[EM] Election Reform (fwd)

[Richard Moore]

Forest,

I think on the whole it is a very good article, especially the paradox of
elimination methods pointed out in the closing paragraphs. It has already
been pointed out that if people interpret this in the context of the present
political climate the rankings of Faction 1 seem unrealistic. In today's
climate there might be a Faction 1A and a Faction 1B, with the 2nd and
3rd choices reversed between them, but more populous of the two
subfactions would be the one with Rep > Dem > Green. One thought
is to replace these with Conservative, Liberal, and Moderate. Another
is to use Conservative, Liberal, and Progressive (since the last of the
three is descriptive of Greens, though I don't think of Republicans as truly
conservative or Democrats as truly liberal, in the original senses of those
words).

The second paragraph seems to be implying that the methods you will be
discussing are all types of runoff election. When the word "runoff" is
mentioned, some type of elimination procedure involving two or more
stages comes to my mind.

The only other thing I caught is the misspelling of "consensus" as
"concensus".

 -- Richard


Forest Simmons wrote:

> 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.