[EM] CMU's "cake cutting" solution to gerrymandering

[Rob Lanphier]

Hi folks,

I see this article making the rounds among some of my friends:

<https://www.axios.com/researchers-propose-a-gaming-solution-to-gerrymandering-2507567048.html>

I haven't done the deep dive on this yet, and have some gut instinct
reactions, but I'm curious: what do you all think? Assuming dividing
states into voting districts is a necessary evil, is this as good a
way as any to do it?

Rob
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[Kristofer Munsterhjelm]

Post by Rob Lanphier
Hi folks,
<https://www.axios.com/researchers-propose-a-gaming-solution-to-gerrymandering-2507567048.html>
I haven't done the deep dive on this yet, and have some gut instinct
reactions, but I'm curious: what do you all think? Assuming dividing
states into voting districts is a necessary evil, is this as good a
way as any to do it?

I suppose it might lead to "bipartisan gerrymanders", where the parties
reach an agreement about how which incumbents should survive until the
next election, rather than the voters being the ones to choose. In
effect, you would get something between closed party list and SNTV, with
two parties.

Furthermore, the proposal doesn't specify who gets to participate in the
cake-cutting process. If it's the parties who are currently in power,
rather than the cake-cutting process being done just after the election
(before seats are given out), then incumbent parties could cooperate to
block a growing challenger party by cracking the challenger party's
support across multiple districts. Thus it could strengthen Duverger's law.

I would prefer the independent commission solution if the commissions
can be trusted to be independent. If they can't be, then closed party
list with a (variable, implicit) threshold could be preferrable to the
kind of one-sided gerrymander that exists now.
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[robert bristow-johnson]

Post by Kristofer Munsterhjelm

Post by Rob Lanphier
<https://www.axios.com/researchers-propose-a-gaming-solution-to-gerrymandering-2507567048.html>

i read through this article and got the gist of it.

Post by Kristofer Munsterhjelm

Post by Rob Lanphier
I haven't done the deep dive on this yet, and have some gut instinct
reactions, but I'm curious: what do you all think? Assuming dividing
states into voting districts is a necessary evil, is this as good a
way as any to do it?

I suppose it might lead to "bipartisan gerrymanders", where the parties
reach an agreement about how which incumbents should survive until the
next election, rather than the voters being the ones to choose. In
effect, you would get something between closed party list and SNTV, with
two parties.
Furthermore, the proposal doesn't specify who gets to participate in the
cake-cutting process. If it's t1/he parties who are currently in power,
rather than the cake-cutting process being done just after the election
(before seats are given out), then incumbent parties could cooperate to
block a growing challenger party by cracking the challenger party's
support across multiple districts. Thus it could strengthen Duverger's law.
I would prefer the independent commission solution if the commissions
can be trusted to be independent. If they can't be, then closed party
list with a (variable, implicit) threshold could be preferrable to the
kind of one-sided gerrymander that exists now.

and i think that algorithms that make a meaningful measure of compactness or convexity of the districts is important to use.  and i think they could weight this convexity measure along with other properties that maybe can have objective measurement.  like how well
"communities" (however they are defined) are kept intact.  so when district boundaries for some legislative district align well with existing city or town or county boundaries, that gets you points of some weight also.  but also given demographic maps of cultural
populations.  of course a salient measure is the variance of the district population (or a 1/C scaling of the population if the district has C candidates at large).
another salient metric is, of course, given known precinct vote counts, how proportional legislative body is to the voting
population.  i have an idea how to define that metric.
there could be different weighting factors but you could literally have a "goodness" vector that would evaluate all of these different metrics and represent that as a dimension of the vector.
then commissions could
transparently display all of the different maps they cooked up and what that vector might look like for different sets of weighting factors.  it's still a political and "qualitative" decision by a commission, but it would bit quantitatively restricted. (e.g. the Supreme Court allows
for a 10% max variation of population per elected seat in the district, but does not require each district to have the same number of elected seats. my state senate district is known to be the legislative district in the U.S. with the most number of elected seats, which is 6.)
This
redistricting and gerrymandering problem really needs to be solved.  this is actually a more salient problem than the dearth of ranked-choice voting in the U.S.

--
r b-j                  ***@audioimagination.com
"Imagination is more important than knowledge."

[Kristofer Munsterhjelm]

Post by Rob Lanphier
<https://www.axios.com/researchers-propose-a-gaming-solution-to-gerrymandering-2507567048.html>
i read through this article and got the gist of it.

Post by Kristofer Munsterhjelm

Post by Rob Lanphier
I haven't done the deep dive on this yet, and have some gut instinct
reactions, but I'm curious: what do you all think? Assuming dividing
states into voting districts is a necessary evil, is this as good a
way as any to do it?

I suppose it might lead to "bipartisan gerrymanders", where the parties
reach an agreement about how which incumbents should survive until the
next election, rather than the voters being the ones to choose. In
effect, you would get something between closed party list and SNTV, with
two parties.
Furthermore, the proposal doesn't specify who gets to participate in the
cake-cutting process. If it's t1/he parties who are currently in power,
rather than the cake-cutting process being done just after the election
(before seats are given out), then incumbent parties could cooperate to
block a growing challenger party by cracking the challenger party's
support across multiple districts. Thus it could strengthen Duverger's

law.

Post by Kristofer Munsterhjelm
I would prefer the independent commission solution if the commissions
can be trusted to be independent. If they can't be, then closed party
list with a (variable, implicit) threshold could be preferrable to the
kind of one-sided gerrymander that exists now.

and i think that algorithms that make a meaningful measure of
compactness or convexity of the districts is important to use. and i
think they could weight this convexity measure along with other
properties that maybe can have objective measurement. like how well
"communities" (however they are defined) are kept intact. so when
district boundaries for some legislative district align well with
existing city or town or county boundaries, that gets you points of some
weight also. but also given demographic maps of cultural populations.
of course a salient measure is the variance of the district population
(or a 1/C scaling of the population if the district has C candidates at
large).
another salient metric is, of course, given known precinct vote counts,
how proportional legislative body is to the voting population. i have
an idea how to define that metric.
there could be different weighting factors but you could literally have
a "goodness" vector that would evaluate all of these different metrics
and represent that as a dimension of the vector.
then commissions could transparently display all of the different maps
they cooked up and what that vector might look like for different sets
of weighting factors. it's still a political and "qualitative" decision
by a commission, but it would bit quantitatively restricted. (e.g. the
Supreme Court allows for a 10% max variation of population per elected
seat in the district, but does not require each district to have the
same number of elected seats. my state senate district is known to be
the legislative district in the U.S. with the most number of elected
seats, which is 6.)
This redistricting and gerrymandering problem really needs to be
solved. this is actually a more salient problem than the dearth of
ranked-choice voting in the U.S.

From over here, I'd say the best way to solve the problem is to
dissolve the problem, as it were; to make the thing that leads to the
problem in the first place, go away.

In other words, replace single winner districts with multimember ones,
or add top-up seats like in MMP.

I guess the second order problem is that such solutions may be
unpalatable due to US political history. In addition, where they have
been tried (e.g. New York STV), they've solved the problem too well,
drawing ire of those who benefitted from the old way of doing things.

Even if the redrawing can be made impartial, there's a difficulty with
single member districts in that you can't ensure that the natural
boundaries (different communities, landmarks, etc) line up with the kind
of boundaries you'd need to get political proportionality or fairness.

(You could probably redraw districts just after the election, before any
seats are apportioned, in such a way that you'd get political
proportionality, but then the method would in effect be a multiwinner
one - it'd just look like a bunch of single-winner ones after each
redrawing.)
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[Rob Lanphier]

Hi folks,

I really appreciate the quick analysis I can count on from this
mailing list, (particularly robert and Kristofer this time). Thanks!

I agree with robert that the gerrymandering issue is ripe for a
solution. Proportional representation is getting some airplay in the
wonkosphere[1], but it still doesn't quite seem like even many of the
voters that would bristle at being called "anti-intellectual" are
willing to listen to us math nerds.

[1]: https://www.vox.com/policy-and-politics/2017/10/11/16453512/gerrymandering-proportional-representation

The cake-cutting solution intuitively seems wonderful. It definitely
implies two sides, but an Approval style variant occurs to me:

1. A list of generated maps (as described by robert) is put in front
of a proportionally-selected commission, which then uses approval
voting for the maps
2. If a single map is approved unanimously, it wins. If multiple maps
are approved unanimously, then ...I don't know....that'd be a fun
exercise. We'll just assume that won't happen for purposes of this
email. If none is approved unanimously, then we keep going:
3. The map with the highest approval rating is selected first, with
the commission divided between those that approved of the map (A), and
those that didn't (B)
4. Group B gets to decide which district to freeze out of the map, and
optionally adjusts the remaining districts
5. Continue using the process described in the original paper.

The interesting thing about this variant is that there's the
additional cake-cutting conundrum of choosing to approve of a
particular map. One complexity comes if the commission has (say) 10
people, and 9 approve of one particular map. That means 9 people are
in group A, and one person is in group B. Does that give too much
power to that one person, where people would try to game their way
into being in group B? Also, assuming that each group does
majoritarian Robert's Rules of Order style decision making, what would
be the size of an effective super-majority that could ensure that one
party is able to dominate both group A and group B?

It seems to me that the group A/group B divide would cause committee
members to be stingier with their approval then they otherwise might.
The collusion to optimize the map and formation of the A/B teams could
become similar to a game of Diplomacy[2] and could have ugly ways of
gaming the system. Still, intuitively to me, it seems like the rules
I describe seem to have the same cake-cutting fairness properties
described in the original paper.

[2]: https://en.wikipedia.org/wiki/Diplomacy_(game)

Kristofer: your suggestion of redrawing the districts *after* the
election (thus simulating a multiwinner election) is interesting.
It's a good thought experiment. What would the ballot look like for
the typical voter, though?

Rob
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[VoteFair]

... , I'd say the best way to solve the problem is to dissolve the
problem, as it were; to make the thing that leads to the problem
in the first place, go away.

I strongly agree! That's why I support using a method where the
boundaries can be manipulated to anyone's content and the balance of
power among political parties stays the same.

I've described my recommended approach in my book, Ending The Hidden
Unfairness In U.S. Elections. Specifically each district has two seats,
which are filled by the most popular candidate and the second-most
representative candidate. A few additional "statewide" or "nationwide"
seats -- the number of which depends on how proportional the results
need to be -- are filled according to which non-winning candidates best
represent the voters who are not well-represented by the voters who
dislike the district-based winners.

All of the methods I've seen for "fairness" in choosing boundaries
result in unfairness. Expressed as a metaphor, using a coin toss is
"fair" in terms of process, yet the outcome always gives an advantage to
one side or another. In other words, a fair process does not
necessarily yield fair results.

Richard Fobes
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