[EM] IRV vs BC

[David Catchpole]

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. 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.

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.

Saari seems to have the hypothesis ready before the
investigation, doing crazy stuff like paying attention only to
election methods that use some linear aggregate of the vote (FPP,
Borda and intermediates), dumping Condorcet cycles, dumping other voter
profiles that might cause Borda some harm, comparing Borda to obscure
election methods and using criteria that aren't, ahem, the most
intuitively appealing in the world.

I've basically given up on single-winner election methods, because due to
the nature of the problem they are all open to attack. I potter
around now expecting election methods with a few more winners start to
lose some of the "fuzziness" of the single winner problem.

On Sun, 11 Mar 2001, Steve Barney wrote:

> Election-Methods-List:
>
> It seems to me that there is a glaring weakness in arguments that the
> Borda Count (BC) is inferior, overall, to the Instant Runoff Vote
> (IRV) because it is more manipulatable, even if it is more
> manipulatable.
>
> First of all, it is worth noting that it has been mathematically
> proven that all voting procedure necessarily must be manipulatable
> (M. Satterthwaite, "Strategy-proofness and Arrow's conditions,"
> _Journal of Economic Theory_, 1975, 10: 187-217). Therefore, since
> manipulatability is only a matter of degree, the most you can claim
> is that the BC is more manipulatable than, for example, the IRV.
>
> Anyway, lets take it for granted that the BC is relatively vulnerable
> to successful manipulation by strategic or insincere voting, in
> comparison to the IRV; that is to say, that the BC can elect someone
> other than the voters' truly most preferred candidate, to the benefit
> of voters who strategically submit dishonest or insincere votes.
>
> 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? That is,
> what about Saari's mathematical proof that the BC is the only method
> which always gives an accurate accounting of THE VOTES THEMSELVES,
> regardless of whether those votes are honest and sincere or not?
> Shouldn't that count for something? (For the sake of argument, let's
> take Saari's analysis for granted, and assume that it is true that
> the BC is indeed the best method for determining the most preferred
> candidate from SINCERE votes.) Given the soundness of Saari's
> analysis, couldn't the accuracy of the BC outweigh its
> manipulatability, in comparison to the IRV?
>
>

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