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

Blake Cretney bcretney at postmark.net
Fri Apr 20 18:23:30 PDT 2001

```On Thu, 19 Apr 2001 06:13:24 -0000
"MIKE OSSIPOFF" <nkklrp at hotmail.com> wrote:

> 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.

Good point.  I intended this to say "pairwise beats" and have a link
to the "pairwise victory" section of my definition page.  Thanks for
catching this.

> 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.

If you look at the section you quoted, it says:

> Application: Ranked Ballots

Mike continues:

> 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.

I agree that it would be misleading to define Condorcet's criterion so
that it is passed by plurality.  I disagree that Condorcet's criterion
is sloppy and useless if it doesn't apply to plurality.  It can be
precisely defined, and is quite useful, at least for ranked ballots.

---
Blake Cretney

```