[EM] IRV inconsistency

[Forest Simmons]

On Fri, 18 May 2001, Markus Schulze wrote (among other stuff):

> > Markus wrote (17 May 2001):
> > > On the other side, Condorcet methods are criticized very
> > > frequently because the winner depends "only" on the pairwise
> > > matrix while other information is ignored.

To summarize more succinctly my reply:

The IIAC says that all of the information that is not in
the pairwise matrix is irrelevant. So to the extent the celebrated IIAC is
a valid principle those critics that you mentioned can be placated.

On the other hand, how does IRV justify its massive waste of information?

In addition to the above I was going to say that another answer is
possible:

Yes, Condorcet and other methods dependent on the pairwise matrix do throw
away some information. That's why they are no match to the Borda Count on
social utility. Of course, IRV throws away much more information and
information of higher calibre, so it cannot come as close in social
utility to the Borda Count as the Condorcet methods do.

Of course, the Borda Count has other problems with clones, severe favorite
betrayal, etc. Nevertheless, it is the preferred method in mechanical
applications (robotics, etc.)where these problems are of no concern.

But now you tell me that the Borda Count can be recovered from the
pairwise matrix. I wasn't aware of that. Are you sure? I haven't had time
to think about that yet.

> 
> Example: The Borda method is a pairwise method but not a Condorcet
> method. The Dodgson method is a Condorcet method but not a pairwise
> method.
> 
> 
> I don't deny that "there can be degrees of compliance and degrees
> of violation of various criteria and conditions." However, I don't
> consider your relaxation of the consistency criterion promising.
> 
> Your relaxation of the consistency criterion says:
> 
>    Whenever there is a Condorcet winner in each precinct and
>    candidate A wins in each precinct, then candidate A must be
>    the overall winner.
> 
> A reader who doesn't consider the Condorcet criterion important
> won't consider your relaxation of the consistency criterion
> reasonable. A reader who considers the Condorcet criterion
> important doesn't need to be convinced anymore.
> 

Then substitute the word "definite" for "Condorcet".  All systems are
excused from compliance when there are ties. I know you Condorcet folk do
not consider members of the Smith set to be tied, but I consider it a kind
of tie where there is no definte winner.

Forest