[EM] What is canonical Bucklin voting?

[culitif at tuta.io]

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 at gmail.com:

> 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 at tuta.io> > escribió:
>
>> Hi, I know what's labelled as "Bucklin" is messy and it's more a category of methods, but I thought I figured what would make sense as the most conventional choice of what a Bucklin system would refer to.
>>
>> But then I read about Fallback Voting and realized I just coded that. There's also another system I've seen referenced that uses a top-two system. I named this "historical Bucklin", but now I'm wondering if that is the most canonical Bucklin system. Am I missing something?
>>
>> Thanks,
>> Culi.
>> ----
>>  Election-Methods mailing list - see >> https://electorama.com/em>>  for list info
>>

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