[EM] Approval-based replacement for jungle primary

[Rob Lanphier]

Hi Ted,

Thanks for helping refine the idea.  More inline:

On Mon, Dec 3, 2018 at 12:57 PM Ted Stern <dodecatheon at gmail.com> wrote:
> In that light, I'm getting toward being on board with your MAF idea.

Cool!

> However, I'm still unclear on how you set up the opposition candidate pool.

So am I.  Before I respond to the rest of this, I'm going to lay out
some goals that occurred to me as I started thinking through my reply.
As I type these words, I have no idea whether or not your method
complies with the goals I set out.

Here's the main goal: an Approval-based system that advances truly
viable candidates to the general election, creating a ballot approved
by a large portion of the electorate (i.e. with a high ballot
satisfaction score)

Now to assign some arbitrary metrics to the subjective terms expressed
or implied above:
*  "viable candidate" - a candidate who receives greater than 25%
approval in the primary
*  "truly viable candidate" - a candidate who receives greater than
50% approval in the primary
*  "marginally viable candidate" - a candidate who receives less than
50% approval, but greater than 25%
*  "non-viable candidate" - a candidate who receives less than 25%
approval in the primary
*  "ballot satisfaction score" - percentage of primary election voters
who approve of at least one candidate on a ballot containing a given
subset of primary election candidates
*  "high ballot satisfaction score" - Greater than 90% ballot satisfaction

A rough outline for MAF version 3:
*  Identify the approval winner, and advance that candidate
*  Advance all truly viable candidates (>50% approval)
*  Advance a small number of marginally viable candidates to create a
ballot with a high ballot satisfaction score (>90% ballot
satisfaction)

That last step is one that I'm still trying to figure out.  There's a
couple of testcases that I'm still trying to think though, and design
MAF v3 around:

Testcase A: Let's say that after we select all truly viable
candidates, we only have a ballot satisfaction score of 85%.  Let's
also say that among the marginally viable canidates we have candidate
A1, who is the next highest rated candidate that has 49.9% approval,
but only just barely brings the ballot satisfaction score to 90%.
Let's say there's a different candidate (A2) who only receives 35%
approval, but brings the ballot satisfaction score up to 99%.  I think
my preference in that case is to have an algorithm that selects
candidate A1.

Testcase B: Once again, after all truly viable candidates (TVCs), we
only have a 85% ballot satisfaction.  Let's say that B1 is next
highest, with 45%, but only brings the ballot satisfaction to 86%.
Next is B2, with 44%.  Adding B2 to the ballot also only gets us to
86% satisfaction, and adding both B1 and B2 only gets us to 87%
(TVCs+B1+B2=87%).  Let's say we keep stepping through the marginally
viable candidates, and we only get 1% at a time, such that
TVCs+B1+B2+B3+B4+B5=90%.  However, let's also say there's a candidate
B9 that only has 35% overall approval, but adding that candidate alone
would improve the ballot satisfaction score to 99%.  I *think* I would
prefer an algorithm that selects B9 rather than adding (B1, B2, B3,
B4, B5).

It could be very difficult to find an elegant algorithm that selects
A1 for Testcase A, and B9 for Testcase B.  Now to see what your
proposal does....

> So I understand you have the Approval Winner (AW), plus, if AW's
> approval is less than a threshold, all candidates with approval > 50%
> and complementary approved candidates.  The question is, after you have
> chosen the first complementary approved candidate, the candidate who is
> approved on the most ballots that don't approve AW, how do you form the
> complement for the other opposition candidates?

That's what I'm still struggling with.

> In my opinion, when you have a runner up highly approved candidate, the
> complementary candidate should be the candidate with highest approval on
> ballots that don't approve of the runner-up, not the AW.  And if that
> complementary opposition candidate is already in the runoff, take the
> next-highest approved on those ballots until you find a new candidate.

I think we agree on the first point.  The complementary opposition
candidate should be complementary to the candidate(s) that barely get
greater than 50% approval, not to the Approval Winner (AW).  The best
algorithm may involve starting with the truly viable candidate with
the lowest approval rating (e.g. a candidate with 50.01% approval) and
working our way up to the AW until we have an acceptable ballot
satisfaction score.

> For example, if the approval winner is A with approval less than the
> dominance threshold, also include complementary opposition candidate B
> (highest approved on ballots that don't approve A), plus highly approved
> runner up C with approval > 50%, plus complementary opposition candidate
> D (highest approved candidate who is not A or B, on ballots that don't
> approve C).  If there is another highly approved runner up E with approval
> > 50%, then include complementary candidate F, who is the highest approved
> non-(A,B,C,D) candidate on ballots that don't approve of E.  And so on.

I fear that this algorithm would bias toward selecting candidates A2
and B9 in my test cases up above.  Both of those candidates are likely
to be the most polarizing candidates, most inclined to rile up their
base voters without aspiring to achieve 50% approval.

An elegant algorithm that selects A1 and B9 might be hard to come by.
My preference for B9 over (B1, B2, B3, B4, B5) is not very strong, and
in fact, it may be that reducing the minimum ballot satisfaction score
from 90% to 85% might be the right solution for that particular test
case (thus not allowing B1, B2, B3, B4, B5 or B9).  "90%" and "85%"
are arbitrary percentages, and in fact, maybe 75% is high enough.
There would be a certain elegance to choosing the same percentage
(75%) for both the "highly approved candidate pool" and the "high
ballot satisfaction score".  That would be great motivation for
candidates to try to get to 75% approval; by doing so, they could lock
out marginally viable candidates from the general election ballot.
But candidates getting greater than 75% approval would still have to
face other highly viable candidates (candidates between 50% and 75%)
in the general election.

Rob