Random Ballot fails your IIAC

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Jan 24 19:39:20 PST 2002

Markus recommended:

Prasanta K. Pattanaik, Bezalel Peleg, "Distribution of Power Under
Stochastic Social Choice Rules," Econometrica, vol. 54, p. 909-921,

I reply:

Thank you. Let's check it out. It's going to define IIAC the same
way you do, and then say that RB passes that IIAC, right?

Still, before we find that reference, I note that you haven't
told me anything that is wrong with the example that I posted,
in which RB is shown to fail your IIAC.

Are you going to say what you think is wrong with that example, or
with its use to show that RB fails your IIAC, or are you just going
to say that RB meets your IIAC because someone says so. Until I
check your reference, I say that, though you say so, and even if
someone else says so, you're still incorrect. I've shown with an
example that RB fails your IIAC, and you haven't told me what you
believe is wrong with the example or with the conclusion that, due
to the example, RB fails your IIAC.

Yes I asked you for a reference. I also asked you to say why you
believe that my example doesn't show that RB fails your IIAC.
You haven't done that.

As far as your reference is concerned, it will be a matter of whether
or not the article defines IIAC as you do & says that RB passes it.

But, whether it does or not, I've shown that RB fails that criterion
and you haven't refuted that demonstration. If your article says
that RB passes that criterion, but doesn't justify its claim, then
that won't count for a whole lot.

Markus continued:

You wrote (20 Jan 2002):
>Some define CC in terms of actual votes, with the result that
>Plurality passes, and so, to keep Plurality from passing, they
>say that the criterion, by their definition, applies only to rank
>methods. That greatly reduces the meaningfulness and usefulness
>of CC, and it's a shabby contrivance to avoid an undesired result.

Who is "some"? Could you please tell me 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

I reply:

I didn't say that anyone claimed that Plurality passes Condorcet.
I said that someone defines Condorcet to only apply to rank methods,
and does so in order to keep Plurality from passing Condorcet.

"Some" refers to Blake Cretney. I don't know if anyone else
uses that contrivance to keep Plurality from passing Condorcet.
If I implied that more than one person defines it that way, it was

For all I know, Condorcet himself might have only been talking
about rankings when he said that a BeatsAll candidate should win.
But that doesn't mean that, if a criterion is written about that,
he wouldn't want the criterion to compare pairwise-count methods with
nonrank methods.

It's obviously more useful for a criterion to apply to all methods.
I'm not saying that CC is an important criterion, but I do claim
that my definition of it is the better one.

Do you want a CC definition that doesn't
compare pairwise count methods to Plurality?

Also, when we have to say that a criterion doesn't apply to
certain widely-used &/or widely proposed methods, because when
applied to them it acts contrary to how we'd expect or want it to,
that suggests that there's something wrong with the definition that
acts in that way.

Mike Ossipoff

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