FPTP family theory, REDLOG shadowing

[Markus Schulze]

Dear Craig,

you wrote (9 Dec 1999):
> I am never going to promote Borda, actually.

I bet you will promote some positional [*] election
method. Saari's geometrical model will force you
to do that.

If you think that you didn't yet walk into
Saari's trap, then: (1) Could you -please- give me
a concrete example of an election method that is
not a positional election method and that can be
described geometrically for any number of
candidates? (2) Could you -please- give a
geometrical description of Alternative Voting for
102 or 103 candidates (or whatever your favorite
number of candidates was) and explain how a violation
of the monotonicity criterion or the participation
criterion [**] looks like geometrically?

You wrote (9 Dec 1999):
> I never use probability; rather I use logic of
> geometry (inequalities return Boolean values).

Saari doesn't use probability either. Saari uses
logic of geometry too.

You wrote (9 Dec 1999):
> Have I ever referred to a cube?
> The fully general two 3 candidate preferential voting
> problem, can be solved by considering the interior of
> a tetrahedron (having vertices: AB, AC, B, C). I have
> two A4 sheets here that contain a 1 winner IFFP solution
> derivation. It is based on (P1). Adding (1,1,1,...) to
> (x:A,y:B,z:C,...) makes no difference to winners, etc..

So you think that you can circumvent the limitations of
Saari's model simply by using the term "tetrahedron"
instead of "cube"?????

Markus Schulze

[*] A "positional" election method (e.g. FPTP, Borda)
is an election method where a voter ranks the candidates
and where a candidate gets A1 points for every first
preference and A2 points for every second preference etc.
and where A1 >= A2 >= ... and where that candidate is
elected that has got the largest number of points.

[**] The participation criterion says that an additional
voter who strictly prefers candidate A to candidate B
must not cange the winner from candidate A to candidate B.
In other words: A voter must not be punished for going to
the polls and voting sincerely.