[EM] Looking for the name of a Bucklin variant

[mrouse1 at mrouse.com]

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.

Thanks!

Michael Rouse