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

Rob Lanphier robla at robla.net
Fri Dec 28 22:29:09 PST 2018

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

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

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

Ted Stern replied:
> [...] 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.

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...

> 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?

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

> 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.

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.

> 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".

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"  ;-)

> 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 reasonable chance for a single winner, with no runoff."

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:

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).

> 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.

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

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":

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:

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.


More information about the Election-Methods mailing list