[EM] IRV inconsistency

[Markus Schulze]

Dear Forest,
dear Richard,

Richard wrote (14 May 2001):
> Another consequence of the summability failure is that reporting
> IRV results will be very complicated. At least for Condorcet you
> could publish the overall pairwise matrix (and also the pairwise
> matrices for individual counties or precincts or whatever the
> desired resolution is).

Forest wrote (17 May 2001):
> 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.
>
> [snip]
>
> Do Condorcet methods violate the IIAC? Yes, absolutely, so. But
> they only violate the intent when there is no CW. Remove somebody
> besides the CW from the game, and the CW still wins.
>
> [snip]
>
> No other method (based on preference ballots) can come closer
> to compliance with the IIAC than a method that is based solely on
> pairwise comparisons.
> 
> [snip]
>
> In other words, the methods that come the closest to satisfying
> Arrow are Condorcet methods, which satisfy all of his axioms except
> one, and come closer than any other kind of method to satisfying it.
>
> [snip]
>
> Note that restricting ourselves to the pairwise matrix does serve
> several clear purposes like near compliance with the IIAC and
> minimization of need for strategy, and minimization of strategic
> incentive for voting someone over your favorite.

It seems to me that you use the terms "pairwise method" and
"Condorcet method" synonymously.

Actually, there is a difference between "pairwise methods" and
"Condorcet methods." A "pairwise method" is a method where (at
least in those situations where the winner is unique) the winner
always depends only on the pairwise matrix. A "Condorcet method"
is a method that picks the Condorcet winner whenever such a
Condorcet winner exists.

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.

******

Forest wrote (17 May 2001):
> A common thread of recent postings is a lack of acknowledgement
> that there can be degrees of compliance and degrees of violation
> of various criteria and conditions.

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.

Markus Schulze