FPTP family theory, REDLOG shadowing

[David Catchpole]

Saari also uses a triangle, but the triangle doesn't go far enough in an
analysis of what's a possible configuration of votes and what's not.
That's where the Saari octahedron kicks in in his analysis.

On Fri, 10 Dec 1999, Markus Schulze wrote:

> 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.
> 
> 
> 

-------------------------------------------
Nothing is foolproof given a talented fool.