[EM] "CDTT criterion" compliance desirable?

[Markus Schulze]

Dear Chris Benham,

you wrote (25 Dec 2008):

> "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)?

Woodall's main aims are to describe and to investigate
the different election methods. Compared to the
participants of this mailing list, Woodall is very
reluctant to say that some election method was good/bad
or that some property was desirable/undesirable.

You wrote (25 Dec 2008):

> 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]

As Ossipoff's "strategy-free criterion" refers to
situations with a Condorcet winner, I guess you mean
Ossipoff's "generalized strategy-free criterion"
instead of his "strategy-free criterion":

> Generalized Strategy-Free Criterion (GSFC):
> Preliminary definition: The sincere Smith set is the
> smallest set of candidates such that every candidate
> in the set is preferred to every candidate outside
> the set by more voters than vice-versa.
>
> There's always a sincere Smith set. When there's a CW,
> that CW is the sincere Smith set.
>
> GSFC:
> If no one falsifies a preference, and X is a member of
> the sincere Smith set, and Y is not, and if a majority
> of all the voters prefer X to Y and vote sincerely,
> then Y shouldn't win.
>
> [end of definition]

Suppose candidate B is not in the sincere Smith set.

Then, to guarantee that candidate B isn't elected,
Eppley's "truncation resistance" criterion and
Ossipoff's "generalized strategy-free criterion"
presume that there is a candidate A, who is in the
sincere Smith set and who is strictly preferred to
candidate B by a majority of the voters according
to the cast preferences.

However (as, when no voter votes any insincere strict
preference, there cannot be a majority beatpath
according to the cast preferences from a candidate B
outside the sincere Smith set to a candidate A inside
the sincere Smith set), it is --to fulfil the
presumption of my criterion-- sufficient that
there is a majority beatpath according to the cast
preferences from some candidate A of the sincere
Smith set to candidate B. [This doesn't necessarily
mean that a majority of the voters strictly prefers
candidate A to candidate B according to the cast
preferences. It could also mean e.g. that, according
to the cast preferences, (1) a majority of the voters
strictly prefers candidate A to some candidate C
outside the sincere Smith set and (2) a majority
of the voters strictly prefers this candidate C
to candidate B.]

As the presumption that a majority of the voters
strictly prefers candidate A to candidate B according
to the cast preferences is stronger than the
presumption that there is a majority beatpath from
candidate A to candidate B according to the cast
preferences, my criterion is stronger than Eppley's
"truncation resistance" criterion and Ossipoff's
"generalized strategy-free criterion".

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

You wrote (25 Dec 2008):

> 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'?

In the beginning of this mailing list,
MinMax(winning votes) was called "Condorcet[EM]",
where "Condorcet" refers to the MinMax method and
"[EM]" refers to winning votes.

Markus Schulze