Finding the probable best candidate?

[Rob LeGrand]

Steve,

You have a different way of calculating the Borda winner than I do, so I won't
go to the trouble of finding the errors in your math.  I'm so used to compiling
the pairwise matrix for other methods that I use it for Borda too.  You can see
the way I do it at http://www.onr.com/user/honky98/rbvote/calc.html (enter the
votes in the box and press the Borda button).  It gives the Borda societal
outcome of my example as Bush>Browne>Gore>Nader>Buchanan.

> So, what's the point?

Well, looking at the ranked votes, do you think Bush is the "best" candidate? 
I don't.  Bush's Borda score is propped up by his near-clone Buchanan.  Borda
is the only ranked-ballot method I know (besides Black) that gives the win to
Bush.

As a simpler example, consider an election with three candidates.  Eric is
freedom-loving and Fran and Gary are socialist.  63% of the voters are
freedom-loving, 37% are socialist and all of the voters prefer Fran to Gary
because of a scandal involving Gary, so the ranked votes are

63:Eric>Fran>Gary
37:Fran>Gary>Eric

Borda gives the win to Fran even though Eric received a majority of first-place
votes and would have won in a landslide if Gary hadn't run.  Borda encourages a
party or ideology to run lots of candidates.  Some methods, like Simpson (i.e.
Minmax, Condorcet(EM)), fail clone independence only in contrived cases, but
Borda fails badly.

Blake's page http://www.fortunecity.com/meltingpot/harrow/124/path/pos.html
also has some good intuitive arguments against Borda.

=====
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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