[EM] Condorcet vs Approval

[Forest Simmons]

I have ambiguous feelings about my two favorite methods.

Sometimes it seems like Condorcet is over-elaborate, making fine
distinctions between the deck chairs on the sinking Titanic. (How's that
for a mixed metaphor?)

On the other hand, there are times when Approval strategy leaves me in a
quandary about whether or not I should extend my approval down into the
40% utility level to help keep a zero utility candidate out of office.

I have a couple of suggested compromises starting with Condorcet and
moving towards Approval, but stopping short of ordinary Approval.

I.  Condorcet.  I prefer the version of Condorcet that allows voters to
give a partial preference list, with all unlisted candidates considered to
fall below the last listed candidate. (These implicit preferences are
counted along with the explicitly marked preferences.)  If voters were
instructed to list (only) their APPROVED candidates in order of preference
(and leave their unapproved candidates off of the preference list), this
would be one small step in the direction of approval.

To put teeth into the instruction, voters should be informed that if there
is a Condorcet cycle of winners, then that tie will be resolved by the
approval scores ... all of the listed candidates will be considered
approved, and the non-listed candidates unapproved. 

Alternatively, before this drastic cycle breaker is applied, the
preferences among the approved could be discounted by half to see if that
less drastic action would resolve the cycle.

II. In this second method the voters are instructed to indicate which
candidates are approved and which candidates are highly approved, and to
cross off the other candidates from the ballot, for good measure. 

The ballots will be scored by the Condorcet method (head-to-head counts)
with H>A, H>U, and A>U, where H, A, and U stand for any members of Highly
approved, Approved, and Unapproved, respectively.

If this method results in a Condorcet cycle among the top candidates, that
cycle can be broken by gradually discounting the H>A preferences as in
Method I above. 

Well, there they are.

Note that both of these methods retain the same level of immunity from
insincere voting that Condorcet and Approval enjoy.  In particular, in
method II, if I prefer C to D, and I confer High Approval status on D,
then there is no reason to with-hold that status from C. 

In method II how would I decide where to draw the lines between the
three categories?

I would draw the line between Approved and Unapproved on the same basis
that I do now.  After having done that I would choose between the Highly
Approved and the (merely) Approved using exactly the same strategy with
the Unapproved totally removed from consideration.  (Pretend they don't
even exist.) For this inside strategy calculation the probabilities and
expectations would be conditioned on the event that the winner is to be from
among the approved. 

One simple way to mark the ballots for method II would be to cross off
all the Unapproved names (with one or more lines through the name so that
it can no longer be read by the machine) and to mark the Highly approved
names by filling in the machine readable dot.  Any name that was not
crossed out or marked by the usual dot would be considered (merely)
Approved.

If nothing else, these two methods help elucidate the close relationship
between Condorcet and Approval.

Bye for now,

Forest