[EM] IRV vs BC

[Steve Barney]

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>).

>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. 
That seems to be a widely accepted and non-controversial statement of 
fact. To draw a claim that it is the "best," in an evaluative sense, 
would be to violate the is/ought dicotomy; therefore, it is true that 
"accurate" in a mathematical sense certainly does not imply "best" in 
an evaluative sense. But accuracy should count for something, 
shouldn't it?

>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),

But Saari has included IRV, pairwise comparison, Black's method, 
etc., in some of his articles, as well.

>dumping Condorcet cycles,

How you can say that Saari ignors Condorcet cycles and other voters 
profiles. If you read either of the two references in my orginal 
message, you will see that he pays a whole lot of attention to 
Condorcet cycles and Condorcet's pairwise comparison method.

>dumping other voter
>profiles that might cause Borda some harm,

This is very interesting. Can you give me any examples of such profiles?

>comparing Borda to obscure
>election methods

I will not deny he does that, but it seems to me it is justified in 
the way of illustration and analysis. He uses some odd methods to 
make a point, here and there, and to explain a mathematical 
relationship.

>and using criteria that aren't, ahem, the most
>intuitively appealing in the world.

Are referring to mathematical symmetries?