[EM] Looking for the name of a Bucklin variant

[Kristofer Munsterhjelm]

mrouse1 at mrouse.com wrote:
> I was wondering if someone on the Election Methods list could give me the
> name (or better yet, a link to more information) on a particular variation
> of the Bucklin method.
> 
> In Bucklin, you check first place votes to see if a candidate has a
> majority. If not, you add second place votes, then third place votes and
> so on, until at least one candidate has a majority.
> 
> In the variation I'm thinking of, you look at first place votes. If one
> candidate has a majority, then he or she is the winner; otherwise, you
> start adding second place votes *one at a time* (rather than all at once),
> until you have majority candidate. If no candidate has a majority, you
> start adding third place votes one at a time, and so on. In other words,
> you find the candidate who needs the fewest added votes at a particular
> rank to be a majority winner. If candidate A needs only 2 second-place
> votes to have a majority and candidate B needs 100, it wouldn't matter
> that candidate A has only 3 second place votes and B has 1000.
> 
> I know this has to have a name (or at least someone has looked at it and
> given a nice description of its properties), and I'm interested in seeing
> how it would apply to multi-winner elections without reinventing the
> wheel.

That sounds like QLTD. QLTD is like Bucklin, except "continuous". 
Quoting Woodall, who invented that method:

> One starts by crediting every candidate with
> all their first-preference votes. If no candidate
> exceeds the quota (of half the number of votes cast),
> then one gradually adds in the second-preference
> votes, then the third-preference votes, and so on,
> until some candidate reaches the quota. For example,
> it may be that if one credits every candidate with all
> their first-preference votes, all their
> second-preference votes and 0.53 times their number of
> third-preference votes, then exactly one candidate is
> brought up to the quota; that candidate is then
> declared elected.

In reality, one would probably add in preferences one by one until at 
least one candidate gets more than a majority, then do a binary search 
or equation solving to find the factor for the last preference that 
gives a majority to one of the candidates -- e.g. if after counting the 
first four preferences, two of the candidates has a majority, but none 
have after the first three, count the first three plus 0.5 times the 
number of third preferences, then either 0.25 or 0.75 and so on.

-

You could make this method multiwinner by adding the same "elect and 
punish" mechanic as STV. Set the quota to a Droop quota, then elect, 
remove the candidate, reweight those who voted for the candidate, and 
repeat. As far as I remember, it's not quite as good as STV, though.