[EM] Markus' Econometrica reference on RB & IIAC

Markus Schulze markus.schulze at alumni.tu-berlin.de
Sun Jan 27 04:14:23 PST 2002

Dear Mike,

you 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.


You 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.

Markus Schulze

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