[EM] "CDTT criterion" compliance desirable?

[Chris Benham]

Marcus,

Thanks for the prompt explanation. You wrote:

"I had already proposed this criterion in 1997."

Why then do you list it as "Woodall's  CDTT criterion"
instead of your own "Generalised Majority Criterion"?

Did, as far as you know, Woodall ever actually propose
the "CDTT criterion" as something that is desirable for
methods to meet  (instead of just defining the CDTT set)?

Would you agree that it (and your GMC) is essentially the
same thing as the "Truncation Resistance" criterion on
Steve Eppley's MAM page?

http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm

One of several wordings given there:

Truncation Resistance:  If no voter votes any insincere strict preferences, 
alternative x is not in the sincere top cycle, and an alternative in the sincere top 
cycle is ranked over x by more than half of the voters, then x must not be chosen


And also to Mike Ossipoff's "Strategy-Free Criterion"?

http://www.barnsdle.demon.co.uk/vote/stfree.html

Strategy-Free Criterion (SFC): 
Preliminary definition: A "Condorcet winner" (CW) is a candidate who, 
when compared separately to each one of the other candidates, is preferred 
to that other candidate by more voters than vice-versa. Note that this is about 
sincere preference, which may sometimes be different than actual voting. 

SFC: 
If no one falsifies a preference, and there's a CW, and a majority of all the voters 
prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win. 
[end of definition] 

In the interesting link you gave, and elsewhere in the EM archive, I see reference
to the  "Smith//Condorcet[EM]" method.   What is that method, and what does
the "[EM]" stand for and mean?  I gather "Condorcet" meant  'MinMax'?
 
 
Chris Benham

 
Marcus Schulze wrote (Tues.Dec 23:

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



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