[EM] Election Reform (fwd)

[Forest Simmons]

Dear EM folk,

here's my second draft.  I still need suggestions, especially for websites
for people to get more information on pro's and con' of different methods.

Thanks,

Forest


---------------------------------------
Dear Editor:

As mentioned more than once in your newsletter an important priority is
election reform, including some kind of instant runoff method that
ameliorates the "spoiler effect."

One of many such methods, Instant Runoff Voting (IRV), has pre-empted the
phrase "instant runoff" as part of its name, giving the false impression
that it is THE instant runoff method.  That false impression wouldn't be
such a big deal if IRV were clearly better than any of its serious
competitors. 

To compare some of these methods, let's imagine some future election where
a third party candidate has a little more support than Nader did, but
still cannot command as many first place votes as either of the two
corporate party candidates. Let's also assume that neither of the other
candidates has more than half of all the first place votes.

Suppose that there are three major factions with preferences as summarized
in the following table:

preference: first to last (left to right)
-----------------------------
Faction 1:   Repub > Green > Democ
Faction 2:   Democ > Green > Repub
Faction 3:   Green > Democ > Repub


Now let's consider who would win the election according the the various
leading methods.

First IRV:

Since we are assuming that Faction 3 is the smallest, its first choice,
the Green candidate, would be eliminated, and the election would go to
the Democrat, since the first faction (which is not a majority) is the
only faction in which the Republican is not in last place.

Next Coombs:

In Coomb's method, when there is no first choice majority, the candidate
with the greatest number of last place votes is eliminated. Under the
above assumptions that would be the Republican candidate. In the instant
runoff the Green candidate would win since only the second faction (which
is not a majority) would prefer the Democrat candidate over the Green.

IRV and Coombs disagree on the winner, so let's pit their winners against
each other:  Green beats Democrat except in Faction 2, which is not a
majority, so Green is the stronger winner. It looks like Coombs did better
on this example. (IRV could do better on some other example.)

We could make a hybrid method that compares the IRV and Coombs winners
head-to-head to get the grand winner.  This idea naturally leads to the
Condorcet method.

Condorcet:

In Condorcet the candidate who wins all the head-to-head contests wins the
election. In our example (as noted above) Green beats both Republican and
Democrat in head-to-head contests, so Green is the Condorcet winner.

Next Borda Count:

In Borda Count, first, middle, and last place preferences receive two,
one, and zero points, respectively.  Under our assumption of no majority
faction, the Green candidate would win. (This can be proven by solving a
system of algebraic inequalities based on our assumption of no majority
faction.)

A natural question is, "Why not allow the voters to assign points to
the candidates directly (as opposed to this indirect point system)?"

The method that goes by the name Cardinal Rating (CR) is an outgrowth of
that question.

Cardinal Rating (CR):

In this method each voter rates each candidate on a scale of zero to four. 
(Other scales can be used, but this one is amply adequate for three
candidates, as well as being the familiar basis for grade point
computations: A=4, B=3, C=2, D=1, and F=0 .) This allows the voter to
distinguish degrees of preference that cannot be expressed on a plain
order of preference ballot.  In other words this method has finer
resolution than the Borda Count, and is potentially more expressive of the
voters' will.

Let's assume that all three factions give their first place choices A's
and their last place choices F's. The middle candidates could be rated
anywhere between F plus and A minus. But it is very likely that the
average rating of the Green candidate in Faction 2 would be at least a B,
and likely that the average rating of the Democrat candidate by Faction 3
voters would be no better than a B. (In a CR election many Greens would
realize that they have enough strength to win outright, so there's no need
to hold the nose and give maximum support to the lesser evil.)  And let's
be pessimistic and suppose that the average rating of the Green candidate
by Faction 1 is between a C and a D.

Solving the system of algebraic inequalities based on these assumptions
yields the result: Green wins again.

Approval:

This last method is based on the fact that when a CR election involves
hundreds of voters (any major election) the average ratings of the various
candidates will suffer at most negligible change if the voters are limited
to the extreme ratings. In other words if each voter grades each candidate
on a pass / no pass basis, the law of averages dictates that the
candidates' grade point averages will be virtually the same, except
perhaps in elections with only a few dozen voters. 

An analogy is in order. As a math instructor I award partial credit for
good work (despite the wrong answer) for psychological and educational
purposes, NOT because I am under any illusion that it will make a
significant difference in the students' course grades.

Approval would almost surely give the same result as CR. Green wins again.

Well then, if Approval (almost) always gives the same answer as CR, why
not just stick to CR ? 

For one reason only: The Approval ballot is the simplest of all the runoff
method ballots. (The Florida fiasco has sensitized us to the dangers of
ballot confusion.)

In fact, Approval ballots are identical to normal ballots. The voter uses
a number two pencil to shade the ovals adjacent to the names of each
candidate that she considers acceptable, and leaves the other ovals blank. 

However, the psychological advantage of CR might be strong enough to
justify using the more complicated ballots. Even these ballots would be
familiar and easy to use for anyone who has ever taken a scantron graded
multiple choice test. 

In our example a CR ballot might look like this:

Candidate |  Grade |   A   B   C   D   F
-----------------------------------------
Bush      |  ____  |  ( ) ( ) ( ) ( ) ( )
-----------------------------------------
Gore      |  ____  |  ( ) ( ) ( ) ( ) ( )
-----------------------------------------
Nader     |  ____  |  ( ) ( ) ( ) ( ) ( )

The voters would be instructed to print each grade in the space provided
under the heading "Grade", and to shade the corresponding oval to the
right with a number 2 pencil.

By way of comparison the Approval ballot would look like this:

Candidate | Vote
-------------------
Bush      |  ()
-------------------
Gore      |  ()
-------------------
Nader     |  ()

What would a preference ballot look like? It would be a lot more confusing
than either of these.  If it asks you to number the candidates in order of
preference, some people are going to be confused about whether the high
numbers go with high preference or low preference, even if the ballot
instructions clearly address that issue. If the instructions are to list
the candidates in order of preference, then someone is going to have to
interpret the voters' handwriting, etc.

So far we have seen that of all the leading contenders among runoff
methods, only IRV gives the election away to a corporate candidate.
This was based on realistic minimal assumptions about some future election
when a progressive, populist third party candidate has a broad enough base
of grass roots support to get most of the second place votes if not as
many first place votes as the corporate candidates.

What would it take for IRV to join the concensus of the more reputable
methods?  What if Faction 3 made up 33% of the voters, and the other two
factions were roughly equal in size, with about 33.5% each.  Suppose
further, that no voter rated Green less than a B plus. Would that be
enough for IRV? 

Well, almost. Another half of a percent added to Faction 3 would finally
satisfy IRV and let the third party candidate into the club. Any of the
other contending methods above has a much better chance of lowering the
third party entrance barrier to the level that someone other than a
returning war hero (not likely to be progressive) could break through. 

IRV is one of the worst methods for breaking the two party duopoly. In
fact it helps maintain the status quo by giving the appearance of majority
support for one of the two corporate parties. The embarrassment of last
November's election would be solved by IRV, pleasing the entrenched
powers.

But as we have seen, that "majority win" with IRV is an illusion because
after the inadvertent elimination of the head-to-head winner, the last
comparison is a sham.

In a short article I cannot run through all the various advantages and
disadvantages of the various competing methods. I will just mention a
few of the most important considerations. For more information visit the
following web sites:
-----------------------
----------------------
----------------------

Of all the leading methods, only CR and Approval never suffer from any
strategic incentive to reverse a preference on a ballot; all of the other
methods still suffer from this distortion of the public will (and violence
to the voter's conscience) in one degree or another.  Condorcet is almost
immune to this problem, as well, and would be completely immune if it used
random methods to break ties.  But three way ties in Condorcet are just
common enough to make the random tie breaker undesirable.

The Borda Count suffers strongly from strategic incentives to insincere
rankings. For this and other reasons it is generally not considered to be
as good as Approval or Condorcet. 

Another reason for choosing CR or Approval over IRV or Coombs, is that
both IRV and Coombs suffer from the basic problem of all methods based on
sequential elimination. When the election is close, how can you tell whom
should be eliminated first?  How do you know you are not eliminating the
best candidate? One rule might give the best result in one situation,
another elimination rule in another. 

No simple elimination rule can always eliminate the worst of three
candidates. 

If it could, applying that simple rule to the same ballots with
preferences reversed would choose the best candidate. There would be no
need to go through the elimination process.

In this connection, IRV sometimes picks the same candidate when all of
the preferences are reversed, even when head-to-head comparisons show that
there is an obvious winner.

Since no simple elimination rule can always eliminate the worst of three
candidates, there is no way of knowing if the two runoff candidates are
the best two candidates. The runoff is a sham, especially if all three
candidates are strong contenders, as in the examples of interest to us.

In summary, IRV makes a rather poor showing compared to other proposed
reform methods.  Let's back one of the methods worth fighting for, namely
Condorcet, Approval, and/or Cardinal Rating.