Markus' Econometrica reference on RB & IIAC

[MIKE OSSIPOFF]

Markus wrote:

I consider Pattanaik and Peleg's Regularity to be the natural
probabilistic extension of Arrow's IIAC. The fact that Pattanaik
and Peleg call this extension "Regularity" and not "IIAC"

I reply:

...and the reserve the name "IIAC" for a different criterion...

Markus continues:

is
quite irrelevant for the current discussion since I use the term
"IIAC" in the same manner in which they use the term "Regularity".

I reply:

...and you use "IIAC" for something different from what Pattanaik &
Peleg call "IIAC"

What it's relevant to is: You're using "IIAC" for a criterion different
from the one for which it's used by the authors for whom you posted
a reference. If you want to do that, fine. But I merely was letting
you know about that.

By the way, you're mistaken to say that you use "IIAC" to refer to
Pattanaic & Peleg's Regularity. Regularity has that initial clause
about preferences, implying a relation between preferences & votes,
while you stated that you make no assumption that there's such a
relation. Even if you want to disagree about what their initial
clause means, it still makes their Regularity different from your
"IIAC".


I'd said:
>So there's some relation between a voter's preferences and his ballot.
>
>Obviously, unless there's assumed to be a relation between a voter's
>preferences and his ballot, then, with the ballots completely
>independent of the preferences, it's easy to make RB fail your
>"IIAC", as I've demonstrated. Obviously RB can't meet Regularity
>without an assumption of a relation between voters' preferences and
>their ballots.

Markus replied:

It is sufficient to assume that in the _casted_ profile of
individual preferences the original candidates are still
preferred in the same order by the individual voters. But
it is not necessary to assume that "there's some relation
between a voter's preferences and his ballot".

I reply:

Are you now saying that that's what you meant when you posted your
"IIAC" definition? You didn't say so. Do you remember when I asked
you if there were any unstated assumptions in your "IIAC"? You
said there weren't.

If you're now changing your IIAC definition by making explicit
the unstated assumption that you're now adding, then I say that
you're doing the right thing, changing your "IIAC" after I've pointed
out to you what was wrong with it.

We may be getting into a language problem here. In English, unless
otherwise expressly stated, "preference" means an instance of preferring
one thing to another. When you refer to a cast preference, presumably
you mean a preference in accordance with which a voter has marked
his ballot, or the a pairwise ordering on that ballot that was cast
in that way.

But when "preference" is used alone, it doesn't mean a voted
candidate ordering or a "cast preference". It means a preference.
The voter prefers one candidate to another. So you're reading
something into Pattanaic & Peleg's Regularity definition that
just isn't there. If you add to your criterion your previously
unstated assumption that candidate order-relations on the ballots
don't change, your criterion is still different from Regularity,
since it talks about preferences, not ballot-orderings.

That's aside from the fact that their mention of preferences, and
your statement that you had no unstated assumptions, itself is
a reason why your "IIAC" is different from Regularity. As I said,
then, when I invited you to post a reference to a journal article
that defines your "IIAC", and says that Random Ballot meets it, you
responded by posting a reference to an article that doesn't even
mention your "IIAC".

And even if you'd correctly copied their wording when you posted
your definition of your "IIAC", your criterion would still be
different from Regularity, since your meaning for preferences is
different from theirs, since you're using it in a way that no
English-speaker would, to mean voted candidate-orderings rather
than instances of preferring one thing to another. A preference
and acting on a preference are 2 different things.

Markus continues:

By the way: I want you to remember that you haven't yet told a
reference for an article (1) that says that plurality passes
Condorcet or (2) that says that Condorcet may be applied only
to rank methods to keed plurality from passing?

I reply:

My answer to that hasn't changed since I answered it last time
you asked it:

1. No one, that I'm aware of, says that Plurality passes CC.

2. Blake Cretney says that his CC applies only to rank methods.
   He does that in order to keep Plurality from passing. I don't
   claim that anyone other than Blake uses that way of preventing
   Plurality from passing CC. I didn't say
   that there's an article that does that. I don't claim that there's
   an article that does that. I said that Blake, in his website,
   does that.

Mike Ossipoff




Markus Schulze







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