[EM] Who First Proposed Winning Votes?

[Markus Schulze]

Dear David,

you wrote (25 Feb 2005):
> I know Mike Ossipoff advocates WV as opposed to WM for
> the completion of methods such as Ranked Pairs, Schulze,
> etc. Was he actually the first person to come up with
> the idea as the sentence above seems to imply?

As far as I remember correctly, two different approaches
have been discussed at this mailing list.

First approach: Mike Ossipoff suggested that when a given
voter strictly prefers candidate A to candidate B then this
voter "approves" candidate A and "rejects" candidate B. In
the archives of this mailing list, Mike calls a candidate B
"majority rejected" or "majority beaten" when there is a
candidate A such that a majority of the voters strictly
prefers candidate A to candidate B. Mike always said that
"majority rejected" candidates shouldn't be elected.

In my opinion, this approach is very problematic because
it isn't clear how it can be generalized to other election
methods than MinMax.

As far as I know, Mike still uses this approach. See e.g.:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/013047.html

Second approach: The second approach says that when some
voters cast only a partial ranking (because of strategic
considerations or other reasons) then the effect of this
behaviour should be as small as possible.

For example, in 1997 I proposed the following criterion
("majority beatpath criterion"):

   "X >> Y" means that a majority of the voters strictly
   prefers candidate X to candidate Y.

   A "majority beatpath" from candidate X to candidate Y
   is an ordered set of candidates Z(1),...,Z(n) with the
   following properties:

      1. Z(1) is identical to X.
      2. Z(n) is identical to Y.
      3. Z(i) >> Z(i+1) for all i = 1,...,(n-1).

   If there is a majority beatpath from candidate A to
   candidate B and no majority beatpath from candidate B
   to candidate A, then candidate B must be elected with
   zero probability.

The intention of this criterion is that when some voters
cast only a partial ranking then when these partial
individual rankings can be completed in such a manner that
candidate A is a Schwartz candidate and candidate B is not
a Schwartz candidate and these partial individual rankings
cannot be completed in such a manner that candidate B
is a Schwartz candidate and candidate A is not a Schwartz
candidate then candidate B must be elected with zero
probability. This guarantees that not unnecessarily a
candidate is elected who would not have been a Schwartz
candidate when not some voters had cast only a partial
ranking because of strategic considerations or other
reasons.

As far as I remember correctly, it was me (and not Mike
Ossipoff) who suggested that "winning votes" should be
used for the Schulze method (aka Schwartz sequential
dropping, cloneproof Schwartz sequential dropping,
beatpath winner, beatpath method). I used the majority
beatpath criterion as an argument.

Markus Schulze