[EM] The rise and fall of Bucklin voting in the United States

[Abd ul-Rahman Lomax]

I've long been interested in the history of Bucklin voting, also 
called the Grand Junction method, or sometimes simply "preferential 
voting," in the United States, there is a peculiarity in what is 
available on Googlebooks on the topic. We see, beginning in 1909 or 
1910, much comment on this method, and praise for how it worked, 
though it must be said that Bucklin himself seems to have been a 
tireless promoter for a time.

http://en.wikipedia.org/wiki/User:Abd/Preferential_voting_notes

Sometime roughly around 1920, Bucklin drops off the radar. Before 
1920, many publications documented how it had been implemented by up 
to around ninety cities and towns, and there were enthusiastic 
reports of the election results, how Bucklin actually functioned to 
find a better winner than the first preference choice, how "the 
people" were able, using the method, to "negotiate a majority."

Then references to the Grand Junction method almost totally cease. In 
every jurisdiction, Bucklin was replaced by something else. A decent 
historical study would look at each place, what incidents or 
arguments preceded the method being dropped, and the process by which 
it was dropped. I know of only two situations: Duluth, where Bucklin 
was ruled unconstitutional by the Minnesota Supreme Court, in an 
idiosyncratic ruling, and Cleveland, Ohio, where the story is more 
complex. The Cleveland story, though starts to bring up what is now 
an operating hypothesis for me.

Bucklin was replaced because it worked. It allowed candidates from 
powerful political parties to lose, when someone else had broader 
support. The story with PR/STV in the U.S. was similar; in Cleveland, 
ironically, the Bucklin method was superseded by PR?STV (I don't know 
the details about the single-winner mayoral elections, though), and 
then PR/STV was in turn axed after a decade, in 1931. What was 
happening? The Democratic Party was becoming a majority party, and it 
had no more need for voting systems which allowed minorities to find 
fair representation. PR/STV in Cleveland, as well as it did in New 
York, allowed "Negroes" and Socialists to win representation.

Okay, we can understand the political forces that repressed 
proportional representation. Did this same set of forces do the same 
with Bucklin?

The clue that I've found is something that I'd overlooked before.

Bucklin had succeeded in putting through a thorough reform of the 
city government in Grand Junction, and this model covered many 
different issues, not just voting method. Whether as part of this 
reform or a previous one, political affiliation information was not 
allowed on the ballot for city government offices. This reform, in 
many places, stuck, it's still true in lots of towns across the U.S., 
including San Francisco. The reform included a version of the Bucklin 
method, which was first used in 1909. I had seen the results from 
this election many times, but hadn't realized the significance of 
what was really one of the most notable things about it: the winner 
was "affiliated with" the Socialist Party.

I first picked up on this in reviewing arguments about the Bucklin 
implementation in San Francisco. Before the charter amendment passed, 
there was a report prepared by the Commonwealth Club, which included 
debate over Bucklin. And, there, it was claimed that a Socialist had 
won because, allegedly, it is a "matter of religion" for a Socialist 
to never vote for anyone but a member of their party, whereas 
supporters of, say, the Republican, Bannister, in Grand Junction, 
would, my reading of the argument, generously and in good civic 
spirit add votes for the Socialist.

Of course the votes actually cast in that election show that the 
support for the Republican, who was the plurality leader in the first 
round of counting, was very narrow, the Republican got hardly any 
additional vote support, whereas the Socialist, Todd, had come up 
from third place to win. I have never seen a result like this from 
IRV, by the way, and it is rare, in a nonpartisan election, for a 
candidate to rise up from even second place to win.

But, in the end, the election was not particularly close. With 1799 
total ballots containing an enumerated vote, Todd had 1051 votes. The 
runner-up was Slocomb, with 912 votes. I have previously written that 
there were thus two candidates with majorities, but that was an 
error, and only applies to a majority of votes for the candidates on 
the ballot, I had neglected this:

I have just now noticed on the record provided by Bucklin for this 
election that there is a note: Total Votes Cast: 1847. Majority to Elect: 924.

They were following the standard rule of parliamentary procedure that 
any non-blank ballot counts in the basis for a majority, it appears. 
I saw what appeared to be a contradiction, in the election of the 
Commissioner of Finance and Supplies. But the rules apparently 
provided for additional ranking, one additional rank if there were 
three candidates, two additional ranks if there were four or more; 
and no additional ranking if there were only two candidates. It is 
not mentioned in the ballot instructions, but, for each office, there 
is a space for a write-in vote. Considering this, the instructions 
seem a bit confused. There is an instruction to "omit voting for one 
name for each office," if there is more than one name on the ballot. 
That would be a device for a voter to approve all candidates, there 
is no harm in it, it is also a device to in effect void the ballot 
for that office, if the voter doesn't want to return the ballot to 
get a new one. (This works with present ballots, and may explain some 
percentage of overvotes.)

In any case, all the offices were thus won with a majority of votes 
on the ballots; Grand Junction, in my viewed, erred in providing no 
ranking in the single-candidate case, because there are actually two, 
and it is possible that there could be two significant write-in 
candidacies, and thus majority failure, and, in this situation, a 
voter voting first preference for a write-in and then second for the 
candidate on the ballot makes sense.

Definitely in the two-candidate case, ranking should have been 
allowed because of the write-in possibility.

This was, however, a plurality system, the winner is the candidate 
with the most votes, in the end. It is thus equivalent to "instant 
runoff" Approval voting. It is a shame that we don't have raw ballot 
data. We should fix that, by promoting and encouraging the use of 
Bucklin, particularly in jurisdictions where runoff voting is used. 
 From the Grand Junction election, we can see how the method 
functioned better than IRV, almost certainly. It would have avoided 
runoff elections in every case except the 2-candidate election, which 
almost certainly would have found a majority (and sensible runoff 
rules might be satisfied with less than a majority if the result is 
such that a majority is practically certain in the runoff, but I'd 
not want to set such rules until there is a history of elections and 
runoffs showing this, statistically. In a context where a majority is 
required, purely and simply, it is an improvement, at practically no 
cost, to implement Bucklin, reducing runoffs that are, then, clearly 
not necessary. And still allowing for them in situations where a 
majority hasn't been found.)

I've settled on this as the number one reform to promote, because, in 
fact, it is Approval Voting with a process twist that addresses the 
most common objection to Approval: an inability to express a 
preference for their favorite, should voters wish to vote for more 
than one candidate. Bucklin can start with pure 
vote-for-your-favorite in first preference, and voters can decide to 
leave the other ranks blank. The charges of unfairness -- raised in 
Brown v. Smallwood in Minnesota, and defective even there -- don't 
apply at all if this is a primary election. By leaving all other 
preferences blank, the voter is indicating a preference for a runoff 
election if the preferred candidate doesn't win. And nobody will win 
(in the primary) unless a majority of voters vote for the candidate.

The ballot that feeds the Bucklin counting method is really a range 
ballot, using only the approved ratings, in sequence. The election 
results for Grand Junction showed how some voters voted for a 
candidate in first preference, for no candidate (or possibly a 
write-in, not tabulated) in second preference, and then for someone 
else in third rank. This is quite equivalent to a range ballot, 
specifically Range 4, with no ballot position assigned to a rating of "1."

So, then, some further improvements can be seen: Add in the missing 
rating, and/or use a pure Range ballot with enough ratings above the 
approval cutoff -- which might be assumed to be midrange -- to allow 
approval of all candidates but one, including write-ins. Because of 
the write-in provision, this means that with N candidates on the 
ballot, and mid-range approval, it should be, at least, Range (N+1).

And, of course, voters should be allowed to equal-rank in all ranks. 
Most won't do it, but this will reduce ballot spoilage and is not 
only harmless, it improves collection of more accurate range data.

With proper ballot and counting design, it looks to me like the 
optimal ballot is sincere, never rewarding preference reversal. The 
judgment of whether or not to equal rank is a complex one, and with 
three-rank Bucklin, equal ranking can involve the suppression of a 
preference, especially at the lowest-approved rank. There are complex 
strategic considerations if one wants to absolute optimize the power 
of a ballot, and these depend on the accuracy of the knowledge of the 
voter, but the gain in voter benefit from such optimization is 
probably well below the cost of figuring it out accurately. Voters 
can simply vote with an easy judgment, and, in a primary, the 
standard for voting for a candidate at all, i.e., at any rank, is an 
answer to the question: would you prefer the election of this 
candidate to the holding of a runoff election? If so, vote for the 
candidate, at least in bottom approved rank, if not, then don't.

Bucklin satisfies the majority criterion. It does not satisfy the 
Condorcet criterion, unless we require the preferences used be the 
criterion to be expressed. It's like Approval in this, except that 
pure Approval also fails the majority criterion. In a runoff context, 
though, if there is majority failure, voting systems criteria must be 
applied not to the primary, which is a "nomination method," but to 
the runoff, and it would be enough for a fair satisfaction of the 
Condorcet criterion if a Condorcet winner apparent from the ballot 
data in the primary is included in the runoff, is thus in the set of 
candidates who "win" the primary election by making it into the 
runoff. With an adequate range ballot feeding the Bucklin sequential 
counting process, a condorcet winner can be found, and suppression of 
preference, where it exists, is purely voluntary and not 
strategically necessary.

I think we should start drafting modern Bucklin voting statutes, and 
developing and publishing position papers on this. I'd suggest this 
to the Approval Voting mailing list, but I believe I'm still banned 
there, a situation which is ironically hilarious. The moderator shot 
himself and the list and the Approval Voting advocacy organization in 
the foot, based purely on his personal preferences. I could subscribe 
under a new address, but *I don't do that.* (Actually, I did 
subscribe, to avoid loss of list access for the purposes of reading 
it, should I be fully removed, but I won't pretend to be someone else.)

Bucklin is Approval voting. Which means that prior claims by many 
that Approval Voting was never used in the U.S. were based on a 
narrow view of what Approval Voting is. Bucklin was, and is, an 
improved Approval Voting, which implements in a single ballot a 
series of pure Approval elections with declining approval cutoff. 
Bucklin-ER can be voted as pure Approval, if that's what voters want.