[EM] Majority Approval Filter (MAF) - Draft 3

[Rob Lanphier]

On Thu, Dec 13, 2018 at 12:25 PM Ted Stern <dodecatheon at gmail.com> wrote:
> Your proposal makes sense to me for elections with a certain amount
> of consensus.  However, it would be prudent to ensure that your method
> can still yield a reasonable solution in the absence of clear consensus.
>
> For example, say candidate A1 is the approval winner with 40%.
> There are no candidates in the Plurality Approval or Opposition
> Candidate pool.

Hmmm, that does seem like a problem.  We should clarify one thing:
there would be a candidate in the Plurality Candidate Pool in this
scenario. In step 1b of Draft 3, candidate A1 enters the Plurality
Candidate Pool (as the Top Candidate), but as such, A1 would be the
only candidate that enters one of the three pools.  Because of step
4a, candidates with 39.9% or less are eliminated from consideration.
Because voters will probably be inclined to bullet vote in the early
uses of the system, this seems like a pretty likely scenario until
voters start considering candidates from adjacent parties.

Given that this is a system that is meant to be a replacement for
California's top-two system, I agree it makes sense to choose at least
two candidates when the Top Candidate has such low approval.  It
sounds like you're inclined to allow for three (or more) candidate
elections in the name of achieving the highest ballot satisfaction.
My fear is this scenario seems to imply an electorate that doesn't
fully understand approval voting, so forcing them to deal with 3+
candidate general elections in those circumstances seems more
dangerous than having a low Ballot Satisfaction Score.

For the sake of this discussion, I'd like to give the 75%, 50%, and
40% thresholds names, to make it clear that almost all of them are
subject to debate (and subject to tweaking):
75% - the "Ballot Satisfaction Threshold"
75% - the "Supermajority Threshold"
50% - the "Majority Threshold"
40% - the "Opposition Threshold"

I'll use these definitions in my response below...

Ted also wrote:
> My preference in such a situation would be to include
>
> A1, the approval winner,
> A2, the approval runner-up,
> B, the approval winner after excluding all ballots that approve A1,
> and must have excluded approval strictly less than 40%.

If we dropped the Opposition Threshold to 33%, would we pick up A2
and/or B in your example?  What about 20%?  How much does A2 add to
the Ballot Satisfaction Score?  What about B?

My reason for picking 40% as the Opposition Threshold is that it's a
good minimum aspiration for minority parties (like the California
Republicans in 2018).  MAF is admittedly built with an assumption of
being introduced in a highly-polarized two-party electorate over a
single left-right dimension.  That said, my assumption is that there
would be jurisdictions in California (e.g. in the Bay Area) where one
of the third parties might get higher approval than one of the
nationally-dominant two parties.  I think MAF gives those parties a
much better chance of building support than the status quo.

A nightmare scenario could envision in being too generous about
allowing candidates (my examples below use an electorate of 100 voters
rather than using percentages to avoid implying percentages of
percentages).:
Example 1 - Total - 100 voters
A1 - 40
A2 - 35 (20 of which also approve A1)
B - 25 (none of which approve A1)

Letting A1, A2, and B into the general election creates a confusing
general election, and I suspect could lead to a backlash for voting
reform if B somehow won.  It's hard to sympathize with B voters if B
were knocked out of during the primary, given that only 25% of voters
approve of B.

I would prefer to assume that such a result is the product of a
candidate set and electorate that doesn't yet have a sophisticated
strategy for MAF and also probably doesn't yet have a sophisticated
knowledge for an Approval Voting general election.  Moreover, due to
the political reality, it *may* be the case that a MAF primary would
need to be paired with a vote-for-only-one FPTP general election.  It
seems preferable to have the first three-or-more-candidate general
election caused by a MAF-primary to have a set of candidates that have
high approval rather than a tangled mess of low approval candidates.
I think the latter case would be way more likely to appreciate/desire
Approval Voting in the general, and make it less likely that the
winner of the general would be a champion for returning to the old
FPTP status quo.

Ted also wrote:
> If total approval for A1 and B is less than 75%, I would continue
> including the approval winner on ballots that exclude A1, B, and
> previous complementary opposition candidates, until the 75% threshold
> is met.  In the example above, A1's approval plus B's excluded approval
> could very easily fall below 75%, so it would likely be necessary
> to include candidate C, the candidate whose approval is highest on
> ballots that do not approve of either A1 or B.

In this case, I'd be inclined to coldly declare "elections have
consequences" and deal with the ramifications of only two candidates
advancing and the Ballot Satisfaction Score being way less than 75%

Now, the bigger question is: should A2 or B advance?  From the way you
phrased the example, it would appear that A1 + B gives a higher Ballot
Satisfaction Score than A1 + A2.  My "Example 1" tries to be
consistent with what I think you were describing in your A1, A2, B
example.  It seems to me that it should be possible tweak Draft 3 to
advance A1 and B.

For example, in step 4a, in reference to admitting a candidate to the
Opposition Candidate Pool the current Draft 3 says:
"If this candidate has less than 40% approval, no further candidates
qualify to be added to the Opposition Candidate Pool. Proceed to step
5."

Perhaps we can change it to read
"If this candidate has less than 40% approval, determine if this
candidate qualifies for the Opposition Candidate Pool in step 5."

Then we can insert a new step 5:
to read:
5. If the Ballot Satisfaction Score is greater than 50%, skip to step
6.  If the Ballot Satisfaction Score is under 50%, ensure at least two
candidates advance to the general election using the following steps:
5a. If there are no candidates in the Opposition Candidate Pool, find
the Non-advanced Candidate with the highest approval score.  If this
candidate increases the Ballot Satisfaction Score by more than 10%
(the "Candidate Differentiation Threshold"), add this candidate to the
Opposition Candidate Pool, and skip to step 6.  Otherwise, advanced to
step 5b.
5b. Consider each Non-advanced Candidate in order of approval score.
Find the first candidate who increases the Ballot Satisfaction Score
by more than the Candidate Differentiation Threshold (10%), and add
this candidate to the Opposition Candidate Pool, and skip to step 6.
Otherwise, advance to step 5c.
5c. Find the Non-advanced Candidate with the highest approval rating.
Add this candidate to the Opposition Candidate Pool, and advance to
step 6.
6. Candidate selection is complete. Advance all candidates in the
Supermajority Candidate Pool, the Plurality Candidate Pool, and the
Opposition Candidate Pool to the general election.

This new Step 5 looks complicated, and is admittedly imperfect, but I
think achieves the goal of ensuring that we advance two candidates.
Here's a worst-case scenario I can imagine with these rules is, with
100 voters:

Example 2 - Total 100 voters
A1 - 41 approve
A2 - 39 approve (31 of which also approve A1)
B - 10 approve (none of which approve of A1)
C, D, E, F etc- less than 4 approve of each

This would be a case where, under my new step 5 above, A1 and B
advance.  However, if A2 had just gotten to 40 votes, then A2 would
advance instead (regardless of how many of A2's voters also approved
of A1).  And if B had only gotten to 9 votes, then A2 would still
advance with 39 votes (despite a low Candidate Differentiation
Threshold of 8%).  Most importantly, if two more A2 voters had not
approved A1, then A2 would also advance instead of B (thus the
Favorite Betrayal of A2 by adding A1).   This example might be the
best argument against my proposed tweak, but I think it's sufficiently
pathological as to be unlikely.

A Candidate Differentiation Threshold of 10% intuitively feels like
the right number.  An argument can be made that this number should be
higher to ensure a higher Ballot Satisfaction Score, and to close off
selecting candidate B in my "Example 2" above.  But it seems like
*any* election that gets all the way to step 5a is going to be a mess,
so I'd prefer to keep the threshold suitably low to ensure that the
"skip to step 6" part usually gets enacted, rather than looping
through all of the low-approval candidates who couldn't muster 40%
approval.  Candidates should aspire to higher approval scores, not to
higher "candidate differentiation".

Ted also wrote:
> Unfortunately this method does require a recount, but you can get A1,
> A2 and B with just a single summable count (accumulating the pairwise
> array of votes for candidate i when candidate j is not approved), and
> in subsequent counts, that pairwise array can help find both C and D
> if necessary.

This is the part that I need to admit my inability to know if a system
is summable or not.  I know what summabilty is[1], and I agree it's
important, but I guess I don't yet know if these goals for MAF are
possible in combination:
1.  Ensure the candidate with the highest approval score (the Top
Candidate) advances to the general election
2.  When no candidate gets greater than 50% approval, limit the
candidates who advance in a MAF election to two
3.  When the Top Candidate gets less than 50% approval, ensure that a
very strong opposition candidate is selected, rather than a clone of
the Top Candidate (maximizing the Ballot Satisfaction Score)
4.  Ensure the resulting system is summable across voting precincts

Can we retrofit summability onto MAF, while still also only picking
two candidates when no candidate gets over 50% approval?

Rob

[1] Summability: https://electowiki.org/wiki/Summability_criterion