[EM] Participation Criterion

[Forest Simmons]

It seems a shame that some otherwise excellent methods have the defect of
counting ballots that work against the wishes of the voter; the voter
would have been happier with the outcome of the election if he (and
possibly like minded voters) had stayed at home and left the voting to
others.

I'm a math instructor, so I see something analogous to this all of the
time.  Students want an extra credit problem that cannot hurt their grade
if they botch it.

Sometimes I cave in from sympathy and give them an extra problem on the
test that I average in with the other problems only if it will not hurt
them.

If you have a favorite method that fails the Participation Criterion,
consider the following modification designed to not count ballots that
would work against the intentions of the voter (assuming sincere ballots):


Let N be the total number of ballots cast.  Let n be the square root of N
or one percent of N, whichever is larger.


For each ballot B, apply your method twice ... once to the set of all
ballots except B, and once to the set of ballots with B included and
replicated n times.

Let the letters C1 and C2 represent the respective winners for the two
distinct ballot sets.

If C2 is ranked or rated lower than C1 on ballot B, then label the ballot
with the letter "HO" for "hopelessly optimistic."

After this procedure has been applied to each of the ballots, remove all
of the ballots with the HO label, as a favor to their voters, and perhaps
tabulate them separately for educational purposes.

Apply your method to the remaining ballots to determine the winner.


I'll explain the choice of n in a separate posting ... I'm almost late for
class.

Forest