[EM] WDSC

[Markus Schulze]

Dear Mike,

you wrote (18 Apr 2001):
> Markus wrote (18 Apr 2001):
> > Your definition of WDSC looked as follows:
> > > If a majority of all the voters prefer A to B, then they should
> > > have a way of voting that will ensure that B cannot win, without
> > > any member of that majority voting a less-liked candidate over a
> > > more-liked candidate.
> >
> > Does that mean?:
> >
> >    If a majority of the voters strictly prefers A to B then
> >    --independently on how the other voters vote-- there is always a
> >    way of voting such that B doesn't win, without any member of that
> >    majority voting a less-liked candidate over a more-liked candidate.
> >
> > Or does that mean?:
> >
> >    If a majority of the voters strictly prefers A to B then
> >    there is always a way of voting such that --independently on how
> >    the other voters vote-- B doesn't win, without any member of that
> >    majority voting a less-liked candidate over a more-liked candidate.
>
> Neither. You didn't specify for whom there's a way of voting that
> will achieve that. So that's my answer. I meant neither of those.
> You can put "independently on how the other voters vote" where you
> want to. Did my wording say anything about dependence on how others
> vote? It didn't? Then I'd say that you may put "independently on how
> the other voters vote" anywhere you want to. Or you can leave that
> unnecessary phrase out, as I did. Since I didn't say anything about
> how the others vote, and since I said that given a certain premise
> a certain requirement must be met, then any conditions that isn't
> in the criterion's premise is not part of the criterion's premise.

(1) If I understand your comment correctly, then "it ensures that B
cannot win" simply means: "B doesn't win." Then your WDSC looks as
follows:

   If a majority of the voters strictly prefers A to B then there is
   always a situation where B doesn't win and where no member of that
   majority votes a less-liked candidate over a more-liked candidate.

(2) You wrote that you "didn't say anything about how the others vote."
Does that mean that it is sufficient when there is at least one (not
necessarily sincere) voting behaviour of the voters of the minority so
that B doesn't win and no member of the majority votes a less-liked
candidate over a more-liked candidate?

Markus Schulze