FPTP family theory, REDLOG shadowing

[Markus Schulze]

Dear Craig,

you wrote (11 Dec 1999):
> The only methods I favour are IFPP, FTP, and STV. The last is a bad method
> to be elected under, but it has no particular competition that satisfies
> SPC. IFPP is undefined for 4 candidates.

In so far as you couldn't define IFPP for all situations, you favour only
two methods: FPTP and Alternative Voting.

Didn't you say that Alternative Voting was "a method too defective to be
used in practice" (20 Oct 1999)? [Alternative Voting can punish voters
for voting.]

What has caused this change of your opinion?

******

You wrote (11 Dec 1999):
> Markus Schulze wrote:
> > 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 [3] explain how a violation
> > of the monotonicity criterion or the participation
> > criterion [**] looks like geometrically?
>
> If any preferential voting method can't be described geometrically in
> the simplex of all possible ballot paper count ratios, then the method
> is not defined. The existence of equations is not reduced if they are
> very long.
>
> Therefore an answer to the first question is: 'every defined method
> that is not a "positional method"'.
>
> Regarding question (2), the Alternative Vote most certainly has a
> algebraic polytope formula for 103 candidates. It would be symmetric
> with the number of similar regions equalling the factorial of 103.

Whether you can draw something or whether a given drawing has any
geometrical meaningfullness are two different questions.

If you think that the "simplex" has any non-trivial geometrical
meaning, then -please- explain this meaning for the above mentioned
two situations.

If you don't think that the "simplex" has any non-trivial geometrical
meaning, then -please- explain why you always use geometrical terms.

******

You wrote (11 Dec 1999):
> Regarding the 3rd: Monotonicity roughly says that when a point moves along
> a line parallel to an edge and from one simplex corner to another corner
> having on the preference for the candidate unde consideration nearer to
> the first preference, then the candidate never changes from a winner into
> a loser.
> Monotonicity seems to be defined in public to apply to changes in a
> single paper only. In that case, a point may be able to move along (say)
> three directions parallel to edges, but it may not move along any other
> direction that is a weighted average of those three lines. That constraint
> can be removed simply and without problem.
>
> Regarding participation...
>
> > [**] The participation criterion says that an additional
> > voter who strictly prefers candidate A to candidate B
> > must not change 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.
>
> Adding or discarding a paper shifts a point in the simplex, along a line
> that passes through the paper's vertex.

But does a violation of monotonicity or paticipation has any non-trivial
geometrical meaning that could justify the introduction of your geometrical
interpretation of elections?

Markus Schulze