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.


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 The story with PR/STV in the U.S. was similar; in Cleveland, ironically, the Bucklin method was superseded by PR?STV (I don't know the details about the single-winner mayoral elections, though), and then PR/STV was in turn axed after a decade, in 1931.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.

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