[Election-Methods] Bucklin

Abd ul-Rahman Lomax abd at lomaxdesign.com
Mon Dec 10 20:54:05 PST 2007

At 04:30 AM 12/9/2007, Jan Kok wrote:
>On Dec 7, 2007 7:54 PM, Abd ul-Rahman Lomax <abd at lomaxdesign.com> wrote:
> > The case in Brown v. Smallwood was one where the result
> > overturned by the court was clearly just, and the reversal -- a long
> > time after the election -- was very poor public policy. Problem is
> > that the voters counted on the system, thus very likely did not first
> > rank with standard plurality strategy.
>Sorry, I haven't studied this case. Would you show the vote results,
>and also explain what you mean by "the voters counted on the system,
>thus very likely did not first rank with standard plurality strategy"?

see http://rangevoting.org/BrownSmallwood.html

I wrote this piece, then it was edited and additional comments 
inserted by Warren Smith.

The decision itself is available as 1.7 MB pdf from

The votes from the invalidated election, taken from the decision 
(which reports them)

Canddt          1stChoice       2nd Choice      AddlChoice      totals
Louisell        992             734             402             2128
Norton  3417            1501            167             5085
Smallwood       3496            2845            240             6581
Windom  4408            604             54              5066
totals  12313           5684            863             18860

Windom is the plurality winner. But this was a Bucklin election. 
Voters would know that they could vote for their true first choice. 
Smallwood got a huge block of second-choice votes. In a plurality 
election, many voters, I'd assume, could know that votes not for a 
frontrunner would be wasted, and they might have voted for Smallwood. 
But they thought they were safe. They did not count on the Court 
throwing out the result.

The number of ballots with valid votes was 12313. A majority is thus 
6157 votes. Smallwood was the only candidate with a majority, and he 
reached it in the second round. The "Additional choice" round was moot.

(To repeat how this worked: first and second choices only allowed one 
candidate to be named. Addl choice did allow as many as the voter 
desired. The same candidate could not be named as more than one 
"choice," so the method only allows one vote per candidate. If there 
was no majority in the first choice votes, then the second choice 
votes were added. If no majority then, the third choice votes. I'm 
not sure if the election required a majority; if not, the third round 
was final even if a majority was not obtained; otherwise, there would 
have to be further process.)

The Court's remedy of awarding the judgeship to Windom was an insane 
result. Normally, if there has been some error in election process, a 
court will order a new election; the basis for awarding the election 
to Windom seems thin to me. The FairVote people argue that the 
problem with Bucklin was that second choice votes could interfere 
with one's first choice. Suppose the ballots had been IRV ballots 
instead of Bucklin. Same ballot. Probably the same result! STV was 
known to Minnesota and was in use there, apparently.

I have argued that Brown v. Smallwood would have considered IRV also 
unconstitutional, but that STV was in use in Minnesota could be a 
counterexample. But what if a challenge to STV never got to the court?

Single-winner STV, i.e., IRV, was apparently used for a couple of 
years in Minnesota, for primaries, but repealed. Not clear if it was 
ever challenged. However, the Court in Brown v. Smallwood notes that 
primaries might use election methods that would be unconstitutional 
for regular elections.

In my reading, the language of Brown v. Smallwood appears to prohibit 
any sort of alternative votes. The Bucklin method was called 
"preferential voting."

The Court quoted with apparent approval a prior opinion that "Our 
system of government is based upon the doctrine that the majority 
rules. This does not mean a majority of marks, but a majority of 
persons ... and the number of such persons is ascertained by means of 
an election."

And, remarkable, the Court then proceeds to consider the total number 
of marks! "In the case at bar, it may be noted that the number of 
persons who voted were 12,313, and the number of cross marks 
considered on the plurality election were 18,860."

The FairVote analysts seem to have been diverted by the first 
argument found in the decision, prior to that above. In that, we can read:

"When the Constitution was framed and as used in it, the word "vote" 
meant a choice for a candidate by one constitutionally qualified to 
exercise a choice. Since then it has meant nothing else. It was never 
meant that the ballot of one elector, cast for one candidate, could 
be of greater or lesser effect than the ballot of another elector 
cast for another candidate. It was to be the same effect. It was 
never thought that with four candidates, one elector could vote for 
the candidate of his choice, and another elector could vote for three 
candidates against him. The preferential system directly diminishes 
the right of an elector to give an effective vote for the candidate 
of his choice. If he votes for him once, his power to help him is 
exhausted. If he votes for other candidates, he may harm his choice, 
but cannot help him. Another elector may vote for three candidates 
opposed to him. The mathematical possibilities of the application of 
the system are infinite."

This is, I'm sure, the source for the FairVote argument that the 
decision applies to Bucklin but not to IRV. Maybe. But later on:

"[There is] the idea, which permeates all legal thought, that when a 
voter votes for the candidate of his choice, his vote must be counted 
one, and it cannot be defeated or its effect lessened, except by the 
vote of another elector voting for one. A qualified voter has the 
constitutional right to record one vote for the candidate of his 
choice, and have it counted one. This right is not infringed by 
giving the same right to another qualified voter opposed to him. It 
is infringed if such other voter is permitted to vote for three 
opposing candidates."

"We know of but two cases involving the preferential system. One is 
State v. Portland, 65 Ore. 273, 133 Pac 62. The Constitution of 
Oregon distinctly authorizes such system and it is valid. The other 
is Orpen v. Watson (N.J.) 83 Atl 853. The court there reached a 
conclusion directly opposed to our views. We have given it full 
consideration. It does not accord with our views, and we do not follow it."

Note that they do not appear to cite and respond to the contrary 
precedent. Unless that case, which I have not seen, did not bring up 
any arguments not considered in Brown v. Smallwood, this would seem 
to be a serious defect. Of course, they were not bound by it, it was 
a different state. But surely the arguments would have been 
important. They merely dismiss it.

The dissenting opinion in this case was generally how most of us 
would now think about it. For example:

"For the purposes of this case it may be conceded that no voter can 
give more  than one vote for any candidate. The legislation before us 
does not do this."

A request for reconsideration was filed with they Court, and, in 
their answer, they wrote what most clearly indicates that they would 
have likewise ruled IRV unconstitutional:

"We reached the conclusion that a system of voting, giving the voter 
the right to vote for the candidate of his first choice, and against 
the first choice of another voter, and, in addition, by a 
manipulation of second and additional choice votes, vote for 
different candidates all against the first choice of such other vote 
to a number of times limited only by the number of candidates, was 
contrary to the intent of the Constitution, and that it was none the 
less so because such other voter was permitted to engage in a like 
manipulation of second and additional choice votes. Our further 
examination confirms us in our view. The decision is sound; and we do 
right in upholding the right of the citizen to cast a vote for the 
candidate of his choice unimpaired by second or additional choice 
votes cast by other voters."

The situation they are rejecting is precisely what happens in IRV. In 
particular, suppose a voter casts only a vote for one candidate in an 
IRV election, perhaps this is the only one the voter could support. 
Arrayed against this voter (in their mind) are alternative votes cast 
against this candidate. They have no problem with other first choice 
votes, only the other ones.... They are rejecting, it appears, all 
forms of preferential voting, not merely Bucklin. They were also 
aware that they were not following the precedents of other courts. 
They were unconcerned that the election they reversed clearly showed 
a majority preference for Smallwood over Windom.

Approval Voting *looks* like it allows more than one vote per voter, 
but, in the end, the only vote that counts is a vote cast for a 
winner (and, one might add, for a runner-up). If a voter has cast two 
votes, one for a winner and one for the runner-up, that voter has 
effectively abstained, the voter has *not* gained additional power. 
The "simultaneous" votes of Approval are, no less than with IRV, 
alternative votes, since all but one (at the most are moot: they 
could be eliminated, erased, and the election result would not change.

I conclude that they had a motive: to prevent the continued use of 
Bucklin and its spread to partisan elections. Bucklin was working. It 
was a danger to the status quo.

>Do you have any information about where this "one-voter, one-vote
>principle" came from and what it really means?

There is mention of it in the decision. Not with those words. This 
was, by the way, 1915.

>The phrase "poetic justice" comes to mind, as applied to FairVote.
>Unfortunately, we, the people, would all lose if BvS is used to block
>all departures from Plurality voting.

I think it's unlikely, though not impossible. It may depend on 
political considerations.

>Rob Richie himself said that Bucklin is a form of Approval voting, in
>his presentation to the Colorado Voter Choice Task Force.

They claim that Bucklin was Approval when they want to make a point 
that it may be unconstitutional, and that Approval hasn't been used 
when they want to make a point that it is some new wild-eyed 
proposal, untested. Political argument. Don't you love it?

>Of course, he also said that Bucklin had "failed" because most voters
>would not specify a second choice. ("Only" about 12 or 13%, in one

Right. Spin. It's an argument that sounds good, typical of Richie. 
That, of course, is not failure, it's success -- that is quite enough 
to fix the spoiler effect. In the Smallwood election, many more than 
that used additional choices.

It's the same as with the IEEE, which dropped Approval voting making 
the same claim. But Approval Voting doesn't cost anything, and in 
most IEEE elections, perhaps, it was not necessary to have additional 
votes. Two candidates, why bother? The IEEE example appears to be 
corrupt: the board implemented Approval to head off vote-splitting 
when a dissident candidate threatened to do that, and then they 
dropped it when the danger was past, for to leave it might allow 
other dissident candidates to arise. Can't have that, can we?

Approval voting isn't going to make much difference to most 
elections, at least not at first. But when an election is close, and 
there are third party candidates gaining some significant percentage 
of the vote (a few percent is quite enough to spoil an election), 
Approval can prevent it, *at no cost.* I'm not claiming that Approval 
is ideal. It isn't. It is simple and essentially free. And pretty 
good. Bucklin is also pretty good, and likewise cheap. (Like Range, 
it can be implemented simply with a few more ballot positions, it is 
summable). Cheap reform could mean more reform opportunities later.

> > On the other hand, when it suits some of them, it is claimed that
> > early U.S. presidential elections were a form of Approval. If so,
> > it's nothing like any form of Approval I've seen. The essence of
>As someone who frequently votes for third party candidates, I do
>object (somewhat) to the single-first-choice version of Bucklin,
>because it fails the Favorite Betrayal Criterion. Suppose the
>candidates and 1st and 2nd round expected vote results are:
>  2%, 10% My Favorite
>49%, 55% Good
>49%, 56% Awful
>It's really a race between Good and Awful. My Favorite has no
>realistic chance of winning. I would rather have Good than Awful. So I
>am pressured to "betray" My Favorite and vote Good as my first choice,
>hoping to push Good over 50% in the first round.

I consider the hazard shown here to rely upon a fairly complex 
expectation of voting patterns. I certainly wouldn't hesitate to vote 
for my Favorite in Bucklin. Probably even if there were some 
possibility of the scenario described. And, in fact, that scenario is 

>One might argue that there is no good reason for the Good and Awful
>voters to vote for the other frontrunner as their second choice. But
>even if that was true, real voters are not perfectly rational!

Indeed. Here is where it might happen: the voters *hate* "My 
Favorite." and really want to make that point. Far more likely, so 
likely that I doubt that an election such as described would *ever* 
happen, would be that we would see truncation. From the first 
preference votes, neither Good nor Awful are going to gain a 
majority, and those voters, being supporters of the frontrunners, are 
almost entirely going to leave the second and third rank votes empty. 
Just as FairVote claims they will. It's a *feature*, not a *bug*.

Then, second round, we *only* have the supporters of "My Favorite" 
adding votes. They easily decide the election, if they vote for only 
one of the frontrunners. And thus "My Favorite," if the leader of his 
or her party, may have some influence in future elections.

This kind of scenario easily appears in the theoretical election 
scenarios we are so fond of here on Election Methods. It is truly 
preposterous, as applied to real elections, certainly to partisan 
political elections; and with other elections people are far less 
likely to be so concerned that they would even bother with these 
tight and highly speculative strategic considerations.

I prefer that all ranks allow multiple votes, it then allows voters, 
should they have some kind of imagination like Jan suggests, to vote 
for two in first rank. It's harmless, at worst. It means less spoiled 
ballots, probably.

(And I would not discard a ballot if a voter votes for a candidate in 
more than one rank, I'd simply count it in the highest rank, that is 
minimal harm, less harm than dropping it or counting it at the lowest 
rank. It makes it into an Approval Vote instead of a ranked one, 
relatively speaking, which is, again, not a bad outcome.)

>  Many
>voters will just see the horserace aspect of the election and do
>whatever they can to help their preferred frontrunner. "Whatever they
>can" = vote for their preferred frontrunner as their first choice.

Right. Simple enough.

> > Bucklin, because it satisfies the Majority Criterion, may be more
> > palatable than pure Approval.
>I think there are several versions of "the" Majority Criterion. Which
>one are you using?

The one that reads minds.

It would be useful if more readers of this list would look at the 
Election Methods Interest Group, and, in particular, the Wikipedia 
Committee, where there has been consideration of the Majority 
Criterion and how it is defined. It's clear that the standard 
definitions are defective, there is persistent realization that, wait 
a minute, what does it mean to "prefer" a candiate that you don't 
vote exclusively for? There seems to be some kind of rough agreement 
that there are two Majority Criterions, one based on actual votes 
cast. Approval passes that one, but not Range.

(The Majority Criterion, however it is sliced, is defective, that is, 
it's clear that there are election scenarios where the optimum result 
requires violating the Criterion, including ones where every voter 
would agree, and, in particular, where the majority would, in fact, 
ratify the result that allegedly violates the Majority Criterion. But 
this is another story; the concern on the Committee is simply the 
definition of the Criterion.)

Then there is the Criterion where a "preference list" is posited that 
is distinct from how the voter actually votes. It's in the voter's 
mind. If the voters set an Approval cutoff and votes for the top two, 
it's quite possible that the first preference of a majority will lose.

Problem is that no definition is given for how the voter translates 
their "preference list" to actual votes. If a voter can have a 
preference list and then vote any old way, no criterion considering 
the preference list could be satisfied. I did come up with a way to 
state it; what is remarkable to me is that, apparently, nobody else 
has ever stated it that way. James Armytage-Green tried and failed 
(and he's aware that his definition is problematic.)

The problem with my definition is that it defines sincere vote in a 
way that takes the charge out of it, it becomes more difficult to use 
the Majority Criterion, so defined, as some kind of indictment of 
Approval Voting.... So the IRV supporters haven't rushed to accept it!

(And this, of course, in real elections, requires that lots of voters 
vote for both frontrunners! Quite simply, not. It's a theoretical 
failure, not a practical one.)

>Well, I consider almost any form of Bucklin more palatable than IRV,
>and of course it is better than Plurality.

Yes. The argument for Bucklin would be that it preserves the 
tradition of voting clearly for a first preference. (Bucklin would be 
almost as good if there were only two ranks, but, hey, why not three?)

Election Methods Interest Group:

By the way, EMIG is an FA/DP organization (Free Association with 
Delegable Proxy). Just might be the first one to actually get something done.

One of the concepts is to ask the membership, which includes some 
noted election experts, to function as a peer-review board to more 
rapidly and cheaply "publish" peer-reviewed papers in the field of 
election methods. If it's done right, such publications would be more 
thoroughly reviewed than what is the case with standard journals. 
Delegable Proxy should make it efficient, if it starts to do some 
real work and gets significant traffic.

Anyone can create an EMIG committee to study some problem related to 
election methods, and any committee could develop a report for 
approval by the full membership. Such "approval" actually doesn't 
create any official status for the report, but merely measures the 
degree of consensus it enjoys. However, an *independent* web site 
could set some criterion of acceptance (such as a two/thirds vote of 
all EMIG members, or a two-thirds vote of those it recognizes as 
experts, or whatever was reasonable), and then publish the report or 
paper on that site as "peer-reviewed." Reports would probably be 
consensus documents coming out of a committee, and would include 
minority reports, etc.

Because of the importance, I made sure that certain IRV supporters, 
affliliated with FairVote, were invited to join EMIG, and they did.

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