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

[Ted Stern]

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:
> > 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?


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


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 at robla.net> wrote:

> 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
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20181226/642d059b/attachment-0001.html>