# [EM] Proof that the CDTT is monotonic

Kevin Venzke stepjak at yahoo.fr
Mon May 30 10:30:44 PDT 2005

```Hello,

While this may be obvious to some, I don't think it was ever
shown, that the CDTT is monotonic.

So: Raising A, when A is a CDTT set member, can't cause any other
candidate to enter the CDTT.

Let "A>B" mean "A has a majority-strength win over B," and let
"A->B" mean "A has a majority-strength beatpath to B."

Raising a candidate can only make a difference if it creates a
majority-strength defeat. So suppose that A obtains such a defeat
over B, so that A>B.

A candidate X is in the CDTT, unless there is some other candidate Y
such that Y->X, but not X->Y.

If some other candidate C will move into the CDTT, then it must be
the case that some candidate D->C, and C>A, so that when A>B is
added, C->D, so that D doesn't disqualify C.

But if D->C and C>A, then D->A. If A was already in the CDTT, then
it must be that A->D, since A isn't disqualified. But if C>A and
A->D, then also it must be that C->D, so that D couldn't disqualify
C.

Kevin Venzke

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