Conditional vote wording. CD fix.
Of course the conditional vote option needs for voters to indicate their
favorite. But that isn't so onerous when conditional votes bring CD
compliance (not just Weak CD).
Besides, it's more expressive. Anyone getting a favorite mark from a
majority should automatically win.
By the way, in any Bucklin version that allows equal ranking & doesn't
assume (as Bucklin B or A does) that a voter who equal top-ranks will top
rank all hir top-set & not vote for anyone else--For any such method:
If a ballot equal-ranks n candidates at a rank-position, then the
count-rule should skip n-1 rounds before giving the votes at that ballot's
next rank.
In pairwise-count or Bucklin, the favorite-mark shouldn't be counted
in the rank count, because doing so would prevent equal top-ranking.
A better statement of the definition of the conditional votes option:
Using Approval as an example:
Say the A voters give to B some combination of conditional & unconditional
votes.
...& vice-versa from the B voters to A.
Say that the fraction of A voters voting for B (called Fab)
is greater than the fraction of the B voters voting for A (called Fba).
Then disregard just enough of the A voters' conditional votes for B, so as
to make Fab = Fba.
If the number of A voters' votes for B that are conditional isn't
sufficient to achieve that, then disregard all of the A voters' conditional
votes for B.
...in order to achieve it as nearly as possible.
That applies straightforwardly to Bucklin.
This can be used with rankings:
When some 1st-rankings are conditional, compare 1st-rankings just as votes
are compared in Approval. ...& disregard conditional 1st-rankings
accordingly.
When some 2nd-rankings are conditional, compare the sum of 1st + 2nd
rankings (of B by A voters, & vice-versa), just as votes are compared in
Approval. ...& disregard 2nd-rankings accordingly.
With conditional votes. any method meets CD. ...in it's strong original
version, not just Weak CD.
CD fix:
Requirement:
While voting as described in the premise, the A voters should have a way of
voting by which B doesn't win.
(end of CD requirement)
...needed because complying methods need A voters to use a special option.
Michael Ossipoff