[EM] Condorcet Criterion for plurality.

[MIKE OSSIPOFF]

Markus said:

>you wrote (13 Dec 2000):
> > It doesn't make sense to define systems with reference
> > to themselves, which is what Mike is attempting to do,
> > because this makes it impossible for any meaningful kind
> > of comparison between systems.
>
>I absolutely agree with you.
>
>Markus Schulze

When did I define a method in terms of itself? Here's how I define
Plurality: Voters are allowed to mark one candidate. The candidate
marked by the most voters wins.

In what sense have I defined that in terms of itself?

Because I didn't change it so as to make it different from every
actual Plurality implementation? When you make such a change,
you really should call it something other than Plurality.
Define Plurality any way you want to, but understand that now
your "Plurality" isn't the same as the Plurality in actual use.

As I told Markus, I didn't say that it's impossible to define
Plurality in terms of a false assumption that it collects rankings.

If we have to define all the methods in terms of rankings,
then, as I've been telling Markus, those definitions aren't
complete, because Markus hasn't told us how we're to interpret
those rankings for each method. For Plurality I assume that you
say:

Use the rankings to determine who should win by the criteria.
For each ranking, give a Plurality vote to its top-ranked candidate,
to determine who actually wins the Plurality count.

Then the question is, how do you decide who wins in Approval,  based
on those rankings. Or single-winner Cumulative.

Now, Craig, you said that you want a uniform way to compare the
methods, and you'd do that by falsely assuming that they all
collect the same kind of ballots. But if you really want it
to be uniform, then there also must be a uniform rule for determing
how to get from the rankings (or ratings?) the information that the
particular voting system needs in order to do its count &
choose a winner.

That means one rule, no matter whether the method is Plurality,
Approval, single-winner Cumulative, IRV, or Condorcet.

Without that, the uniformity that you expect to get by
the false assumption that they all collect the same kind of ballots
is illusory.

And if there isn't a uniform rule, then we have an absurd mess:
using different rules for different methods to determine how to
get from the rankings the information that the particular voting
system needs for its count, to pick the winner.

You want  applicability to all methods? The following
definition of Condorcet's Criterion applies to all methods.
No it doesn't assume that they all use the same balloting system.
That's because they don't use the same balloting system. Hey,
while you're at it, why not assume that they also use the same
count rule? :-)

Condorcet's  Criterion:

If there's a sincere CW, and everyone votes sincerely, then that
sincere CW should win.

A voter votes sincerely if he doesn't vote a false preference or
leave unvoted a sincere preference that the balloting system in
use would have allowed him to vote in addition to the preferences
that he actually voted.

Of course voting a false preference means voting X over Y when
the voter doesn't really prefer X to Y.

By "preference", I mean pairwise preference.

[end of definition]

I use the same sincerity definition with other criteria that
stipulate sincere voting.

That CC applies to all voting systems. It does so without
pretending that they all use the same balloting system.

Additionally, unlike Markus's system that assumes rank (or ratings)
balloting for all methods, my CC definition is complete.

Markus asked what a sincere  CW is. It's someone who, when compared
separately to each one of the other candidates, is preferred to
him by more voters than vice-versa.

Mike Ossipoff

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