Approval Vote: reply to Bart Ingles

[Bart Ingles]

Markus Schulze wrote:
> 
> Dear Bart,
> 
> you wrote (2 Mar 2000):
> > Sincere Borda points with three candidates, for a single voter with
> > preferences ABC:
> > A = 2, B = 1, C = 0
> >
> > Points for same candidate who truncates (standard Borda):
> > A = 2, B = 0.5, C = 0.5  (or A=1.5, B = 0, C = 0)
> >
> > Points for truncator in Saari's version:
> > A = 1, B = 0, C = 0
> >
> > (I got this directly from Prof. Saari, in response to a question)
> 
> Do you have more information?
> 
> Example: If a given voter votes A>B=C>D, does that mean that A gets
> 3 points, B and C each get 2 points and C gets no points or does that
> mean that A gets 2 points, B and C each get one point and C gets no
> points in Saari's version?


It was my impression that your second interpretation is correct. 
Following is my question to Dr. Saari, and the reply I received (I
wasn't interested enough to pursue the subject any further).

Re-reading the reply, it looks as though this version of Borda is only
used internally in Saari's department, for whatever reason -- he may not
actually be advocating it for use elsewhere (the Economist article only
mentions the standard version):

> > In Borda count, at least as you propose it, is a voter required to rank
> > all candidates?  Or can he, in a 3-way race, give two points to his
> > favorite and zero to the rest?

>         The voter must rank all alternatives.  As described in
>         my book, there are times when a voter only knows his
>         top-ranked candidate.  But, to tally such a ballot
>         as 2 points for one and zero for others is to 
>         strongly encourage strategic voting and to give that
>         voter's preferences undue weight.  The correct values
>         are 1 1/2 and zero, zero.  In our department, however,
>         we give 1 0 0.  The argument is that the number of 
>         points is not important; it is the differential between
>         what is given to other candidates.  As the Borda count
>         has a single point differential, that is how we tally
>         ballots with only one name.
>