Hi Rob,

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.

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 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.

I think including A2 (even if A2 is different than B or C) is important
because with less than 50%, there isn't a strong consensus on A1.

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.

On Sun, Dec 9, 2018 at 8:32 PM Rob Lanphier robla@robla.net wrote:

On Thu, Dec 13, 2018 at 12:25 PM Ted Stern dodecatheon@gmail.com wrote:

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:

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:

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:

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

Hi Rob,

You discussed a lot of complicated stuff.  For a public proposal, I think
you should consider that it probably needs to be made as simple as possible.

Referring to your final goals for MAF:

Ted also wrote:

In reverse order:  it is possible to tabulate the array W[x,y] in a
summable manner, where W is the approval for X when Y is not approved.
Then for a given Approval Winner A1, the complementary approval winner is
the candidate with highest value in W[*,A1] (excluding W[A1,A1]).  Call the
complementary approval winner B.  Then Approval[A1] + W[B,A1] , call this
TA[A1,B], gives you the number of ballots that approve of either A1 or B.

I think it would be appropriate to have at least A1 and B as runoff
candidates when A1 has approval <= 50%.  I think we agree on that?

The only remaining question is whether you want to include more
candidates.  If TA[A1,B] is not sufficiently large, it seems that you would
want to look for the approval winner on ballots that don't approve of
either A1 or B.  It would not be practical, currently, to tabulate an array
to find that winner summably, therefore you would have to make an
additional count.  So if summability is an issue for you, that's the best
you can do.

The more I think about this, the more I think that we really need to step
away from calling MAF, or any first round of a two-round election, a
"primary".  It would be better to have a fairly robust single-winner
election with a runoff contingency.  That would have the advantage of
putting more stakes on the first round, and getting voters to pay attention
to the candidates.  When viewed as a primary, many voters currently don't
bother to do their homework, if they participate at all.

So I think that you could add another goal for MAF, or any other
up-to-two-round method:

5. Let the stakes on the first round be high enough so that there is a

This line of thinking has led me to re-examine Kevin Venzke's Improved
Condorcet Approval (http://nodesiege.tripod.com/elections/#methica), which
is "nearly" Condorcet and is, I think, more of an improvement on Approval
that retains FBC compliance than a Condorcet method.

Using 3 ratings (Preferred, Approve, Disapprove), with Kevin's original
"tied-at-top" defeat rule, there is the potential to find a "near"
Condorcet winner while FBC is satisfied, with burial resistance.  As part
of a general-election + contingency runoff method, you could use it as

1. If the ICA winner has > 50% approval, they win outright.
2. If the ICA winner has <= 50% approval, have a second round with the ICA
   winner, the overall Approval winner (if different), and the ICA winner's
   approval complement.
3. In the final round, also use ICA.

I think this would have my desired effect of increasing the stakes for the
election.

I'm debating whether including the strict Condorcet winner (if one exists
and is different from the first round ICA winner) would be useful or
counterproductive.

On Wed, Dec 19, 2018 at 2:23 PM Rob Lanphier robla@robla.net wrote:

Hi Ted,

Long writeup below.  Short summary: you're right that an electoral
reform proposal needs to be simple, and that MAF is probably too
complicated at this point (though that didn't stop me from publishing
"Draft 4").  Some of the folks discussing this on reddit seem to be
converging around a much simpler proposal, described in more detail
below.

On Wed, Dec 26, 2018 at 3:37 PM Ted Stern dodecatheon@gmail.com wrote:

Agreed.  Near the end of this email, I talk about the simple proposal
that was floated over in the /r/ApprovalCalifornia subreddit.  It gets
a lot easier to devise a simple replacement for the primary if the
reform effort also involves switching the general election to Approval
Voting (or some other election method that provides an effective and
fair system in an election with 3 or more candidates)

I wrote:

Ted Stern replied:

Thanks for this explanation of the W[x, y] matrix.  Assuming I
understand this correctly, I offer some musing about a complicated
direction to take things below...

With gritted teeth, I'll say "yes" to that.  I don't especially like
saying "yes" to that unconditionally, though, since it's possible for
B to have a very low overall approval (i.e. "Approval[B]" in your
notation).  I'll grant that in cases where A1 has low overall approval
(i.e Approval[A1]<=50%), then it's very unlikely that B's overall
approval rating will be much more than 10% lower.

What I dislike about this: it motivates candidates to pursue
maximizing their votes among opposition supporters ("TA[A1,B]" for
candidate "B" in your notation) rather than pursuing higher overall
approval ratings ("Approval[B]" in your notation).  I think Candidate
B should still want to get approval votes from voters who have already
decided they will approve of candidate A1.  Declaring B deserves to
advance to the general election gives B license to pursue a cynical
strategy of ignoring A1 supporters (or worse, scapegoating A1
supporters).

Let's explore the practicality of this a little bit.  This notion of
summable W[x, y] matrices tempts me to come up with systems that rely
on W[x, y1, y2], W[x, y1], and W[X, y2], matrices from each precinct,
where W is the approval for X when Y1 and/or Y2 are not approved.  I
can see the danger of allowing for W[x, y1....yn] for arbitrary values
of "n", but I'm curious: is n=1 truly the practical upper bound of n?

That question is mainly for theoretical fun. From a practical
perspective, I prefer developing a system where candidates mainly
focus on their own approval, regardless of whether voters disapprove
of their opposition.

That doesn't seem like an effective tactic to me.  I shudder to
imagine saying: "Ok, everyone, as a first step of reform, we need
everyone to stop using certain words. Smart people tell us that
'primary' is a bad word"  ;-)

I fear that this sort of voter reform will likely be unpopular among
voters. It's hard to blame voters for their disinclination to research
the full field of candidates in each race, when each race frequently
has over 10 candidates.  Complaining that voters "don't bother to do
their homework" is not effective advocacy.  This sort of preachy
rhetoric is why many voters hate third parties, since third party
advocates seem to frequently blame their losses on voters who
allegedly can't be bothered to learn about candidates other than
Democrats or Republicans.

Moreover, as I've long been saying, a two-stage election is better
than a one-stage election, especially for California.  Candidates
deserve two elections worth of vetting.  Moreover, if we can develop a
system that effectively screens out crackpots in the primary, then
voters are more likely to take the general election seriously.

I've updated MAF to "Draft 4", which is essentially the same set of
modifications I proposed a couple weeks ago:
https://electowiki.org/wiki/MAF

The changes I made unfortunately make it longer (and implicitly more
complicated), but I think it's possible to simplify for purposes of
explanation by summarizing the 6 steps as follows:

1. Advance the "Top Candidate"
2. Advance all candidates who receive over 50% approval
3. Skip to step 6 if the Ballot Satisfaction Score is over 75% (where
   "Ballot Satisfaction Score" is the percentage of the electorate which
   approves of at least one candidate on a given ballot)
4. Add some candidates with greater than 40% approval to boost the
   Ballot Satisfaction Score
5. Deal with some special cases where the Ballot Satisfaction Score is
   still under 50% after step 4
6. Candidate selection is complete

This seems complete enough for most contexts (assuming access to a
detailed version remains available).

Kevin's ICA system looks intriguing, and one that I feel like I should
spend some time learning at more than a cursory level.  How does it
stack up next to STAR?  Is there an explanation of ICA out there that
a layperson would be able to understand?

My fear is that a 3-rating ballot creates ballot complexity, and makes
it more likely that IRV supporters will successfully insist that IRV
should be used instead.

I'm afraid that an ICA-based system would be too complicated to be
politically viable in California.  I'm becoming convinced that MAF is
also too complicated, though I'm not giving up on it yet.  [MATT] may
still be simple enough, though per my concerns above, it may punish
very good candidates who don't garner the approval of voters that
support the frontrunner.
[MATT]: https://electowiki.org/wiki/Maximum_approval_top-two

A few of us had a conversation over on reddit in the new
/r/ApprovalCalifornia subreddit.  That conversation converged around
having an Approval Voting-based primary with simply "all candidates
with greater than X% of approval qualify":
https://www.reddit.com/r/ApprovalCalifornia/comments/a7953q/an_update_for_rapprovalcalifornia_121818/

With a system that guarantees advancement for primary candidates who
receive less than a majority, it's theoretically possible for a
coordinated minority to overwhelm the general election ballot with
clones candidates.  In practice, it seems like a high enough X
threshold (e.g. 40%) would make this entirely impractical, and even
X=20% makes it unlikely to be an effective tactic.

Let's revisit your proposed goal #5:
"5. Let the stakes on the first round be high enough so that there is
a reasonable chance for a single winner, with no runoff."

A threshold of X=40% (or even X=30%) would seem to make it likely that
only one candidate would emerge in a splintered race, thus making it
effectively a one-round election (since the winning candidate would
run unopposed in the general election)  Would that make the stakes
high enough?

One thing that bothers me about having an "X% of voters" threshold in
a primary election: it motivates a well-coordinated fringe candidates
to drive down turnout, and hope that they can get X% of a small number
of voters.  One possible solution to that problem: base the minimum
threshold for getting through the primary to be "X% of the total votes
cast for Governor at the last gubernatorial election", similar to the
signature requirements for ballot measures in California:
https://ballotpedia.org/Signature_requirements_for_ballot_measures_in_California

That removes some of the motivation that candidates might have to
drive down turnout for their competitors, and would hopefully keep
them focused on turning out more voters to approve of them.

Rob