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

classic Classic list List threaded Threaded
5 messages Options
Reply | Threaded
Open this post in threaded view
|

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

Rob Lanphier
Hi everyone,

I've made some progress on the Majority Approval Filter proposal,
which (as of December 7) I've published as "Draft 3" on electowiki;
<https://electowiki.org/wiki/MAF>

The current draft is more verbose, but I hope that it's clearer and
more straightforward than the last two drafts.  I've also published a
blog post introducing latest draft on my personal blog[1] and on
Medium[2]
[1]: https://blog.robla.net/2018/12/09/replacing-the-jungle-primary-december-edition/
[2]: https://medium.com/@robla/replacing-the-jungle-primary-december-edition-cf971801402c

Here's my simplified version of the explanation:
1. Select the candidate who receives the highest approval rating
2. Also add all candidates who receive greater than 50% approval
3. Possibly add opposition candidates if doing so is necessary to
ensure that at least 75% of the electorate has someone they hope to
vote for in the general election.  Limit the number of candidates who
qualify with 40%-50% approval to be less than or equal to the number
of candidates who qualify with 50%-75% approval.

I realize there's some handwaving in this simplified version, so I'm
including the full text of the important bits below.

Thanks especially to Ted Stern, but also to everyone who replied on
the "[EM] Approval-based replacement for jungle primary" thread.  I
greatly appreciate the later replies from Kristofer Munsterhjelm and
Richard Fobes, and I owe you two more detailed and direct replies to
their emails now that I've published Draft 3.

Rob
--------------
Addendum - Full definition of Majority Approval Filter (Draft 3)
Copied from <https://electowiki.org/wiki/MAF>):

### Goal ###

A set of rules for holding a primary election with an Approval
Voting-style ballot, providing motivation for all candidates to achieve
the highest approval rating, and resulting in a general election Ballot
Satisfaction Score of at least 75%. The "Ballot Satisfaction Score" is
the percentage of the electorate which approves of at least one
candidate on a given ballot.

### Pools ###

Candidates advancing to the general election must qualify for one of the
following "Pools". Candidates that don't qualify for one of the Pools
below are "Non-advanced Candidates". By default, all candidates are
Non-advanced Candidates until they qualify for one of these Pools:

-   "Supermajority Candidate Pool" - all candidates who receive greater
    than 75% approval
-   "Plurality Candidate Pool" - all candidates who receive greater than
    50% approval, but do not qualify for the Supermajority Candidate
    Pool. If no candidate receives greater than 50% approval, this pool
    will contain the leading candidate, who may have less than 50%
    approval.
-   "Opposition Candidate Pool" - a subset of candidates who receive
    greater than 40% approval, but do not qualify for the Plurality
    Candidate Pool

### Rules ###

Sequential steps for filling the above Pools with qualified candidates:

1.  Select the candidate who receives the highest approval rating. This
    is the "Top Candidate" and automatically qualifies for the general
    election ballot by one of the following rules:
    -   1a. If the Top Candidate receives greater than 75% approval, add
        this candidate to the Supermajority Candidate Pool.
    -   1b. If the Top Candidate receives less than 75% approval, add
        this candidate to the Plurality Candidate Pool.
2.  Complete the Supermajority Candidate Pool and the Plurality
    Candidate Pool using the following rules:
    -   2a. Add any Non-advanced Candidates with greater than 75%
        approval to the Supermajority Candidate Pool
    -   2b. Add any Non-advanced Candidates with less than 75% approval,
        but greater than 50% approval to the Plurality Candidate Pool
3.  Evaluate the Ballot Satisfaction Score (defined above) using the
    following rules:
    -   3a. If the Ballot Satisfaction Score is greater than 75%,
        candidate selection is complete. Skip to step 5
    -   3b. If the Ballot Satisfaction Score is less than 75%, proceed
        to step 4.
4.  If there is one or more candidates in the Plurality Candidate Pool,
    attempt to add an equal number qualified candidates to the
    Opposition Candidate Pool, evaluating each Non-advanced Candidate
    using the following steps
    -   4a. Find the Non-advanced Candidate with the highest approval
        score.
        -   If this candidate has less than 40% approval, no further
            candidates qualify to be added to the Opposition Candidate
            Pool. Proceed to step 5.
        -   If this candidate has greater than 40% approval, add this
            candidate to the Opposition Candidate Pool, then proceed to
            step 4b.
    -   4b. Compare the size of the Plurality Candidate Pool and the
        Opposition Candidate Pool
        -   If the Plurality Candidate Pool has more candidates than the
            Opposition Candidate Pool, skip back to step 3.
        -   If the Opposition Candidate Pool contains an equal number of
            candidates to the Plurality Candidate Pool, proceed to
            step 5.
5.  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.
----
Election-Methods mailing list - see http://electorama.com/em for list info
Reply | Threaded
Open this post in threaded view
|

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

Ted Stern
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 <[hidden email]> wrote:
Hi everyone,

I've made some progress on the Majority Approval Filter proposal,
which (as of December 7) I've published as "Draft 3" on electowiki;
<https://electowiki.org/wiki/MAF>

The current draft is more verbose, but I hope that it's clearer and
more straightforward than the last two drafts.  I've also published a
blog post introducing latest draft on my personal blog[1] and on
Medium[2]
[1]: https://blog.robla.net/2018/12/09/replacing-the-jungle-primary-december-edition/
[2]: https://medium.com/@robla/replacing-the-jungle-primary-december-edition-cf971801402c

Here's my simplified version of the explanation:
1. Select the candidate who receives the highest approval rating
2. Also add all candidates who receive greater than 50% approval
3. Possibly add opposition candidates if doing so is necessary to
ensure that at least 75% of the electorate has someone they hope to
vote for in the general election.  Limit the number of candidates who
qualify with 40%-50% approval to be less than or equal to the number
of candidates who qualify with 50%-75% approval.

I realize there's some handwaving in this simplified version, so I'm
including the full text of the important bits below.

Thanks especially to Ted Stern, but also to everyone who replied on
the "[EM] Approval-based replacement for jungle primary" thread.  I
greatly appreciate the later replies from Kristofer Munsterhjelm and
Richard Fobes, and I owe you two more detailed and direct replies to
their emails now that I've published Draft 3.

Rob
--------------
Addendum - Full definition of Majority Approval Filter (Draft 3)
Copied from <https://electowiki.org/wiki/MAF>):

### Goal ###

A set of rules for holding a primary election with an Approval
Voting-style ballot, providing motivation for all candidates to achieve
the highest approval rating, and resulting in a general election Ballot
Satisfaction Score of at least 75%. The "Ballot Satisfaction Score" is
the percentage of the electorate which approves of at least one
candidate on a given ballot.

### Pools ###

Candidates advancing to the general election must qualify for one of the
following "Pools". Candidates that don't qualify for one of the Pools
below are "Non-advanced Candidates". By default, all candidates are
Non-advanced Candidates until they qualify for one of these Pools:

-   "Supermajority Candidate Pool" - all candidates who receive greater
    than 75% approval
-   "Plurality Candidate Pool" - all candidates who receive greater than
    50% approval, but do not qualify for the Supermajority Candidate
    Pool. If no candidate receives greater than 50% approval, this pool
    will contain the leading candidate, who may have less than 50%
    approval.
-   "Opposition Candidate Pool" - a subset of candidates who receive
    greater than 40% approval, but do not qualify for the Plurality
    Candidate Pool

### Rules ###

Sequential steps for filling the above Pools with qualified candidates:

1.  Select the candidate who receives the highest approval rating. This
    is the "Top Candidate" and automatically qualifies for the general
    election ballot by one of the following rules:
    -   1a. If the Top Candidate receives greater than 75% approval, add
        this candidate to the Supermajority Candidate Pool.
    -   1b. If the Top Candidate receives less than 75% approval, add
        this candidate to the Plurality Candidate Pool.
2.  Complete the Supermajority Candidate Pool and the Plurality
    Candidate Pool using the following rules:
    -   2a. Add any Non-advanced Candidates with greater than 75%
        approval to the Supermajority Candidate Pool
    -   2b. Add any Non-advanced Candidates with less than 75% approval,
        but greater than 50% approval to the Plurality Candidate Pool
3.  Evaluate the Ballot Satisfaction Score (defined above) using the
    following rules:
    -   3a. If the Ballot Satisfaction Score is greater than 75%,
        candidate selection is complete. Skip to step 5
    -   3b. If the Ballot Satisfaction Score is less than 75%, proceed
        to step 4.
4.  If there is one or more candidates in the Plurality Candidate Pool,
    attempt to add an equal number qualified candidates to the
    Opposition Candidate Pool, evaluating each Non-advanced Candidate
    using the following steps
    -   4a. Find the Non-advanced Candidate with the highest approval
        score.
        -   If this candidate has less than 40% approval, no further
            candidates qualify to be added to the Opposition Candidate
            Pool. Proceed to step 5.
        -   If this candidate has greater than 40% approval, add this
            candidate to the Opposition Candidate Pool, then proceed to
            step 4b.
    -   4b. Compare the size of the Plurality Candidate Pool and the
        Opposition Candidate Pool
        -   If the Plurality Candidate Pool has more candidates than the
            Opposition Candidate Pool, skip back to step 3.
        -   If the Opposition Candidate Pool contains an equal number of
            candidates to the Plurality Candidate Pool, proceed to
            step 5.
5.  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.
----
Election-Methods mailing list - see http://electorama.com/em for list info

----
Election-Methods mailing list - see http://electorama.com/em for list info
Reply | Threaded
Open this post in threaded view
|

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

Rob Lanphier
On Thu, Dec 13, 2018 at 12:25 PM Ted Stern <[hidden email]> 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
----
Election-Methods mailing list - see http://electorama.com/em for list info
Reply | Threaded
Open this post in threaded view
|

Re: [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 <[hidden email]> wrote:
On Thu, Dec 13, 2018 at 12:25 PM Ted Stern <[hidden email]> 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

----
Election-Methods mailing list - see http://electorama.com/em for list info
Reply | Threaded
Open this post in threaded view
|

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

Rob Lanphier
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 <[hidden email]> 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
supporters).

> 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:
<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).

> 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":
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
----
Election-Methods mailing list - see http://electorama.com/em for list info