a candidate to a runoff being held, 
which then requires the voter to go to the trouble of voting again 
(unless the voter doesn't care about the choice between the runoff 
candidates), the voter will approve that candidate. If not, not. This 
is an absolute preference, fully sincere and effective in pushing for 
the desired result.

So, then, how to design the ballot? How many ratings? Original 
Bucklin did handle, in one election, about ninety candidates! With 
three ranks, and multiple approvals only allowed in the last rank. So 
three approved ranks isn't shabby, actually! But to allow full Range 
expression, useful for Condorcet analysis, I'd want to make the 
ballot symmetrical, with multiplpe disapproved ranks as well. These 
would not be used for determining the winner in a primary. Adding a 
disapproved rating could not cause your favorite to not win the 
primary if he or she would otherwise win. (Except perhaps in a 
certain very, very rare situation which can safely be neglected; that 
is a situation where your vote changes the Condorcet winner, causing 
a runoff, say, to be cancelled, because now all three possible 
winners are the same, perhaps some other condition is satisfied that 
makes a runoff result a foregone conclusion, and the rules then do 
not require a runoff.)

Adding an approved rating can indeed complete an election for your 
less approved candidate, but, then again, that's the choice one makes 
when approving more than one. It's voluntary, and whether or not one 
will do this *depends on preference strength,* so the votes are 
incentivized to represent real preference strength, at least by some measure.

This method is so close to Condorcet compliant that the difference 
would be purely theoretical. If the runoff is fully condorcet 
compliant, if there is a Condorcet winner among the three candidates, 
then the method is completely condorcet compliant, which is pretty 
cool, I think, for a method that is also a Range method and which 
would get a Range winner into a runoff, where voters can change their 
minds! -- or if they don't care, not show up to vote: where the Range 
winner differs from a Condorcet winner, it is because the Range 
voters have expressed a stronger preference, and the Condorcet winner 
a weaker one. Is that real? A runoff will test it. If it's real, 
turnout will be lower for the Condorcet winner's supporters, and the 
Range winner has a leg up. If it's an artifact of poor voting 
strategy, the Condorcet winner may have the advantage.

There are lots of details to be worked on to optimize this method and 
map out an implementation strategy. It might not start as this 
full-blown Range/Bucklin/Runoff system. But even traditional Bucklin 
probably should have been tried as a primary method. This would be 
far more in accord with democratic practice than what was actually 
done, which was to use it as a plurality method. Bucklin would do 
what Robert's Rules of Order suggests IRV as being helpful for. The 
parliamentarians didn't realize, apprently, that in nonpartisan 
elections, IRV performs almost exactly the same as Plurality, and if 
Plurality would not deliver a majority, IRV would be likely to fail 
also, simply by a smaller margin. The vote transfers tend to behave 
as if the supporters of eliminated candidate A have the same ratio of 
support for B and C as do the rest of the voters who did not prefer 
A. That's an interesting phenomenon, don't you think? Who the hell 
anticipated that? But that's the U.S. IRV election experience, 
repeated over and over, and it only fails to work that way with 
partisan elections, which then show strongly preferential vote 
transfers, and a similar phenomenon showed up in an election where 
there was strong ethnic voting. The supporters of a candidate in San 
Francisco with one ethnicity, when that candidate was eliminated, 
preferentially voted at lower preference for another canidate of the 
same ethnicity. It's like a partisan election, and the names were 
marks of ethnicity!

In any case, some time back I realized that the resolution of a 
Bucklin Range ballot could be increased by allowing multiple rating 
marks. Yes, long ago, I suggested using binary voting, as Forest 
describes above. I'd do it a little differently, perhaps, but this is 
different. The problem with binary voting is that it's not 
particularly intuitive. I've workd with binary numbers for well over 
fifty years, and looking at a pattern of check marks, I don't 
immediately see which number is larger. And a system that requires a 
voter who desires to bullet vote to mark four marks isn't going to 
fly, I'd say. So here is what I have:

In this case, the ballot is Range 10.

But there are only 6 boxes to check for each candidate. They 
represent the ratings of

0 2 4 6 8 10

And the candidate name is printed on the right. The rating of zero is 
the default. For some purposes in dealing with runoff choices, a 
blank might be treated differently than an explicit zero, which this 
has for several reasons.

**************Instructions

This is an election to determine a single winner. You may vote for as
many candidates at any rating, including "Favorite," as you choose.
Each vote is independent of all the others. If you mark the ballot at
more than one rating for a single candidate, the recorded rating for
that candidate will be exactly between the highest and lowest mark
you make. The minimum rating for a candidate to be considered
"approved" by you would be shown by marking both rating 6 and rating
4, which will count as 5.

If you do not mark a candidate, will be counted as 0.

**************Counting procedure

All votes for all candidates at the highest rating will be counted,
and if a majority of ballots contain this vote, that candidate will
be declared the winner. Otherwise the votes from the next lowest
possible rating will be counted, again to determine if there is a
majority winner. This process will repeat until there is a majority
winner or all votes have been counted which are ratings of 5 or
higher. If no candidate has a majority at that point, there will be a
runoff election. The runoff candidates will be determined by analysis
of the full ballots, which is why it may be ivaluable for you to
relatively rate all candidates, not just approved ones, it allows you
to show a preference for unapproved candidates. For complete detaisl
on how the runoff candidates will be determined, please see your
voter information ballot.

**************labels along top
10 Favorite
8
6 Approved
4 Disapproved
2
0 Completely Rejected

***************Sample Ballot

0 2 4 6 8 10
o o o o o o ALICE LYNDELL
o o o o o o BOB DYLAN
o o o o o o CARL SAGAN
o o o o o o DINO SAUR
o o o o o o WRITE-IN

And suppose I prefer the candidates as W>A>B>C>D, my range ratings 
for these, sincere normalized to the two ranges (approved and 
disapproved, based on my estimation of probably outcome and my 
preference for the candidate to the probable outcome, and/or to the 
spectre of a runoff being needed if those are the rules), are;
W:10, A:9, B:5, C:4, D:0.

So my marked ballot would look like this (I'm using period now to 
show blank boxes, the contrast is better):

0 2 4 6 8 10
. . . . X X ALICE LIDDELL
. . X X . . BOB DYLAN
. . X . . . CARL SAGAN
X . . . . . DINO SAUR
. . . . . X WRITE-IN LYSANDER SPOONER

Notice how the eye easily sees that the vote for Bob Dylan is higher 
than that for Carl Sagan. And the Write-in is higher than that for 
Alice Lindell.

With this simply ballot I can fully rank 11 candidates, if that's 
what I want to do. That would make it a Borda ballot as far as the 
Range winner is concerned. But it's really a Range ballot, of course, 
and, at the same time, a Bucklin/Approval ballot. I would have put 
the unapproved boxes, the three on the left, in red, but I can't get 
this version of Eudora to do it....

To bullet vote for a candidate, I just mark the box next to the 
candidate's name.

The counted vote is always midway between the lower and upper marks, 
if it's not just one mark, which is as writ, or no mark, which is 
zero. The zero rating is there for two reasons: to avoid the 
situation that the voter thinks that the first box (nonzero if zero 
isn't explicit) is the lowest rating, and to allow creating a rating 
of 1 by marking both 0 and 2.

Another nifty trick has to do with the ability to shift a vote after 
it's written. I can shift a vote a point down by marking the box to 
the left (assuming that the left box isn't already zero, or I can 
shift it up by marking the box to the right. I can shift it up two 
points by marking the next box over from that, again assuming there is room.

I would vote this ballot in this way, which would make it pretty easy 
even if I haven't planned how I'm going to vote.

I would vote first for my favorite and the worst and for any 
candidates equally rated. I define "equally rated' as my having 
difficulty deciding between them! Then I would look for any 
canddidates I'm also willing to approve. How many are there? If it's 
easy, I would rank them, with the worst of them I would mark the 6. 
I'd distribute any remaining approved candidates in the space between 6 and 9.

Now, have I included a frontrunner? If not, I'd consider whether I"d 
rather wait for a runoff to make this decision. If I decide to go 
ahead and vote for a frontrunner, not having done so, I'd vote 5, 
i.e, mark the 5 and the six. If I decide not to vote for the 
frontrunner, I would then mark the 4 on the worst approved candidate 
to make that vote a 5, the minimum approved vote. Generally, unless 
there are a lot of approved candidates, I haven't used up all the 
approved ratings and I've marked my favorite as the top approved and 
the least favored approved candidate as the minimum approved rating.

Then I distribute the other disapproved candidates. Turkey-raising is 
a dangerous strategy that can backfire, and I dobut I't be tempted. 
It gets really difficult if there can be *three* candidates in a 
runoff. I have five disapproved ratings. That should be plenty to 
rank them reasonably. Condorcet analysis may be where this is 
important, and also Range analysis.

These ballots would be collecting reasonably accurate, the best 
available, Range ratings for candidates, allowing the study of voting 
system performance in real elections with an accuracy not previously 
attainable. With an ability to fully rank eleven candidates, this 
could handle large elections, but it is still a simple ballot.

Voters can igore the facility to add "mid-ratings." It is only a 
refinement, adding just a little mroe specificity. A voter who wants 
to bullet vote can just do that, and it's easy to see it and it only 
takes one mark.

Exactly how to analyze ballots if a majority is not found is an open 
question. I've gone over some ideas and have discussed thtem, but I 
certainly don't consider it a fixed thing.

I'm interested in

1. Getting some kind of Bucklin into public use, especially as a 
primary method to reduce runoffs. It should do this better than IRV. 
(IRV is proposed as a complete runoff replacement, which simply 
ignores that IRV, in the nonpartisan elections where IRV has been 
recently implemented in the U.S., usually fails to find a true 
majority. The Robert's Rules suggestion of IRV is actually of IRV as 
a way to supposedly more efficiently find a true majority winner. 
This has apparently been overlooked by many organizations who though 
they were following the Robert's Rules suggestions, and the vote 
counting rules were just ambiguous enough to allow that impression. 
Because I first read this on the page handily provided by FairVote, 
and it was framed as being "IRV," I missed it. But, in fact, they are 
explicit when they suggest that the clerk educate votes to rank all 
the candidates, because, otherwise, the election may fail to find a 
majority "and will have to be repeated." It couldn't be more 
explicit, in facr. When I pointed this out, Richie et al excoriated 
me for claimng what was preposterous, were all these organizations wrong?

Well, if they though they were following Robert's Rules, yes, they 
were. And a parliamentarian should have noticed it, because the 
meaning of "majority" to a parliamentarian should be clear. It means 
that a majority of those who cast a non-blank ballot supported the 
winner. That's right. If you deface your ballot, you can cause the 
election to fail. Voting "NOTA" is an effective vote under Robert's 
Rules. And Robert's Rules does not condone candidate elimination.

So, to make this Bucklin/Runoff method Robert's Rules compliant (but 
just a bit more efficient), I would not eliminate, technically, any 
candidates. Rather, the primary ballot becomes a nominating ballot, 
if there was no majority, and write-ins would still be allowed in the 
runoff. Voters remain free to vote however they please. So, yes, 
Virginia, the Mayor of Long Beach can be re-elected, even though term 
limit legislation in California prohibited her name from appearing n 
the ballot. She was the leader in the primary election, so the 
runner-up was the only name on the top-runoff ballot. There was 
another write-in candidacy then, but she was the plurality winner in 
the runoff. Write-ins can win, if they are popular enough.

2. Starting to collect Range data from real elections, so that voting 
systems can be better designed to maximize voter satisfaction, and 
also to minimize cost.

I've also come up with the idea that, on the runoff ballot, the 
results from the primary would be printed. Voters would then know how 
to vote with the best strategy (which in a method like this does not 
involve insincerity, just how to arrange the votes across the scale, 
which has no single fixed "sincere" pattern. Notice above, when I was 
making the only true strategic decision, it caused me, if I decided 
to add a vote for an otherwise-disapproved frontrunner to shift one 
vote a single click.

The other strategic decisions were in deciding the original approved 
set. I glossed over that, but my basic standard would be something 
like "would I be disappointed to find out that this candidate won?" 
If so, I would not start with an approval of the candidate. In a 
runoff system, I can put that kind of decision off, though at the 
cost of possibly having to vote in a runoff.

But I can always put any candidate into the approved set if I like 
the candidate! It won't lower the vote for my favorite or any other 
candidate. This is a Range ballot (if it's Bucklin-ER) and the votes 
are independent except for the effects of normalization, which can be 
truncated normalization, i.e., there is nothing that says I have to 
spread the candidates through the whole range. I can bullet vote if 
that's how I feel.