[EM] Five Slot (Grade) Ballots

[Forest Simmons]

Any public proposal beyond standard Approval should consider using the
easily understood Five Slot Grade Ballot, which allows each voter to grade
each candidate on a scale of zero to four by assigning grades of F,D,C,B,
or A, respectively.  Anything beyond this simple and familiar rating
system would probably try the patience (if not confuse) the average voter
in the USA.

For example, methods that depend on pairwise comparisons can be applied to
pairwise matrices based on Grade Ballots. Although some distinctions may
be lost in races with more than five candidates, the distinctions that
remain reflect intensities of preference, so may be taken more seriously. 

We have barely scratched the surface of possible uses of Grade Ballots.

Here's an example that hints at the possible variety of uses:

This method, which we will call the C1C2 method, uses the voted grade
ballots to single out two candidates, C1 and C2, for a final head-to-head
contest, the result of which is determined from the pairwise matrix based
on the same grade ballots.

Candidate C1 is the candidate with the greatest over all number of A and B
grades. 

Candidate C2 is the candidate (other than C1) with the greatest number of
passing grades (C and above) except that each ballot that approved
candidate C1 at the A or B level only counts half. 

In the C2 nomination we partially discount the influence of the ballots
that approved C1 because we don't want C2 to just be a clone of C1.

We lower the bar one grade for candidate C2 in order to find a candidate
with broad enough support to have a chance against C1.

This method is summable in data on the order of the square of the number
of candidates.

The idea behind the method is to find two non-clone candidates with as
broad support as possible to choose between, and in a way that encourages
sincere voting. 

Note that in the recent (2000) US presidential race the folks that
preferred  Nader(A)>Gore(?)>Bush(F) would have divided into three camps
depending on their grade for Gore (B,C, or D).

The first camp gives both Nader and Gore full support in the C1 and C2
nominations, but would distinguish them in the final head-to-head vote if
they both survived to that stage.

The second camp supports only Nader in the C1 nomination, but supports
both Gore and Nader in the C2 nomination.

The third camp supports only Nader in the C1 and C2 nominations, but still
votes Gore over Bush in the final round if it happens that neither C1 nor
C2 is Nader.

If Nader is C1 or C2, then Nader has broad enough support to have a good
chance of beating the other finalist (whether Bush or Gore).

Thus varying levels of support for Gore can be given by Nader supporters
without spoiling Gore's chances against Bush unless Nader has a better
chance.

Notice the contrast with IRV.  Under IRV survival to the final round
doesn't require broad support, so one of the finalists is likely to be a
straw man, so to speak, in naturally occurring elections.

A variation on the above C1C2 method is to do the final showdown between
C1 and C2 as an approval vote.  Each ballot approves down to half way
between the two finalists (alternately, gives half approval to each
candidate between the two finalists). Conceivably (though not likely) some
third candidate C3 could come out ahead in the final approval count. 

[Even IRV would reliably make a decent choice if its final showdown were
changed to this approval style.]

This final approval count would require summing a data structure with size
on the order of the cube of the number of candidates, still manageable for
several hundred candidates. 

If analysis or simulation shows that (in general) the odds of C1 to C2
winning are two to one, say, then every ballot that has C2 above C1 should
have approval counted down to two thirds of the way between C2 and C1,
while those ballots that show C1 above C2 should approve only to one third
of the way down from C1 to C2. 

Alternately one could give two thirds or one third approval for each
candidate graded between the two finalists in the respective cases.

Comments?

More importantly, any other ideas stimulated by these?

Forest