[EM] Borda Count to the median

[Markus Schulze]

Dear Mike,

you wrote (27 Oct 2000):
> Has anyone played with fractional valuations of the
> Borda count? Like (for instance) all first place votes
> are 1, all second place votes are 1/2, all third place
> are 1/3 (if you are using 1/n) or 1/4 (if you are using
> 1/2^(n-1)), etc? I'm wondering what strange voting
> results might occur with such methods. (I'm thinking of
> using a golden-mean method where the ratio between each
> number remains constant, but that might be too
> complicated!)

That method where all first place votes are 1, all second
place votes are 1/2, all third place votes are 1/3 and
all n place votes are 1/n has originally been proposed by
Thomas Hare in 1857. But this method is usually known as
"Burnitz-Varrentrapp method" because it has also been
proposed by Gustav Burnitz and Georg Varrentrapp in 1863.
The Burnitz-Varrentrapp method was very popular in the
1860s to 1890s. Today it is only used in Nauru.

Markus Schulze