hello internets right now I am uploading
the video to my youtube channel this is
the one about the sneaky plan for the
electoral college now as part of making
my videos I often make spreadsheets so
here is the spreadsheet that I made
while working on the video and while I'm
waiting for that video to upload I
thought why don't I just talk you
through this thing a little bit this
isn't a tight explanation or anything
this is just going to be a scroll down
spreadsheet laying with grey as I tell
you about some of the things that I did
while making the video okay so for this
video going up I originally wanted to
have something about apportionment and
the electoral college every state gets a
certain number of votes right Delaware
has three Georgia has 16 Hawaii has 4
what are the exact details of how this
happens now that part of the video got
cut and I was originally thinking it was
going to become its own little thing and
then that didn't end up going anywhere
for reasons that might become obvious as
we talked through a bunch of this stuff
but so let's begin at the beginning here
we have all of the states their current
estimated populations the flag of each
of these states very important to have
of course the electoral college votes
that they get and then the thing that
drives many people to madness is how
many people per electoral college votes
so this column down here represents how
many people does it take in the state to
get one electoral college vote so in
Hawaii for every 350 5,000 people there
are four electoral college votes if you
go to Arizona there's the formula it
takes 650,000 people per electoral
college vote and you get that number by
just dividing the population by the
electoral college votes they're
colorized here because I've divided them
up into quintiles five groups so you can
see like most proportionate and least
proportionate and we can sort that
column now so here we are in who is
least represented two most represented
as far as electoral college votes are
considered now what's interesting here
is Texas is currently the top contender
for most unrepresented by electoral
college votes and California which was
the winner of this dubious distinction
is currently in third place Florida is
in second and if we go down to the
bottom here hoops we can see the usual
Wyoming is the most represented it only
takes a hundred and ninety two thousand
people to get one electoral college vote
in Wyoming you can think of this as if
you are running for office you need a
majority of the electoral college votes
as you go further down this line you
need to convince fewer people in the
state to vote for you to get an
electoral college vote and if you're in
the top here you need to convince a
larger number of voters to vote for you
to get a proportionally smaller number
of votes so that's how the system works
okay so the question though is how does
this number get determined exactly well
the number of electoral college votes is
dependent on the number of seats in the
US House of Representatives right so the
US House of Representatives has 435
seats
so this 435 is going to be distributed
among the 50 states roughly in
proportion with the population so if we
take the population and put everyone in
population order you can see that
roughly speaking as we go down the
population you can see that the number
of House seats is proportional ish to
that number so the more people the more
House seats you get the electoral
college votes is just the house seats
plus two so that's a very easy
calculation to do now you notice when I
sort by the population over here the
current population of each state the
current population per electoral college
vote it doesn't stay in those nice
quintiles anymore it's gotten a little
broken up why is that well it's because
the house seat number depends on not
what is the current population but
what was the population at the last
census so here we have now what was the
population at the last census and what's
the current population now this is a
little hard to look at so we can add in
this column which shows us the
population growth or in some cases like
with Illinois the population decline of
a state it's if we sort by this to sort
descending so we can see that Texas in
Utah Texas in Utah have grown quite a
lot since the last census and Vermont
West Virginia and Illinois have all
shrunk a little since the last census so
the longer it goes between censuses the
the less the current state of the House
seats represents the current population
which then of course since the electoral
college is just this number plus two
means the electoral college also gets a
little bit whacked
so right now Texas is at the shortest
end of the stick here with having had a
big population growth that isn't
reflected in an increase in House seats
Illinois Vermont and West Virginia maybe
should have fewer seats well not Vermont
because they only have one and one is
the minimum number you can have but
Illinois in West Virginia might lose
seats the next time around because their
population has shrunk now again it's
just useful to keep in mind that if
someone gains a seat like Texas it has
to come from somewhere else because this
435 number is kept the same Congress
passed a law saying they're not going to
be any more seats than that so the seat
numbers just have to get readjusted
every census so then that's the big
question how does that happen how are
these numbers exactly determined well
this led me down a little bit of a
rabbit hole okay so the start of the
process is that each state gets one seat
in the house so let's fill that down so
this is the way things look at the
beginning everybody starts with one no
matter how large or how small your state
now again this process is based on the
census population not what the current
population is so let's sort by census
population
so next Lee
it's unhide this column so here we have
the census population per representative
for calculation so so this is thinking
about the census population divided by
the number of house seats that's what
this formula is showing us here so these
numbers start out obviously hilarious
that's California gets one seat in the
house and three electoral college votes
for 37 million people and then at the
bottom Wyoming has one House seat three
electoral college votes for five hundred
and sixty eight thousand people so part
of what happened in the process of
making this video is I had originally
thought the method for apportioning the
House seats was by taking this number
population per representative see who is
the worst off and you give them a
representative which then drops them low
sort of resource by descending see who's
worst off and do that again give them a
seat sort again you know now it's New
York's turn to now sort again by
descending and just keep going adding
seats always giving one seat to whoever
has the worst representation based on
this column and do that until you run
out of House seats but it turns out that
is not the method by which the seats are
apportioned that's sort of the idea
behind it but the details ended up as
they almost always are being much more
complicated and much more inscrutable so
let's reset these couples numbers and
talk about what actually happened which
is partly why there's no video about
seat apportionment here we are on the
wikipedia page the United States House
of Representatives and we can go to the
section on apportionment okay there's a
little summary of it but let's forget
that we can go to the actual page on
congressional reapportionment so it
turns out there's a bunch of different
methods that have been used over time
okay so blah blah blah blah blah we get
down to here so what is the actual
apportionment method so it turns out
it's this thing called
huntington-hill method is what's
currently used so if we go on to the
more detailed page there's this
description down here which runs through
the math of how it works now this is
talking about the general
huntington-hill method but I wanted to
know the exact details for the US State
House of Representatives so if we go to
the actual Census Bureau who does this
work they have a walkthrough of how the
process works but as I often find
looking through things I come across
these things that I think of as
explanations without explanation like it
tells you how a thing is done but it it
doesn't really give you a why or it just
it always feels like it's missing some
key part so by digging around for a
while I eventually found what I I guess
is the first paper so this is Edward
Huntington of the Huntington method oh
yeah so he's he says that the problem is
is basically that it's really difficult
to give out the seats equally that in in
theory what you would want to do is just
take the whole population of the United
States divided by 435 and that's what
you should have as how many people have
each representative but the states had
different populations and it's like so
you just end up with this more
complicated thing you don't end up with
even numbers and I like this line here
of this problem has been a subject of
violent debate in Congress for the past
100 years okay so I'm just gonna point
out this part here so none of these
methods however possess any satisfactory
mathematical justification so he's
saying that the methods that are used
are just sort of arbitrary that someone
proposes them but they don't have a
great mathematical justification so he
has this method that he's created and I
love this at the end this method may be
called the method of geometric mean
since multipliers are reciprocals of the
geometric means of consecutive integers
the solution of the problem is thus
complete but what I just I sort of love
is that nowhere in this paper at least
to my reading do I feel like he
addresses this part that none of the
previous methods have any satisfactory
mathematical justification and he talks
through this
that is used and the principles that he
is going for but I'm sort of not sold on
why this is the best method compared to
all the previous methods but anyway I
spent a long time sort of working
through this and found it's not easy to
follow so I gave up on this paper
because I found that later this guy who
works for the Census Department wrote up
this much longer description of how does
the huntington-hill method actually work
so this thing is a little bit easier to
understand and I think this was written
for Congress or for the Census
Department itself in order to be able to
understand what's going on in this paper
so let's talk about this just a little
bit so here he provides the actual
answer to the thing that was missing
from the previous paper which is why
this method so by the method of equal
proportions which is the huntington-hill
method the difference between the
representation of any two states is
smallest possible when measured by the
relative difference in the average
population per district and also by the
relative difference in the individual
share in a representative these features
appear to make it superior to any other
method that has been devised so the way
I interpret this is that going back to
my spreadsheet it's not just a question
about take the state that has the worst
representative add a house seat and make
it a little better it's a question of if
you're going to add a seat you have to
consider all of the states together and
the question is more like if you're
going to add a seat somewhere where is
the strategic place to add it that will
bring on average all of these numbers
closer together and adding a seat to the
state that has the worst representative
per population doesn't always achieve
that goal because California ends up
with something like I don't know
it's 50 or something yeah let's say
maybe it's 53 52 53
oops 53 yeah there we go
so California is going to end up with 53
seats we'll just sort of cheat this and
now let's sort by descending so
obviously I haven't given everybody else
the seats but like so California has 53
and it ends up with 704 thousand people
per vote there's a big difference then
between adding one more representative
to California which doesn't change its
average votes per person very much and
say adding one vote to North Dakota
which drops it in half so the way I
interpret what this paper is saying here
is that it's trying to account for this
effect that adding an additional vote to
a state that has a lot of votes already
affects the population per
representative less than adding it to a
state that has very few that's a thing
to consider under this method back to
the paper okay so here's where we start
to walk through the math we say that
there are two states a and B we need to
give a representative to one of them who
should it be the basic idea is that
whoever you give the additional
representative to it shouldn't make the
difference between the two states bigger
you want the differences to be smaller
and that should be true for every single
state that happens now if you're
interested there's a little math proof
that you can follow in the paper which
then gets around to this idea of the
geometric mean skipping skipping
skipping and so at the end you get this
formula which which just says give the
next representative to whichever state
makes the difference between them
smaller which makes sense now that the
Congressional method is doing is a
little bit more understandable is taking
the formula here to calculate out who
should get the next seat assignment so
in the spreadsheet I added a column that
replicates this formula taking the
current population dividing by this G
match
mean and that gives us this cue number
which says what is the order right now
that each of the states should get an
additional house seat but here's the
thing I'm gonna level with you at this
point I can follow this but I can't say
that I truly understand why it works and
this calculation of the priority number
and this cue number is a little bit
taken on faith now hopefully the census
makes all of their data available and so
here is a spreadsheet I downloaded from
the census where they show you their
calculation for the priority value and I
could check it against my own
calculation for the priority value and
know like okay I'm doing this I'm doing
this right but I don't but I don't
really understand why or how it works
but at least like my homework has been
checked against the censuses official
calculations and I know that I've gotten
the right number so I was thinking about
this for a while and trying to come up
with a way to better understand how is
this working like I can crank through
the numbers and say okay we add one
seats to California and then one seat to
Texas and then it's California's turn
again and then it's New York's turn and
then it's Florida's turn right and and
the queue number keeps changing oh let
me pull this up here I made a little
table to show seats left and seats to
allocate and I tested this all the way
to the end and it will get you the
correct answer but then I thought okay
can I make this work in such a way so
that I have a better understanding of
what's going on so let's show you now
everything else that's in this
spreadsheet so there's a lot more that's
going on behind the scenes it's probably
time to make this full screen all right
here what we now have is a calculation
for all of the states versus all of the
others whether adding an additional
representative to
that state right now will bring the
overall average distance between all of
the states closer together so we can see
here's California so this column is
California versus so it's California
versus Texas if we add one
representative to California what is the
difference in percentages look like it
looks like 35% if instead we added that
representative to Texas what does the
difference look like it's a hundred and
ninety-six percent so if you're going to
have two right now
add the first house seat to California
or Texas you want to add it to
California because it brings the
difference in representation between the
two closer together and so you go down
again and say okay California versus New
York adding one representative to
California makes the difference between
them four percent adding one
representative to New York versus
California makes the difference between
them two hundred and eighty five percent
and we get really hilarious numbers down
here at the bottom which is add one
representative to California versus
Wyoming the difference between them is
97 percent had the representative to
Wyoming versus California and the
difference is 13,000 percent so what the
paper before was saying is that you
should add a representative to the state
that wins this comparison versus every
other state at any time and so right now
while everything is really nicely sorted
we can just look I made the cell turn
green for when that's the case and just
by scrolling down you can see the
California wins every single comparison
for where the first vote should go Texas
is that's 49 wins Texas has 48 wins New
York won less and it makes this really
nice little line as we're going down so
this number this column the queue shows
what is the Congressional formula say
should
the next state to get a seat and this
wins is my manual calculation in this
really ugly way of let's just check
let's just let's not trust the math
proof let's actually check each of the
calculations individually and then tally
up how many wins that has so we can
start cranking through the spreadsheet
now and see what happens and this is the
idea like playing with the thing to see
how it works so adding a seat
to California gives us 348 left now you
can see that the number of wins have
changed that the next state we should
add a seat to is Texas because now Texas
has one more win than California does in
terms of bringing all the states closer
and here we can see that the
Congressional calculation method matches
the state with the largest number of
wins 49 so do it again and now we're
back to California as the state that
wins the most so what we can keep doing
now with this spreadsheet is adding one
at a time additional representatives for
each of the states and as we do that we
can see that the wins calculated change
and the census population per
representative changes a lot along with
the current population per electoral
college vote and all the rest of that so
now I'm just going to re sort so
everybody's in queue order here so I've
just added a bunch of seats we're going
to allocate seat 17 there's 369 seats
left and so now at this point we can
just sort of crank through the
spreadsheet and see what it does like
see how see how the apportionment
changes the representation in each of
the states now as you might imagine this
took a little while to get to work right
and to figure out and to play around
with so much so that what I'm doing
right now is I go through each of these
little additions as I ended up building
a keyboard maestro macro shortcuts to
automatically search for the cue number
at the top
and then to add in an additional house
seat so that I don't have to type it
each time I'm just gonna keep adding
seats one by one I'm showing you this
because if it wasn't obvious already I'm
a big fan of spreadsheets and I really
think that spreadsheets are the like a
bicycle for the mind as the saying goes
where they can really help you figure
something out they can really help you
think about something and in the process
of having to make the spreadsheets I
feel like I got to understand the
apportionment method much better but I
didn't have an intuitive sense for how
this works but by playing around with it
and adding seats one at a time and then
going through and checking what do the
winds look like I got a much better
sense of why this method could be
described as a mathematically good
method I don't think it's very
explainable which is why it didn't
really end up as a like a fun
five-minute video but it does have some
internal sense as to as to why you
should use this over just giving a
representative to the most
disproportionately represented state at
any particular time so just stopped here
at a random point so we're gonna give
out the fifty seventh seat which goes to
South Carolina and again if we zoom over
here we go South Carolina on the list
again we can see that in all of the
matchups South Carolina brings the
overall difference between all of the
states closer together I also like
having done this calculation you can
kind of see where things are going in
the future that Louisiana and Kentucky
are gaining a bunch right so is Virginia
but so right now South Carolina gets the
next seat and we can just keep on
cranking through now I am actually going
to sit here and crank through the full
iteration the full distribution of all
of the seats
you don't have to sit here for this
whole thing but I'm gonna do it and but
if you want to play around with this
spreadsheet I'm also going to make a
copy of it available on my blog so there
should be a link in the description or
at the end of the video that you can
click to to go get that so let's just
finish this off with a little relaxing
spreadsheet calculations it might make a
few comments as we go along so I'm just
going to re sort every time California
gets back on top because I think that
helps visually set up the idea of what's
happening that that as we keep adding
seats to that as we keep adding seats to
the houses or then as we keep adding
seats to each of the states
it changes the relative it changes the
relationship between all of them so that
you can kind of imagine that they're all
standing in order that they're all
standing in line to get their seat but
that as each of them gets a seat it
affects the order of the line itself but
it's just kind of a pain to resort every
single time I've added a house seat so
I'm just gonna do it every time we get
to California since California is the
most frequent so there we go again
all right we got Mississippi gets their
first seat at 105 and so does Arkansas
at 106 and then regular Kansas at 109
California sort there we go beautiful
beautiful Utah at 117 Nevada home of Las
Vegas 119 and California sort you also
notice that as we go through this the
quintile positions for census population
per representative for the calculation
change along as the quintile values for
the population per electoral college
votes currently and again obviously
sometimes those changes are quite large
when a small state gets a gets one
additional vote versus when a large
state versus when a state that has a lot
of Representatives already gets an
additional vote but at the end the order
is going to be like not exactly the same
but sort of roughly the same
so here we go New Mexico with the first
at 168 such a good flag New Mexico
California sorts
you
okay here we go
I I find this okay
Idaho at seat 132 gets their first and
only additional representative so now
that we're getting down into about the
last third of the House seats to
distribute that's going to start
happening more and more where a state
just edges it in at some point in the
line to be able to get an additional
seat that they happen to be the optimal
one that reduces the overall disparity I
don't know why I find that sort of fun
and interesting it's like the the
smaller population states I feel like
I'm really rooting for them when they
get there there one additional
representative can in California sort
there we go Hawaii Hawaii gets her
additional one and that's the only and
that's our final one
I think that's the same for Maine yep
same for Maine same for New Hampshire
okay we're really getting down to the
wire less than 100 seats left
all right Iowa's got their final
representative
and organ Mississippi they're set
they're not going to be getting any more
by the way that's not part of the
calculation that they don't get anymore
if this is mainly just I have a little
formula in the spreadsheet that's
comparing the calculated number versus
what I know is the final number and
simply making the House seats bold once
those two match and by continuing to
crank through the spreadsheet the number
just never goes up because we run out of
seats so that's not a predetermined
thing that's just a little indication to
me of when it's going to happen like
right now with Arkansas getting their
four House seats there's six electoral
college votes and it's bold so that's
the final one they're going to get and
ditto New Mexico and Oklahoma three in a
row hat-trick
Louisiana Kansas Missouri just 50 left
Utah gets her final seat same for
Kentucky
Nevada Colorado Maryland at eight
Massachusetts at nine
New Jersey 4:12 Virginia 11 Indiana 9
North Carolina 13 four in a row
Wisconsin West Virginia Arizona sort
Tennessee Nebraska Ohio Rhode Island's
Alabama everybody's getting their final
seats just 14 left Illinois Michigan New
York under 10 now Pennsylvania oops oops
that was my back-row going a little
crazy at the last second
got it got a bit excited hit the wrong
key stroke there okay I believe this is
finally California's last one at eight
nope I was wrong there 53 Georgia South
Carolina Florida Washington Texas that's
right California is second-to-last
California and the final seat goes to
Minnesota and we can see here that if
there was one more seat my adoptive
state of North Carolina would be the one
to get it but okay that is the
spreadsheet we can sort by the House
seats or
actually that's sort by current
population per electoral college votes
but so there we go this brings us back
to the very beginning where I showed you
the decreasing order the quintile
breakdown of the states based on the
seat apportionment and now we've walked
through the whole thing together so
thank you for watching and like I said
the spreadsheet if you want to play
around with it yourself is going to be
available by link to my blog and I hope
you enjoy the video that I made this
whole spreadsheet for and never ended up
using in the actual video itself