[EM] "CDTT criterion" compliance desirable?

[Markus Schulze]

Dear Chris Benham,

you wrote (23 Dec 2008):

> In one of your recent papers and on the Schulze
> method Wikipedia page you list "Woodall's CDTT
> criterion" as one of the criteria satisfied by
> the Schulze (Winning Votes) method.
>
> What, in your opinion, is supposed to be the
> positive point of compliance with that criterion?
> In other words, how would Schulze(WV) be worse
> if it satisfied all the criteria presently on
> your list of satisfied criteria except that one?

Woodall's CDTT criterion can be rephrased as
follows:

   When (1) the partial individual rankings can be
   completed in such a manner that candidate A is
   a Schwartz candidate and candidate B is not a
   Schwartz candidate and (2) the partial individual
   rankings cannot be completed in such a manner
   that candidate B is a Schwartz candidate and
   candidate A is not a Schwartz candidate, then
   candidate B must not be elected.

This guarantees that not needlessly a candidate is
elected who would not have been a Schwartz candidate
when not some voters had cast only a partial ranking
because of strategic considerations or other reasons.

When Woodall's CDTT criterion is violated, then this
means that casting partial individual rankings could
needlessly lead to the election of a candidate B who
is not a Schwartz candidate; "needlessly" because
Woodall's CDTT criterion is compatible with the
Smith criterion, independence of clones, monotonicity,
reversal symmetry, Pareto, resolvability, etc..

****************************************************

I had already proposed this criterion in 1997.
See e.g.:

http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-October/001569.html

In that mail, this criterion is formulated as
follows:

> "X >> Y" means, that a majority of the voters
> prefers X to Y.
>
> "There is a majority beat-path from X to Y,"
> means, that X >> Y or there is a set of candidates
> C[1], ..., C[n] with X >> C[1] >> ... >> C[n] >> Y.
>
> A method meets the "Generalized Majority Criterion"
> (GMC) if and only if: If there is a majority
> beat-path from A to B, but no majority beat-path
> from B to A, then B must not be elected.

The motivation for this criterion was that I wanted
to find a truncation resistance criterion

(a) that is compatible with the Smith criterion and
with independence of clones and that is otherwise
as strong as possible and

(b) that is defined on the cast preferences and
not on the sincere preferences.

Markus Schulze