[EM] Five Slots Approval (was Five Slots and Cranor)

Forest Simmons fsimmons at pcc.edu
Fri Apr 27 17:43:37 PDT 2001

The purpose of this posting is to answer Demorep's concerns (see below) 
about the complexity of the Five Slot Ballot, and to advocate another use
for it (simpler than my median method that he refers to) as our best
chance of making Approval psychologically palatable to citizens of the IRV

First of all here's the five slot ballot:

Candidate | Grade |  A  |  B  |  C  |  D  |  F
Sally F.  |  ___  | ( ) | ( ) | ( ) | ( ) | ( )
Jack H.   |  ___  | ( ) | ( ) | ( ) | ( ) | ( )
Janet R.  |  ___  | ( ) | ( ) | ( ) | ( ) | ( )
Wm. C.    |  ___  | ( ) | ( ) | ( ) | ( ) | ( )
L.A.G.    |  ___  | ( ) | ( ) | ( ) | ( ) | ( )

The only simpler ballot that I know of is the Approval ballot.

There are many possible ways of scoring this ballot, and for each possible
way of scoring the ballot there are many possible ways of using those
scores to determine a winner.

The most obvious (but not necessarily the best) of these methods is to
score the ballots with grade points on a scale of zero to four, and to
combine those scores by averaging, so that the candidate with the highest
grade point average wins the election. This is just standard Cardinal
Ratings (CR) with a resolution of four. 

This method suffers from strategic conflict between the instrumental and
expressive purposes of voting, because the best instrumental strategy is
to grade at the extremes of A and F only, which limits variety of

In particular, if your preferences are Nader > Gore > Bush , and you
believe that Nader has a negligible chance of winning the election
compared to Gore and Bush, then your best instrumental strategy is to give
Nader and Gore grades of A, while awarding Bush with an F, which conflicts
with your expressive inclinations of giving grades of A, C, and F to the
three respective candidates.

Here's another way of scoring these ballots and determining the winner
while resolving this conflict:

Grades A, B, and C count as Approval, whereas D, F, and Blank count as
Disapproval.  The candidate with the highest Approval score wins the
election.  The voters can freely express distinctions within the approved
and disapproved categories without worrying about conflicts with
instrumental strategy.

This simple method is Approval instrumentally, but with greater than two
resolution for expression. Since IRV supporters' main objection to
ordinary Approval is its lack of expressivity, this expressive version is
the kind of method that might have a chance in overcoming their
psychological block.

As I have mentioned before the ballot has a slot for every candidate:
favorite, compromise front runner, in between, despised front runner, and
evil incarnate. For my Green friends the most important distinctions are
among favorite and the two front runners; all else is frosting on the

What about the folks that want to express Gore and Bush as D and F
candidates, but still support Gore instrumentally?

No problem; at no extra cost we can turbo charge the method as follows: 
include the fictitious Least Accepted Grade (LAG) candidate on every
ballot.  Whatever grade the voter gives to LAG is the lowest grade that
will count as approval on that ballot. The default LAG would be C.

Some of my Green friends would set the Least Accepted Grade at D, and give
Nader an A, Gore a D, and Bush, Buchanan, and so forth, F's.  It would
count instrumentally as approval for Nader and Gore, but they would have
the satisfaction of expressing their relative disgust for Gore.

Personally, I would set the LAG at F and leave Gore, Bush, etc. blank, to
express my utter contempt for all of the big name candidates except Nader.

EM list folk will tend to smile at this method: it's like putting a
Volks Wagon engine in a Carmen Ghia. (Well, that's how they come from the
factory, isn't it? ;-)

Now for the only objection that I have heard to this method: voters might
be upset if the official winner based on the approval scores differs from
the "expressive winner" (the one with the highest grade point average).

We feel bad when the winner of the popular vote doesn't get the electoral
vote, which is the one that counts in our current system (next to the
supreme court's opinion). 

Under IRV we would feel bad if the Condorcet Winner wasn't elected.

Others would feel bad if the Borda Count winner wasn't elected. Etc.

"But IRV doesn't ignore preference ballot information like Approval
ignores some of the Five Slot information." 

Are you sure about that? Think again. At each stage of the instant runoff
IRV makes irrevocable decisions about whom to eliminate while ignoring all
but the first column of preferences. IRV ignores and throws away perfectly
good information right and left.

I believe that the Five Slot Approval method would yield agreement between
the Approval winner and the expressive winner more often than IRV would
pick the Condorcet winner, and more often than the electoral vote agrees
with the popular vote in our current system. The candidate with the
highest pass/fail computed grade will almost always be the candidate with
the highest zero through four grade point average. 

The law of large numbers works for discrete random variables as well as
continuous ones.

I'm not claiming that a candidate's grade point average will come out the
same by both methods. I only claim that the relative order is very likely
to be maintained. At the end of a test with hundreds of questions the
determining factor of which student comes out on top is NOT whether or not
partial credit is given. We give partial credit only for educational and
psychological reasons.  We want to encourage more expression on the ballot
for similar reasons.

Note that the Electoral Vote method is a very drastic and biased
discretization, much more prone to distortion than our Grade-to-Approval
transformation. Yet it typically yields the popular vote winner. 

Well it doesn't really matter if these arguments persuade you or not,
because the objection can be fixed with a little spritz of Demoguard:

If the "expressiveness winner" turns out to be different from the Approval
winner, pick the one that the majority prefers in a head-to-head contest
as determined by the Five Slot Ballots.

Since the head-to-head comparison depends only on order of grades, there
is no incentive for inflation or deflation of grades. With this final
tweak, the method is still free of incentives for insincere expression.

So this method could be considered Majority Completed CR/Approval, in the
taxonomy of methods.

In my opinion, this is the version of CR/Approval that has the best chance
of competing with IRV in the minds of the public. 

Among methods based on IRV style preference ballots the one with the best
chance is Demorep's ACMA with the Minimum Acceptable Candidate feature (as
an Approval cutoff marker) for keeping the ballot in the pure ranking
category. We could call it MACACMA (Minimum Acceptable Candidate Approval
Condorcet Most Approval) if that acronym has not already been staked out
by the hamburger chains. 

Remember, Demorep's method is an Approval completed Condorcet method with
an Approval quota at the front end. My version and his differ by how to
mark the approval cutoff. He has the voters mark Yes and No,
respectively, next to the approved and disapproved candidates, along with
their numerical rank. I just have them rank the MAC candidate where they
want to leave off the Yes candidates and begin the No candidates.

Interestingly, it turns out that no candidate meets Demorep's approval
quota (a majority of Yes votes) if and only if the MAC candidate is the
Condorcet winner.

I hope we can get some good, sellable version of Approval or Condorcet,
like one of these, into the public arena before IRV spoils everything.


On Thu, 26 Apr 2001 DEMOREP1 at aol.com wrote:

> Mr. Simmons wrote in part-
> Give the win to the candidate with the highest median score, i.e. the 
> candidate whose list of scores has the highest median.
> ----
> D- There is more than a minor problem involving public education regarding 
> *ANY* *complex* reform method. 
> In other words -- there is a fairly large percentage of dumber than doorknob 
> voters.
> E.G. - the Florida 2000 President election -- circa 2-3 percent of the voters 
> cast illegal ballots regardless of the instructions on how to vote and 
> regardless of the system being used ---- paper ballots, punchcard ballots, 
> scan ballots, etc. (which is the subject of all sorts of private and public 
> studies and reports floating around in the U.S.A.).
> With median voting it would be necessary to vote in a maximum to minimum 
> range such as 100 to 0.
> I assume that equal number votes might have to be prohibited --- i.e. C 100, 
> B 99,
> F 0,  A 1, etc. (to prevent having ALL 100 or 0 votes).
> One can almost hear the moaning and whining about such dumb voters of the Fl 
> variety being even more confused (with more moaning and whining about 
> discrimination, etc.).
> I highly question whether anything more than simple YES/ NO (currently used 
> on ballot questions) and simple rank number voting (1, 2, etc.) can be passed 
> for candidate elections pending some major political I.Q. increase in the 
> general population -- noting that median voting would have elements of both 
> YES/ NO and rank number voting.
> Median voting should be applied to two of my standard examples--
> 26 A
> 25 B
> 49 Z
> 100
> 34 ABC
> 33 BCA
> 32 CAB
> 99

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