[EM] Bucklin strategy (was: Fwd: [ESF #1126] Another bullet vote argument)

[Abd ul-Rahman Lomax]

At 02:12 PM 5/14/2010, Jameson Quinn wrote:

>Thus, for example, if Bucklin is used in a runoff system with good 
>runoff rules,...
>
>
>One of the biggest advantages of Bucklin is its simplicity. Don't 
>give that up so easily.

Remember how FairVote was able to convince top two runoff 
jurisdictions to use a seriously complicated system, IRV, to "save 
money on runoffs." Bucklin can do it honestly.

>This is not against two rounds. Two-round systems have real 
>advantages in terms of legitimacy. However, I find "primary-like" 
>two-round systems better than "runoff-like" ones. That is, you want 
>systems where a marginally motivated voter will show up only for the 
>second, decisive round, not where they'll show up only for the first round.

The problem with this is that it locks in the two-round system. But, 
in the end, *it's up to the jurisdiction.* I just want them to know 
the options they have, and they include some quite good ones that 
will be cheap to count, and easy to understand. Further, when I talk 
about "good runoff rules" I'm not necessarily insisting that the full 
rules be implemented at once. They can be "almost the best" rules 
quite quickly and easily.

>  So the first round should be used to help inform the voting and 
> ballot design in the second round, but there should still be an 
> ample array of choices in the second round (definitely 3-7, I'd say 
> 4-5). Earlier I gave an example of this kind of system: a 
> plurality-based primary which affects ballot placement and public 
> campaign finance, and which eliminates no-hope also-rans, then a 
> decisive round of Bucklin. Bucklin strategy would be easy given 
> that the information from the first round, and simple strategy 
> advice, would be actually on the ballot.

I wouldn't oppose such a system, but I think many would. Bucklin will 
find a majority, usually, in a primary. The basic decision to be made 
is whether or not the primary is before the general election or if, 
alternatively, there is a runoff is after the election. San Francisco 
had the latter, Cary, NC had the former.

Many people assume that lower turnout means that results are being 
manipulated by some oligarchy in a town. Not necessarily. What I've 
come across is reason to think that lower turnout, if it is not 
caused by differential access to voting, may actually improve results.

If there is a primary held with the general election, and if a 
majority is found, there is little reason to hold a runoff. The 
argument for a runoff being held with the general election would be 
the possibly low turnout in the primary. If such a system were run 
for a time with a Bucklin primary (I see no reason not to use Bucklin 
in the primary, and remember that in a primary bullet voting may be 
quite common), one could find out how well the primary predicts the 
general election results and whether or not, therefore, it is 
necessary to continue the extra election. If not, then the primary 
might be moved to the general election and rules designed to detect 
the rarer situation where a reversal might take place in a runoff.

We know that when runoffs involve a major discrepancy in overall 
approval of two candidates, there is high turnout. I believe that 
generally the reverse is true: if the turnout in a runoff is not 
high, it is likely to mean that the voters don't care that much which 
candidate is election. Only those who care vote. Which, from utility 
theory, suggests that results may be improved as a result.

What's really exciting to me is the realization that Bucklin 
incentivizes the voting of a kind of Range ballot that represents 
sincere utility. It may do this better than Range itself, and thus it 
may be that Bucklin implementation, particularly if they are 
three-rank at least, will allow the study of Range in a way not yet possible.

Proposals should be developed for Bucklin/Runoff implementations. 
Suppose there is a four-rank Bucklin ballot that is well-designed and 
explained. The fourth rank is a disapproved rank -- preferred to the 
no-vote default -- this rank is not, in a primary, considered a vote 
that can elect a candidate, the only function would be to collect 
better data and to discover a Condorcet winner, if one exists and is 
shown in the votes, and the division of candidates into five classes 
should be adequate to detect significant preferences for that purpose.

As a suggestion, if the primary does not find a winner, the most 
approved candidate (all rounds summed as approval votes) goes to a 
runoff. But also going into a runoff would be the range winner, based 
on fractional vote analysis of the same ballots, and a Condorcet 
winner, which would be any candidate who beats the most approved 
candidate and the range winner (if the candidate isn't one of these). 
If the approval, range, and condorcet winner are all the same 
candidate, but there is no majority, it could be argued that the 
election would simply complete, but I prefer that the electorate get 
a better look at the situation, so I'd add an approval runner-up 
considering the fourth rank as if it were an approved rank. This 
would usually produce, in fact, only two candidates for the runoff, 
but could produce as many as three.

I would allow write-ins in the runoff.

This would continue to satisfy the Majority Criterion, and Condorcet 
compliance, while not complete, would be due to explicit rejection by 
the electorate, which would know who the Condorcet winner was. But it 
would also get a Range winner into the runoff.

This sounds complicated, but, in fact, the voting would be simple. 
It's just Bucklin voting, seeking a majority, and it terminates if it 
finds one. I've argued that it *might* go to a runoff if there are 
two majorities (or more), but given the strategic incentives, it's 
unlikely that any multiple majority doesn't represent actual multiple 
approval, so I'm fine with the simplicity of the candidate with the 
most votes wins. It should be understood that with a mature 
implementation, that is not likely to be common with Bucklin.

The runoff complication is just a matter of doing some math with the 
results that would already be available, except for the Condorcet 
winner trick. That would require, not a full matrix, but only a 
partial one. (If there is a Condorcet winner who is not already 
selected, this candidate must beat both who have already been selected.

As results are obtained from real elections (with this fully system 
or a partial implementation), the canvassing process could be 
tweaked. If it starts out being more inclusive in the runoff, that 
can be backed off when much data is accumulated, if this data shows 
that it's not necessary.

There are conditions in a primary where the leader falls short of a 
majority that nevertheless predict well that the leader would get a 
solid majority in an immediate runoff. If these can be detected, the 
expense of a runoff can be avoided.

On the other hand, if a mandatory two-round system is to be used, as 
Mr. Quinn is suggesting, the primary should be before the general election.