[EM] IRV inconsistency

[Forest Simmons]

I didn't quite finish my train of thought so here is a cumulative version
which continues from the first installment to the second at the dotted
line below.

On Thu, 17 May 2001, Markus Schulze wrote:

<big snip>

> 
> On the other side, Condorcet methods are criticized very frequently
> because the winner depends "only" on the pairwise matrix while
> other information is ignored.
> 
> Markus Schulze
> 

[First installment]

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.

Examples, analogies, and analyses of pertinent features of processes are
intended to impart some sense of proportion and perspective to those with
eyes to see and ears to hear.

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.

Does IRV violate the IIAC? Yes. But where's the analogous statement of
"almost compliance?"

This brings up an interesting point.

The impossibility part of Arrow's theorem can be attributed almost
entirely (apart from the requirement of preference ballots with a finite
number of candidates and majority win in two way contests) to the IIAC as
follows: 

Step 1. Prove by induction on the number of candidates that IIAC implies
the Condorcet Criterion.

Step2. Show by the following example that the IIAC and the Condorcet
Criterion are incompatible.

2 ABC
3 BCA
4 CAB

This proof brings out two things (for those with eyes to see):

(1) 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.

(2) No method (based on anonymous preference ballots) can satisfy the
IIAC.

On the other hand, there are preference ballot based methods that satisfy
all of Arrow's other conditions. All such methods are necessarily
Condorcet methods. IRV doesn't come close, since it also fails
monotonicty.

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.

In view of these facts, it is extremely ironical that IRV supporters will
quote (or misquote) Arrow's Impossibility as justification for sticking
with IRV and ignoring Condorcet. 

This is an example of the value of considering degrees of compliance.

.........................................................

[Second Installment]

Likewise IRV ignores and trashes lots of information willy nilly while
Condorcet ignores the minimum to satisfy Arrow as close as possible.

The willy nilly nature of IRV's trashing can be seen from the fact that
the eliminations rely on superficial information and from the examples
that have been given, including IRV's early elimination of Condorcet
winners while saving majority last place losers for the final round, i.e.
eliminating candidates preferred by majorities over all other candidates
while preserving easily detected candidates rejected by a majority of
voters, and all the while claiming to be the majority rule method.

The clincher is the IRVie unwillingness to attach a majority check on each
elimination (converting IRV into a pairwise elimination method), which
would allow dipping below superficial information. Sorry, that information
is off limits.

If it served any clear purpose, perhaps we could over look this fault.

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.

Where are the corresponding IRV purposes for much grosser (and willy
nilly) ignoring of information?

Forest