[EM] Five Slot Method

Forest Simmons fsimmons at pcc.edu
Mon Apr 9 16:56:42 PDT 2001

Here's a single winner method with five distinctive slots for the

Here's how you fill in the slots:

First put your favorite and worst candidate, respectively, in slots one
and five.

Next put the better and worse of the two front runners, respectively, in
slots two and four.

Then fill the other candidates in relative to those. In particular, if
you have candidates between the two front runners, put some with one, some
with the other, and those that you would have to flip a coin over, put
them in slot three.

So in a big race each slot may have several candidates in it, though slot
three should be used sparingly.

One way to use these ballots consistent with the above instructions is in
an Approval runoff, where the cutoff for Approval is always the halfway
mark between the first and last non-empty slot.

If the number of slots between the first and last non-empty slots is odd,
then that cutoff will fall smack on top of one of the slots. That cutoff
slot counts as the average of the two extremes in the Approval
possibilities, i.e. if Approved=1 and Disapproved=0, then the candidates
in the cutoff slot get 1/2 point each . If Approved=1 and Disapproved=-1
(as in Demorep) then the current cutoff slot counts as zero in the current
round of the Approval runoff.

I believe that this method approximates Approval Runoff as well as can
be expected without the advantage of increased information with each round
that real Approval runoff has.

It has enough expressivity to make (almost) everybody happy along with a
very simple ballot:

Candidate  | Great |  O.K. | Neutral |  Bad  | Lousy
Jack J     |  ( )  |  ( )  |   ( )   |  ( )  |  ( )  
Jill K     |  ( )  |  ( )  |   ( )   |  ( )  |  ( )
Jane C     |  ( )  |  ( )  |   ( )   |  ( )  |  ( )
John G     |  ( )  |  ( )  |   ( )   |  ( )  |  ( )

The only disadvantage is that typical voters may not understand exactly
how their ballot is being used. 

The ones that care enough to learn to understand can.

If they know who their favorite, compromise, worst front runner, and worst
overall are, and put them in the corresponding slots, then they won't be
far off of their optimum strategy.

Note that if Nader, Gore, and Bush are the only candidates, and they go to
slots one, two, and four, respectively, then Nader and Gore are approved
in the first round, and Bush disapproved.  Since Bush doesn't have
majority support, he is eliminated. The next round is between Nader and

There it is.


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