[EM] Participation Criterion

[Forest Simmons]

Here's the explanation of the choice of n, the number of times to
replicate ballot B in the procedure below for deciding whether or not the
voter who filled out B was "hopelessly optimistic."

If n were sufficiently large, say ten times the number N of voters, then
any reasonable method would give the win to someone with maximal rank or
rating on ballot B.

But we're more interested in what would happen if the voter of ballot B
had as many like minded friends as he could reasonably expect, i.e. the
number who actually voted like he did plus a reasonable margin of error.

The square root of N is on the order of one standard deviation for
estimates of this type, but in human affairs there seems to be an
irreducible one percent uncertainty even when the square root of N is
smaller than one percent of N, as is the case when N is greater than ten
thousand.

If you were to poll one hundred percent of a large human population about
how they would vote, at least one percent would either lie to you on
purpose, misunderstand your question, change their mind, or otherwise mess
up your estimate, so the .01*N margin of error cannot be improved upon in
typical public polls.

If adding this margin n=max(N^.5, .01*N) of identical ballots would yield
a winner C2 as good or better (as judged by ballot B)  than the candidate
C1 who would win without ballot B, then we would not say that (the voter
of) ballot B was "hopelessly optimistic," so the vote should stand.

Otherwise, our natural paternalism begs us to intervene and save the
hopeless optimists from whatever reason they had for casting a ballot that
could not help them (assuming sincerity).

Note that this increases the risk associated with voting insincerely,
since judgment of whether C2 is better than C1 for the voter of ballot B
is based on ballot B itself, which could back fire if this ballot is not
sincere.

Forest

On Mon, 27 Oct 2003, Forest Simmons wrote:

> 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
>
>
> ----
> Election-methods mailing list - see http://electorama.com/em for list info
>