[EM] Arrow's Condorcet Criterion

[Russ Paielli]

Nathan Herring nh.94-at-alum.dartmouth.org |EMlist| wrote:
> On 5/9/05 6:36:35 AM, "Russ Paielli" <6049awj02 at sneakemail.com> wrote:
> 
> 
>>The book itself presents advanced formal mathematics, including
>>theorems, lemmas, corollaries, consequences, and conditions. Yet Arrow's
>>definition of the Condorcet criterion is very informal: "that a
>>candidate who receives a majority as against each other candidate should
>>be elected."
>>
>>Did you get that, Mike? He *assumes* a ranked ballot, just as I
>>suggested, and which you tried to ridicule me for. And where is the
>>gobbldy-gook about sincere preferences, Mike? Or the notion that the CC
>>should apply to all methods, ordinal or not?
> 
> 
> I am not sure if it has any bearing on your and Mike's disagreement, but
> from that wording above, I would not read that he assumes as ranked ballot,

Excuse me, but that's precisely my point. Arrow is talking about ranked 
ballots, but he doesn't even bother to mention that fact explicitly in 
his definition of the Condorcet criterion. In other words, he expects 
the reader to simply *assume* that ranked ballots are the subject 
because they've been the subject throughout the book. And he says 
nothing whatsoever about preferences independent from actual votes, of 
course.

That is completely consistent with my earlier post, in which I said,

"Any reasonable definition of the Condorcet Criterion either assumes 
that ranking is allowed or says so explicitly. CC applies to ordinal 
methods only. Duh!"

For amusement, reread Mike's reply and behold what an absolute fool he 
made of himself. He does that regularly, of course, but this time I hope 
he learns a badly needed lesson. Here's an excerpt from Mighty Mike:

Mighty Mike:

The difficult thing about replying to Russ is that first one has to 
guess what he's trying to say:

What does it mean for a criterion to say that ranking is allowed? Maybe 
Russ is trying to say that the criterion stipulates in its premise that 
it only applies to rank methods. Or maybe he means that its requirement 
requires that the method be a rank method, otherwise the method fails. 
Who knows which he means? Who cares?

And, when a "reasonable" criterion doesn't say that, it "assumes" it, 
Russ tells us. What does it mean for a criterion to assume something 
that it doesn't say?? People assume things, but I've never heard of a 
criterion assuming something unsaid. But maybe Russ does. And if Russ 
thinks that people assume that reasonable CC definitions mean something 
that they don't say, presumably Russ knows that by using ESP.

Russ continues:

CC applies to
ordinal methods only. Duh!

I reply:

"Duh" is right. Blake's CC applies to ordinal methods only, because it 
explicitly says so. Other CC definitions apply to all methods, though 
not necessarily meaningfully. My preference CC applies meaningfully to 
all methods. What I mean by applying to all methods un-meaningfully will 
be clarified after a few paragraphs.

Russ replies:

What a complete and utter ass you are, Mike.