
“I-Cut-You-Choose” Cake-Cutting Protocol Inspires Solution to Gerrymandering - ingve
https://www.cmu.edu/news/stories/archives/2017/november/i-cut-you-choose-cake-cutting-protocol-inspires-solution-to-gerrymandering.html
======
thoughtexprmnt
I feel like this might go a little too far in formalizing the two-party system
in a way that would have undesriable consequences. A better approach to
drawing Congressional districts would be something like this:

[https://bdistricting.com/](https://bdistricting.com/)

"Impartial Automatic Redistricting... optimized for equal population and
compactness only."

~~~
gmiller123456
One better is to not have districts at all, and instead use proportional
representation, which is what's used in more than 50% of all major democracies
around the globe[1].

IMHO, more important than eliminating Gerrymandering, is eliminating the two
party system. In truly competitive governments with 10-15 parties holding
seats, it's incredibly risky to lie, BS, or ignore arguments. In our two party
system most of the arguments are just designed to talk you out of voting at
all if you favor the other party.

[1]:
[http://www.fairvote.org/research_electoralsystems_world](http://www.fairvote.org/research_electoralsystems_world)

~~~
Sohcahtoa82
> eliminating the two party system

The US only has a two-party system because our method of voting ensures that
it devolves into a two-party system. Our two-party system is a symptom of the
problem, not the cause.

Give us ranked voting and proportional representation and we'll see more than
two parties emerge.

------
millstone
California had a statewide ballot initiative (Prop 20) which established the
California Citizens Redistricting Commission, which drew districts ignoring
party affiliation. The resulting districts lean heavily Democratic (because,
duh, California) but are also fiercely competitive; there are very few safe
seats and incumbents have to hustle. Frankly it's fantastic, a model for the
nation.

California has proven out the solution: collect a set of citizens from both
parties as well as some unaffiliated, aggressively de-politicize the process,
give them broad guidelines on how district lines should be drawn, and let them
do their thing. No need for weird cake-cutting machinations.

~~~
SlowRobotAhead
>districts lean heavily Democratic (because, duh, California)

Except that outside of a few cities, California is actually quite red. IIRC
would be a red state if LA and SD were underwater.

[https://www.politico.com/election-
results/2018/california/](https://www.politico.com/election-
results/2018/california/)

~~~
furyg3
This is a weird statement. You're saying California would be a red state if
you removed a lot of Democrats.

About 50% of registered voters in the state are Democrats, and 30% Republican:
[https://en.wikipedia.org/wiki/California_locations_by_voter_...](https://en.wikipedia.org/wiki/California_locations_by_voter_registration)

So yes, if you removed close to 3 million democrats from the state somehow, it
would be a tie. Probably an easier method would be for Republicans to make
their policies more attractive to more people.

~~~
SlowRobotAhead
The topic was on gerrymandering districts - there are more republican
districts. The part of the comment I was replying to was _" DISTRCITS lean
heavily Democract"_ which is not true, more DISTRICTS lean Republican.

------
ende
Just get rid of single member districts. Replace congressional districts with
proportional representation.

~~~
korethr
Since congressional districts were intended to be a form of proportional
representation, what do you propose in their stead?

~~~
beisner
One of the better ways I’ve heard is multi-member districting, where you have
a slightly larger district with multiple reps (maybe 3-5 representatives)
where seats are partitioned proportionately for that district. Voters vote for
a party, and seats are apportioned to each party in accordance with their
share (with some rounding). This guarantees a result that is at least as
proportional (I’d posit significantly more proportional) as the current
representative system, and maintain the ‘theoretical’ locality of
representation, meaning constituents still vote for people representing their
small localities.

There are different ways to assign representatives in proportional
representation systems, but at such small scale you could have district-wide
primaries where the top N finishers for that multi-member district are slotted
into seats in the order in which they finished in the primaries.

Unfortunately this system is still imperfect, as strategic voting can still
occur l, but significantly less so than in our first past the post single-
member system. Also it excludes extremely small parties (>10% of the national
electorate) from influence. It’s a tough problem.

~~~
manicdee
Get rid of FPTP first, since that is the worst of your problems. Multi-member
districts will be an incremental improvement on top, and actually be
meaningful once every vote ends up selecting a representative.

With a STV system like Hare-Clarke you will likely see independents standing
with very centrist platforms, with the major parties quickly scrabbling to get
those centrist votes.

~~~
dragonwriter
> Get rid of FPTP first, since that is the worst of your problems

No, unequal apportionment and the electoral college are the biggest problems,
FPTP and single-member districts in state and federal legislatures are, in
combination, just the biggest problem which isn't federally Constitutionally
mandated and which can therefore be fixed with legislation at the appropriate
level(s) without federal Constitutional Amendment.

> With a STV system like Hare-Clarke you will likely see independents standing
> with very centrist platforms

Perhaps, but every candidate elected being a compromise candidate that
relatively few people feel they would have preferentially votred for first is
_horrible_ for representation, and that's what you get with any STV-like
system with single member districts in an electorate where political views
aren't unimodally distributed (and if views were unimodally distributed, FPTP
would get you exactly the battle for the center you propose and you wouldn't
need STV to get it.) You want compromise in the legislature on policy where
the voices in the legislature reflect those in the populace to the degree
feasible; you don't want the compromise to happen mechanically in selecting
members of the legislature.

~~~
sheepmullet
> No, unequal apportionment and the electoral college are the biggest problems

What do you mean?

I think the biggest problem is giving electoral votes based on total state
population instead of based on citizenship.

California and Texas both end up with more than they should have.

Edit: I'd like electoral votes to be distributed proportionally instead of
winner takes all - it sucks that if you are not in a swing state you have less
influence.

~~~
JamesBarney
California is 87% citizens compared to 93% for the country. That doesn't
change the voting math much. But Wyoming citizens gets 7000% more Senate
representation.

~~~
sheepmullet
Back of a napkin calculations have California with around 25% of all
immigrants in the US.

It's a pretty big chunk of EC votes - more than Wyoming gets in total!

The senate is meant to represent the states - not the people - so it's not
really a fair comparison.

~~~
dragonwriter
> It's a pretty big chunk of EC votes - more than Wyoming gets in total!

No, it's about the same. If you pull non-citizens out of the calculation
nationally, California loses between 3 and 4 seats in the House.

> The senate is meant to represent the states - not the people

That's no more true than saying the House is supposed to be scaled to people
and not citizens. Both are features of the design of the system. “Is supposed
to be X” doesn't stop something from being a problem in terms of a goal other
than X.

~~~
sheepmullet
> doesn't stop something from being a problem in terms of a goal other than X

Sure - I guess it's the difference between a tweak and an overhaul. I'd expect
the overhaul to have 100x the supporting evidence.

------
Felz
We're not constitutionally a two party country, so the solution as described
in the article does not seem to apply.

~~~
madhadron
Not constitutionally, but by using single member districts and our current
voting algorithm, the equilibrium is two parties. So we are a de facto two
party state.

~~~
manicdee
It’s First Past The Post that forces the two party system. Get rid of that,
STV is what will bring lasting change and reduce the the tendency for the two
major parties to be exaggerated opposites of each other.

~~~
contravariant
For the presidential elections approval voting would be more appropriate, for
local representatives proportional representation is the important part for
which you don't really need STV (although I guess voting for political parties
with proportional representation is somewhat similar to STV with a
predetermined set of preferences).

------
Jedi72
How do you evenly split a quantity of something (e.g. drugs) when you have no
scales? One person does the splitting, then presents both halves to the other
person, who can choose either one as the half they keep. Everyone is
incentivized to transact as fairly as possible.

~~~
pryce
My older brother's "solution" to being told he must cut the cake and let me
choose which half to take was: a sloped cut similar to the one in this picture
[1] but which slightly exaggerated the uppermost surface area of the smaller
volume.

An analogous tactic against this "I-cut-you-freeze" task might be to provide
especially appealing district boundary for your opponent to freeze, while
harbouring some knowledge about that district that that your opponent is
unaware of (eg suppose that you know the trajectory of demographic changes
much better than your opponent)

[1] [https://imgur.com/a/Doy6lPg](https://imgur.com/a/Doy6lPg)

~~~
empath75
The competence of the participants to judge the slices is outside the scope of
this. If one of the parties doesn’t know what they’re doing, that’s their
problem.

------
logicallee
I cut you choose is not fair. I actually heard an example in real life about a
week ago when something was being cut for two people (they weren't following
the "I-cut-you-choose" protocol, just trying to be fair). The person doing the
cutting was literally saying "It is very hard to cut it so they're both the
same."

This is true. Many things don't naturally cut into two equal pieces despite
the person's best attempts, and in certain cases it may be impossible. (For
example, if there is are "valuable" toppings that are indivisible.)

It is just plain easier to choose than to cut. The worst case choice for the
person choosing is that they are indifferent to which piece they get, but the
worst case for the person cutting is that they get a worse piece.

Choosing is strictly always better than cutting.

~~~
grasshopperpurp
I used to joke around with my brother that it'd be funny for the cutter to
intentionally cut the cake like 9/10 to 1/10 then get outraged when the
chooser took the bigger piece. But, you're absolutely right - choosing is
better.

------
WisNorCan
Exciting to see an elegant algorithm proposed for a complicated real-world
political problem.

------
viggity
Here is an idea I had awhile ago - the rules should limit the ability of a
boundary to be concave. It isn't reasonable to say "no concave polygons", but
you could create a measure of "concavity". If you look at a ridiculously drawn
boundary, you'll see it can kind of spiral - it'll hop down a street turn a
couple times all in order get the current congressman's house within his
existing district.

How to do that? Use the ray casting solution to the Point in Polygon problem.
([https://en.wikipedia.org/wiki/Point_in_polygon](https://en.wikipedia.org/wiki/Point_in_polygon))

If there is any point within the boundary that has to cross the boundary more
than 3 times to get to a point outside of the boundary, then the proposed
congressional district is too complex. if it crosses 4 times (or any even
number), the point isn't actually within the boundary to begin with. Crossing
the boundary 3 times still allows for some concavity, but 5 is kinda
ludicrous.

------
cestith
This further deepens the two-party system. That's no solution at all.

Districts should be compact, as simply shaped as possible, equally populated,
and ideally follow as many lines of local government concern as possible.

We already have utility districts, school districts, city precincts, county
precincts, townships, drainage and levee districts, cities, towns, villages,
counties, wards, neighborhoods, state police districts, state House districts,
state Senate districts, and more boundary lines within states. Rather than one
county precinct being cut into four parts so each can be a portion of four
different Congressional districts that also overlap other county precincts,
perhaps as much as possible your part of town should have the same candidates
on the Congressional race as your neighbors using the same voting station.

------
Double_a_92
Why do you even need districts? Just split based on the total percentages of
voters.

~~~
dingo_bat
Because that's not what most people want.

~~~
Double_a_92
Why would you not want that as a voter?

------
codedokode
It is an awesome idea, but what if there is more than two parties?

~~~
darkstar999
This article explains how it would work for 3, but I haven't thought about it
enough to figure out if it translates to districting.

[https://www.scientificamerican.com/article/the-
mathematics-o...](https://www.scientificamerican.com/article/the-mathematics-
of-cake-cutting/)

------
trothamel
It seems like the obvious problem with this is that it could lead to districts
that aren't contiguous.

~~~
alkonaut
What is or isn’t a valid division is external to this algorithm.

------
extralego
This will never work. The only hope is honorable experience and strong
leadership.

~~~
davidkuhta
> The major problem—one of the major problems, for there are several—one of
> the many major problems with governing people is that of whom you get to do
> it; or rather of who manages to get people to let them do it to them. To
> summarize: it is a well-known fact that those people who must want to rule
> people are, ipso facto, those least suited to do it. To summarize the
> summary: anyone who is capable of getting themselves made President should
> on no account be allowed to do the job.

\- Douglas Adams (The Restaurant at the End of the Universe)

I think the truth in this humor is quite relevant to those in whom you're
placing your hope.

~~~
bildung
Great quote :) To rephrase I think the problem is that the skill set you need
to _get_ into a political position is completely orthogonal to the skill set
you need to _do good work_ in said position.

~~~
dingo_bat
That's true for far more than political positions.

------
galeforcewinds
The courts exist to provide relief to the people and regardless of whether a
solution like this were applied, the courts could continue to provide relief.
It would be interesting to see a solution which is more self-organizing at a
grassroots level and which might mitigate the whole "from on high" decision-
making. So long as a small group of driven individuals is making decisions
like this, we will continue to have risks from material non-public knowledge
used to game the system, and risks to the successful foothold by minority (of
any sort) populations except those large enough to warrant party support. It's
not an issue that the courts have had to step in -- without the courts the
people would be left without relief.

