# [EM] Evidently math-training isn't enough.

MIKE OSSIPOFF nkklrp at hotmail.com
Wed Apr 18 23:13:24 PDT 2001

```Here's Blake's definition of Condorcet's Criterion, at his website:

Name: Condorcet Criterion
Application: Ranked Ballots
Definition:
If an alternative victory pairwise beats every other alternative, this
alternative must win the election.
Pass: Black, Condorcet(EM), Dodgson, Kemeny-Young, Minmax, Nanson,
Pairwise-Elimination, Ranked Pairs, Schulze, Smith//Minmax, Total Defeats
Fail: Borda, Bucklin, Coombs, IRV

I comment:  I don't know what "victory pairwise beats" means, but
I suggest that it means that more people rank X over Y than vice-versa,
or that more people vote X over Y than vice-versa.

If it's the former, then either Condorcet's Criterion isn't defined for
Plurality, which doesn't use rankings, or else Blake intends to
mean that if you vote for X in Plurality, then you're "ranking"
X over  all the other alternatives. Of course if he means it he
should say it. If that's what he means then Plurality passes
Condorcet's Criterion.

Or what if Blake wants "victory pairwise beats" to mean that more
people vote X over Y than vice-versa, if X victory pairwise beats Y.

That's pure guesswork, since Blake didn't say that and, in any
case doesn't define voting X over Y.

But my point here is that, whichever of these things Blake is trying
to say: Either Plurality meets Condorcet's Criterion, or
Condorcet's Criterion isn't defined for Plurality.

Note that Plurality doesn't appear in Blake's list of passing
or nonpassing methods. So Condorcet (Blake's version) doesn't apply
to Plurality? But Blake says he'll state methods that the criteria
don't apply to, aren't defined for. He makes no such statement about
Plurality & Condorcet's Criterion.

So what does Blake mean?

Blake, did you miscopy your mathematically-trained economists, or
perhaps did they let you down?

I submit that any definition of Condorcet's Criterion, or any
criterion that's supposed to be for comparing methods, and which
is undefined for some method is sloppy and useless. And that
if Blake uses a Condorcet's Criterion version that Plurality passes,
then the criterion is acting contrary to what we all expect.
How many think Condorcet's Criterion should be defined so that
Plurality is a Condorcet Criterion method.

Some of Blake's criteria are a bit sloppily or stupidly defined.
What's that Blake? You say you copied it right from an article?
Oh well then, it must be unassailable. :-)

I notice that Approval isn't listed in the pass group or the fail
group either. Another exempt method?

Mike Ossipoff

_________________________________________________________________