[EM] Yes/?/No

Forest Simmons fsimmons at pcc.edu
Sat Oct 31 18:03:32 PDT 2020

Approval is one of the easiest election methods to explain and to
understand; the ballots are identical to traditional FPP ballots except the
instructions now say to mark the names of all of the candidates that you
like instead of only one of them. As before the winner is the candidate
with the greatest number of likes.

But what about the candidates that you just like a little bit? Do you
include them or not? Where do you draw the line between like and not like?

Lots of perfectly adequate advice has been given on this topic, including
"Approve everybody you definitely like better than the FrontRunner,
including the FrontRunner herself if you definitely like her or if her
strongest challenger is definitely worse than she is."

But trying to apply this excellent advice to a long list of candidates can
be a very daunting task for the typical voter.

A much easier task would be the following: write "yes" next to the names of
the candidates that you definitely like, write "no" next to the names of
the candidates that you definitely dislike, and put a "?" next to the
remaining names.

Now we are faced with the question, what do we do with these ballots? How
do we count them?

 There are several possibilities some better than others. One obvious but
not so good idea would be to elect the candidate with the greatest
difference between the number of yes votes and the number of no votes, or
equivalently, the candidate with the greatest number of yes votes plus half
the number of question marks.

This method suffers from the Dark Horse defect; a candidate with neither
any yes or no votes could win solely on the basis of being an unknown
quantity if for example all the other differences turned out to be negative.

Another method is to have a runoff between the candidate with the greatest
number of yes votes and the candidate with the fewest no votes.

The worst defect of this method is the inconvenience of the runoff.

One way to overcome this inconvenience is for each voter to designate a
candidate as proxy in the runoff.

Which brings us to the method that I like best: the voters designate
proxies to resolve the question marks on their ballots. Once the question
marks are resolved the candidate with the most yes votes is the same has
the candidate with the fewest no votes, so no runoff is necessary.

There are two possible ways to involve the proxies: (1) have them commit
ahead of time how they will resolve any question marks, in other words have
them publish prior to the election which of the candidates they approve and
which ones they don't. (2) allow the proxies to use the delegated question
marks as bargaining chips before deciding which candidates to approve or

Intermediate between these two possibilities is (3) require the proxies to
commit to preference orders before the election, but allow them to choose
their respective approval cut-offs within these rankings after the haggling

I like the second option best but I think option three is a satisfactory
compromise between the first two.

A summable data structure is easy to devise for realizing any version of
this method.

Comments? Suggestions? Especially needed are suggestions for PR venues for
selling the superiority of Approval voting for public elections over any
other election method, in view of the extreme ease of optimal voting for
any voter that this proposed implementation provides.

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