[EM] Borda count in practice

[Richard Moore]

Forest Simmons wrote:

> If your interpretation of the Slovenia election law is correct, so that
> truncations receive zero, and the ranked choices receive the same points
> that they would have received on a ballot without truncations, then
> Slovenia's version of Borda is a kind of hybrid of Borda and Approval,
> hence better than standard Borda.
> 
> Consider, for example, a single winner election with twenty candidates, of
> which a typical voter might approve four.  If that typical voter ranked
> only those approved four, they would receive 20, 19, 18, and 17 points,
> respectively (from that voter's ballot), while the other candidates would
> receive zero.
> 
> That's not so different from giving each of the four approved candidates
> 20 points (and zero for the rest) which would be equivalent to Approval.
> 
> The greater the number of candidates, the closer this method is to
> Approval.
> 
> Suppose that we used Slovania's version of Borda in Borda seeded single
> elimination or in Borda completed Condorcet (Black). It seems to me that
> when the number of candidates is moderately large, then there would be
> very little incentive to rank insincerely. 
> 
> Forest


I believe the strongest objection to Borda is that is fails FBC (correct
me if you disagree). Therefore Borda can be improved by taking steps to
make FBC failure scenarios less common, or less disastrous when they do
happen. Allowing truncations, and counting them in the way suggested
here, is a step in that direction.

Another step that can be made on top of that is to have a NOTB candidate
on every ballot. NOTB is counted in determining the scores of the candidates
that are ranked above it. For example, if there are four real candidates,
then a ballot such as

Nader > Gore > Bush > Buchanan > NOTB

would assign scores of 4, 3, 2, 1, but a ballot such as

Nader > Gore > NOTB

would assign scores of 4, 3, 0, 0 for the four real candidates (for those
who like to keep track of NOTB, NOTB would get two points here).

To make the characteristics even more Approval-like, give NOTB a higher
weight than one. With a weight of three for NOTB, the same ballot as
above would produce scores of 6, 5, 0, and 0.

NOTB would always be in the lowest position on the ballot except
for those not ranked. You would not have to mark NOTB, since it would
be implicit, so the above ballot could be written simply as "Nader > Gore".

Not sure, but I think somebody suggested something very similar a few
months ago.

  -- Richard