[EM] IRV inconsistency

[Forest Simmons]

Markus,

I would like to see an example where the Condorcet winner is B in
precincts 1 and 2, yet the combined ballots make A the Condorcet winner.

It seems to me that if B is preferred by majorities y1 > x1 and y2 > x2 in
the respective precincts, then B is preferred to A in the combined
election by a majority of y1+y2 > x1+x2.

Perhaps you are referring to the case where there is no Condorcet winner
according to one or more of the three counts (precinct 1, precinct 2, or
combined).

If so, that is perfectly understandable, not to be considered in the same
class as IRV's inconsistency, which pretends to discern definite winners
in every case, and which still fouls up, whether or not there is a
definite Condorcet winner in each precinct. 

Precinct 1:

3 ABC
4 BAC
6 CBA

Precinct 2:

8 ABC
5 BAC
4 CBA

Combined:

11 ABC
9  BAC
10 CBA

B is the CW in all three counts, and the IRV winner in the two precinct
counts, but not the IRV winner in the combined count. 

Note that C has a majority of last place votes in each precinct, and so
has no chance of winning, yet A is first eliminated in precinct 1, and B
is first eliminated in the combined count. IRV is too myopic to see that C
should be the first candidate eliminated in every case by any reasonable
standard of elimination.

As Richard says, IRV ignores and trashes valuable information willy nilly
and still pretends to come up with a top notch winner. All of IRV's
shortcomings can be traced back to this wasting of information.

It's like throwing away energy at random and still pretending to be a
perpetual motion machine. The first law of thermodynamics says you cannot
afford to throw away energy if you want perpetual motion. The second
law says even saving every possible erg of energy in insufficient.  These
laws together constitute a kind of Arrow impossibility theorem of physics.

When there is no Condorcet winner in either of the precincts (or in the
dominant precinct) then there is a fundamental ambiguity (i.e. lack of
information) that even preserving all of the available information may not
resolve except by combining the results, which may give a surer result,
but not always one that is totally without ambiguity. This does not
contradict common sense.

This is analogous to the fact that Condorcet methods violate the Reverse
Symmetry Criterion, but not in the gross way that IRV does, and that
Condorcet methods violate the IIAC, but not in the gross way that IRV
does. It is only in the fundamentally ambiguous (no CW) cases that
Condorcet methods fail these criteria, while IRV fails without provocation
or mitigating circumstances, as I have shown in other postings. 


Forest


On Tue, 15 May 2001, Markus Schulze wrote:

> Dear participants,
> 
> Forest Simmons wrote (14 May 2001):
> > Here's an inconsistency of IRV that I wish somebody had told me about
> > before I submitted my article to the Green Voice: It is possible for
> > a candidate to "win" every precinct without winning the election.
> 
> Richard Moore wrote (14 May 2001):
> > I had thought of this problem once before when thinking about IRV's
> > failure to meet the Summability Criterion, but it wasn't on my mind when
> > I reviewed your article. Every elimination in IRV means going back to the
> > original ballots and eliminating the loser of the round, then recounting
> > (you can sum the ballots into bins for each possible combination of votes
> > such as A, AB, ABC, ACB, AC, ACD, etc., but this array gets very large
> > very quickly as the number of candidates goes up, as we saw here a few
> > weeks ago). That means per-precinct vote totals are useless. You have
> > to do the elimination globally, not locally, and that means you can't
> > predict the results from local data. Even if all localities pick the
> > same winner.
> 
> Bart Ingles wrote (14 May 2001):
> > The property not being met here is actually called "consistency", if
> > I'm not mistaken.  Approval, Plurality, and Borda are consistent, but
> > not many others.  Maybe some variants of those three.
> 
> Actually, the consistency criterion and the Condorcet criterion are
> incompatible.
> 
> ******
> 
> Richard Moore 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).
> 
> I guess that IRV supporters will say that --for a voter to see what his
> vote did-- it is sufficient to publish the votes of each IRV step.
> 
> Markus Schulze
> 
>