[EM] IRV vs BC

[David Catchpole]

I'll have to answer in parts.

> David:
>
> Thanks for you comments. My response follows:
>
> At 6:51 AM +1000 3/13/01, David Catchpole wrote:
> >The argument isn't that BC is manipulable. In fact, being one of the few
> >election methods that could be described in some way as "monotonic" (not
> >necessarily an orthodox way!), Borda is eminently resistant to
> >manipulation.
>
> Wow, that is quite a statement - I don't mean to be sarcastic. Thanks
> for redirecting my attention to this. I will have to go back and
> re-read some of Saari's articles on this - hopefully with more
> comprehension this time (I am no mathematician) - starting with
> "Copeland Method II: Manipulation, Monotonicity, and Paradoxes"
> (http://www.math.nwu.edu/~d_saari/vote/man/cmman.pdf).
>
> >However- and this is a big however- Borda is not fair. It
> >fails a basic condition that a candidate who is the first preference of
> >more than half of the voters must be the winner.
>
> Well, Saari has commented on that, and it seems plausible to me that
> majority criterion is not a good one (see D. Saari, "A Fourth Grade
> Experience," <http://www.math.nwu.edu/~d_saari/geom/fo/four.pdf>).

I have to say I missed any dismissal of a majority criterion in that
article. Could give the specific passage?

> >As for Saari's work- while it is interesting, and I think many of his
> >conceptual tools could be extended to great effect in voting theory, I
> >disagree with the indirect implication he seeks to make in his work, that
> >Borda is the "best" single-winner election method. Can't you see the
> >absurdity in the statement "Borda gives an accurate account of the votes"? Any
> >election method worth considering seriously has the winning candidate(s) as a
> >function of the votes.
>
> Perhaps you are right, but I don't know. I certainly take the
> is/ought dicotomy seriously, but it seems to me that mathematics
> weighs in on this question. The basic justification for my statement
> about the accuracy of the BC is that the BC is the only procedure
> which uses all of the information available in a preference ballot.

So what you mean is that the Borda winner is more likely to change with a
small number of ballots changed? Or that there is no uniform way to change
the ballots without changing the Borda winner? I'm not sure whether either
of these are of big appeal. I'll have to check Saari's work again. Do you
have a particular statement that needs checking?