FPTP family theory, REDLOG shadowing

[Markus Schulze]

Dear Craig,

it seems to me that you walked into Saari's trap.

Although you don't promote the Borda Method, you
use Saari's geometrical model of elections. But
Saari's geometrical model of elections implicitely
presumes that there is an even distribution of
candidates. Otherwise it wouldn't be possible that
the Saari cube is spanned only by the candidates
(and not e.g. also by the voters). But if there is
an even distribution of candidates, then the Borda
Method is _obviously_ the unique best possible
method.

Although you don't yet promote the Borda Method,
you check every proposed criterion for compatibility
with Saari's model and you accept a criterion only
if it is compatible with Saari's model and you
reject a criterion if it is incompatible with
Saari's model. If you keep using Saari's model, then
in the long run you will necessarily get to the
conclusion that the Borda Method is the unique best
possible method.

Markus Schulze