[EM] Markus' Econometrica reference on RB & IIAC

[Markus Schulze]

Dear Mike,

you wrote (27 Jan 2002):
> Markus wrote (27 Jan 2002):
> > Mike wrote (26 Jan 2002):
> > > According to that article, Markus was incorrect to say that
> > > the information that Random Ballot fails IIAC, as defined by
> > > Markus, would revolutionize the authors' understanding of one
> > > of Arrow's criteria. That's because Pattanaik & Peleg don't
> > > call that criterion IIAC. The criterion that Markus defined
> > > as IIAC is called "Regularity" by Pattanaik & Peleg.
> >
> > I consider Pattanaik and Peleg's Regularity to be the natural
> > probabilistic extension of Arrow's IIAC. You can disagree, but
> > you cannot say that this is "incorrect". The fact that Pattanaik
> > and Peleg call this extension "Regularity" and not "IIAC" is
> > quite irrelevant for the current discussion.
>
> It's not a matter of whether I disagree. Pattanaik & Peleg disagree.
> They define a different criterion that they call IIAC. So, in their
> article, Regularity is not IIAC.

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

******

You wrote (27 Jan 2002):
> Markus wrote (27 Jan 2002):
> > Mike wrote (26 Jan 2002):
> > > Now, I'll explain to you why Pattanaik & Peleg say that RB
> > > passes Regularity: They assume that people vote in accordance
> > > with their preferences. Here's how they define Regularity:
> > >
> > > "Given the profile of individual preferences, if one enlarges
> > > the feasible set of alternatives by adding one or more
> > > alternatives, then the probability of the society's choosing
> > > any one of the alternatives figuring in the original feasible
> > > set cannot increase after the feasible set is enlarged."
> > >
> > > The unspoken assumption obviously is that people vote in
> > > accordance with their preferences.
> >
> > Where do Pattanaik and Peleg assume that "people vote in
> > accordance with their preferences"? Your claim that this
> > was an "unspoken assumption" is quite speculative.
>
> Take another look at Pattanaik's & Peleg's definition. I'll paste
> it again here:
>
> "Given the profile of individual preferences, if one enlarges
> the feasible set of alternatives by adding one or more
> alternatives, then the probability of the society's choosing
> any one of the alternatives figuring in the original feasible
> set cannot increase after the feasible set is enlarged."
>
> Look at the 1st 6 words of their definition:
>
> "Given the profile of individual preferences..."
>
> What would be the point of starting the wording that way if the
> individual preferences had no role in the outcome? The wording
> implies, and all but says, that the outcome is a result of the
> profile of individual preferences, and of the original
> alternatives and the added alternatives.
>
> Now, how could the profile of individual preferences have a role
> in the outcome? Here's how they can affect the outcome: A voter's
> preferences affect his ballot, and the ballots affect the outcome.
>
> 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.

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".

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?

Markus Schulze