[EM] IRV vs BC

[Blake Cretney]

On Sun, 11 Mar 2001 15:26:14 -0600
Steve Barney <BARNES99 at vaxa.cis.uwosh.edu> wrote:

> Well, what about the argument that the BC has been mathematically 
> proven (see Donald Saari, "Mathematical Structure of Voting 
> Paradoxes," _Journal of Economic Theory_, January 2000, pgs 1-102;
or 
> Donald Saari, "The Symmetry and Complexity of Elections," 
> <http-//www.math.nwu.edu/~d_saari/vote/expos.pdf>) to be the ONLY 
> method which can be guaranteed to always accurately reflect the 
> voters' preferences when they vote honestly and sincerely? 

Saari shows that Borda avoids certain paradoxical results.  The
question is, do Saari's paradoxes show that other methods are behaving
improperly, or just that our intuition is wrong with regard to his
paradoxes.  There are, after all, plenty of counter-intuitive but true
statements about voting methods, and the world in general.

I agree that if we assume that Borda gives the best results when
people vote sincerely, that this is a strong argument for putting up
with some bad results when people don't.  After all, it makes little
sense to favour a method that guarantees bad results over one that can
be manipulated into giving bad results.

However, consider the following example:

60 A B
40 B A

A wins.  No argument there.  But consider what happens if the B party
runs a junior candidates as well.  The result could be something like
this (I'm assuming sincere votes):

60 A B1 B2
40 B1 B2 A

B1 wins.  Note that no one changed their mind about the A side vs. the
B side.  It is still 60-40.  However, by running more candidates the B
side won.  Borda represents the field of candidates as much as the
voters.  The more candidates representing an ideology, the better off
it is.

The problem is that Borda looks at the B1 vs B2 victory compared to
the A vs. B2 victory and uses this as an argument for B1 over A.  If
B1 beats B2 so much more than does A, that seems like evidence that B1
is better than A.  But in fact it just reflects that A vs. B is more
controversial that B1 vs B2.

---------------------------------------------------------------------
Blake Cretney   http://www.fortunecity.com/meltingpot/harrow/124/path

Ranked Pairs gives the ranking of the options that always reflects
the majority preference between any two options, except in order to
reflect majority preferences with greater margins.
(B. T. Zavist & T. Tideman, "Complete independence  of clones in the
ranked pairs rule", Social choice and welfare, vol 6, 167-173, 1989)