[EM] What it takes to give meaning to a criterion "failure"

[Michael Ossipoff]

On Mon, Jul 30, 2012 at 1:45 PM, Jameson Quinn <jameson.quinn at gmail.com> wrote:

> As far as I can tell, you are arguing that ICT meets the majority Condorcet
> criterion

No, I'm arguing that ICT meets Condorcet's Criterion, if Condorcet's
Criterion is about electing the candidate who beats each one of the
others, or who is the only unbeaten candidate. ICT does that, you
know. Yes, it defines "beat" differently, but I claim that unimproved
Condorcet's definition of "beat" is no more valid than that of ICT.
Less valild, if judged by the intent and wishes of the
equal-top-ranking voters.

But yes, it meet the Majority Condorcet Criterion too (I capitalize
names of methods and criteria for clarity).


You said:

 (does it?

[endquote]

Yes. Every method that meets CC, when ICT's "beat" definition is used,
also meets MCC. But the reverse is not true.

You continued:

it seems to...) and that the MCC is more important than
> the CC.

[endquote]

It certainly could be said that MCC is more important than CC in the
sense that failing a more lenient criterion is worse. But, on the
other hand, meeting a stronger criterion counts for more than meeting
a weaker one. So then, who can say which is more important.

But I was talking about CC, not MCC.

You said:

Do I read you correctly?

[endquote]

I'm claiming more than you thought that I was.

I'm saying that ICT meets Condorcet's Criterion.

That sounds like a preposterous thing to say, if you regard the
definition of "beat" to be part of CC's definition, and if you take,
as "beat" 's definition, the "beat" definition used in traditional
unimproved Condorcet.  But "beat" could be regarded as a word defined
external to CC's definition.

And I've told why unimproved Condorcet's beat definition is no more
valid or legitimate than that of ICT. Looked at in regards to the
wishes and intent of the equal-top-ranking voters, the ICT beat
definition is the more justifiable one.

The two beat definitions:

First I'll repeat some terms:

(X>Y) is the number of ballots ranking X over Y.

(Y>X) is the number of ballots ranking Y over X.

(X=Y)T is the number of ballots ranking X and Y at top.

(X=Y)B is the number of ballots ranking X and Y at bottom.

Unimproved Condorcet's "beat"  definition:

X beats Y iff (X>Y) > (Y>X)

Improved Condorcet's "beat" definition:

X beats Y iff (X>Y) > (Y<X) + (X=Y)T

Double-Ended Improved Condorcet's "beat" definition:

X beats Y iff (X>Y) + (X=Y)B > (Y>X) + (X=Y)T

Which method meets CC depends on which "beat" definition you use with CC.

You could say that you consider unimproved Condorcet's "beat"
definition to be part of CC's definition. Or you could say that the
meaning of "beat" is external to CC's definition. I suggest that the
only justification of insisting on the former is if you think that the
traditional "beat" definition, that of unimproved Condorcet is
actually better, more justified. Otherwise, you're just clinging to
tradition.

I've compared the justification of those two "beat" definitions.

ICT meets CC at least as validly, and arguably more validly, than
traditional unimproved Condorcet.

Mike Ossipoff