Currently, the most popular Bucklin variants are versions of Majority
Judgment, and rightly so in my opinion.

For awhile on this list we've neglected MJ  because we have been
concentrating on RCV methods, i.e. Universal Domain methods to show that
IRV/STV is not the only or necessarly best RCV method.

This week we have expanded beyond UD/RCV to include  Score style ballots
...perhaps time to once again discuss methods, like MJ, that take
Grade/Judgment ballot information seriously ... as commonly understood
community wide standard categories, not just relative preferences, but not
treated as additive Cardinal Ratings or numerical utilities either ... a
common sense middle ground between ordinal and cardinal judgments of
candidates/alternatives.

We have seen both ranked choice and score based versions of Bucklin in the
past, but qualitative judgment categories seem to be the most natural
domain.

El vie., 28 de ene. de 2022 7:07 p. m., culitif@tuta.io escribió:

FWIW what I think of as traditional Bucklin was using a three-rank ballot, with equal ranking allowed only at the third level.  IIRC that’s how the wiki entry described it at one point, but clearly it doesn’t any more, and I’m not well versed enough in the history to know if that’s the actual original method (meaning, used in Grand Junction).

—pH

On 29.01.2022 04:06, culitif@tuta.io wrote:

This article provides a reasonably good description of various voting
methods, as they're defined on EM:
http://www.9mail.de/m-schulze/votedesc.pdf

The section on Bucklin agrees with how I've understood it: it's a ranked
method where you stepwise add in first, second, ..., kth rank until
someone attains a majority.

Due to Bucklin's LNHelp feature combined with a lack of LNHarm leads to
a natural idea of letting voters instruct Bucklin to "skip ranks" on
their ballots. This in turn leads to majority grade methods like MJ.

(The article is wrong about supplementary voting being a form of
Bucklin, though. It is a two-step IRV.)

-km

It strikes me that the current documentation on Bucklin on both Wikipedia and Electowiki is really unintuitive. Electowiki points out Fallback Voting as a method that's "strongly related to Bucklin" that was proposed in 2006, but from what I can tell it is exactly what is described in Smith's paper that you linked. And it's also what I'd gather as the general impression most people get when reading the Wikipedia article for it. All of them fail to go into detail however.

Forest also mentioned MJ Bucklin as probably the most popular form of Bucklin right now. But the little detail offered by either Electowiki or Wikipedia (or most general resources) go into zero detail about what that would look like. Despite the fact that they all make mention of the popularity of graded Bucklin methods. 
I'd like to go ahead and make an implementation of MJ Bucklin, but I'm having a hard time finding a description of the algorithm. Could anybody kindly provide a link or resource to what that would look like?

Thank you so much,
Culi.

PS votevote https://elegant-shaw-2cb49a.netlify.app/votevote is now able to simulate a single election in ~18 different methods!

Jan 29, 2022, 5:35 AM by km_elmet@t-online.de:

I agree with this take. My site is able to simulate an election in a wide array of different methods by using a scored ballot as its basis and converting that to other forms where necessary. I feel pretty good about my current solution to these conversions, but if anyone would like to provide some critiques or feedback to how I do this, I'd love to hear it.

For universal domain rankings it's mostly a straightforward matter of ranking each candidate by their given score. The only complex part is when two candidates are tied. This happens very rarely in my program, but the way I'd handle it is by figuring out all k possible permutations of that ballot without ties and giving each of those ballots a weight of 1/k. 

E.g. if a voter has this ballot:

1: a > b, c > d

We can convert it to this:

0.5: a > b > c > d
0.5: a > c > b > d

For approval or combined approval ballots, I take the number of partitions of [0, 1] (note that the default score ballot assigns a value in [0, 1] to each candidate) necessary. For example, in approval, we have two groups: approved, and not approved. So we can split up [0, 1] into [0, 1/2), and [1/2, 1]. All the candidates with a score between 1/2 and 1 are approved. For combined approval, we have 3 groups: disapproved, neutral, and approved. So we can map candidates with scores of [0, 1/3), [1/3, 2/3), and [2/3, 1] to their respective partitions. 
For systems that require a discrete score in a range, like STAR voting, I simply linearly map [0, 1] to [a, b] and then round the values to their nearest integer. In STAR a=0 and b=5. Hmm, now that I'm writing this out it might be better to map them to [a, b + 1) and floor those values...

There's some others, like quadratic voting, that required some more creativity, but so far I've had great success with converting a voters expression of a scored ballot into expressions of other types of ballots. What do people think? Any major flaws you noticed? I'd appreciate any feedback/reviews or more questions about how other situations are handled.

Best,
Culi.

Jan 29, 2022, 12:07 AM by forest.simmons21@gmail.com:

On 29.01.2022 19:51, culitif@tuta.io wrote:

MJ is like this, if I recall correctly:

Assign each grade to a number (it doesn't really matter what number, as
long as higher grades have higher values). Voters submit graded ballots,
i.e. for each candidate the voter provides either no opinion or a grade.

The candidate with the highest median grade wins.

If there's a tie, remove from each candidate one instance of the median
grade. Continue doing so until there's no longer a tie.

-km

Kristofer's MJ just needs one more detail ... the median of an even number
of grades  is the lower of the two middle grades.

For the symmetrical version, it is the one closer to the center of symmetry.

El sáb., 29 de ene. de 2022 2:56 p. m., Kristofer Munsterhjelm <
km_elmet@t-online.de> escribió:

Thanks for the response! This is basically what I've implemented for the algorithm I called majorityJudgement, but is this the same thing as "bucklin majority judgement"? Is majority judgement already considered a Bucklin system? Or is there some variation of MJ that uses Bucklin style rounds? 

Best,
Culi.

Jan 29, 2022, 2:56 PM by km_elmet@t-online.de:

Ah a really useful detail as I was actually stuck on this. I ended up making it so when the median is an even number of grades, it'll actually drop two marks from each candidate instead of one which felt... wrong. Thanks so much for the correction 

Best,
Culi.

Jan 29, 2022, 9:59 PM by forest.simmons21@gmail.com: