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Why it’s mathematically impossible to share fair

Stand-up Maths
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This site was super helpful at explaining the history and math of apportionment. As always though, verify the specifics of the data yourself (but all the general points are definitely correct). www.maa.org/press/periodicals...

You want MY data? Come get my data. www.dropbox.com/s/o8bmzmwcpbl...

George Washington was voiced by my friend Ben Moor. They are in The Queen's Gambit!

The Voice of Alabama is voiced by The Voice of Alabama. They are in Alabama!

Thanks to all of my Patreon supporters who mean I can spend a silly amount of time on a video like this. So much time. So much historical data. You too can help support me: www.patreon.com/standupmaths

CORRECTIONS
- I didn't bother showing me locking cell references in the animations. Things like "=B4/B2" should have been "=B4/$B$2" so I could drag the formula down. We took that out in the interest of clarity.
- Yes, at 13:20 I say "the divisor ceases to lose some of its strict meaning" which is the opposite of what I meant! the sentence needs but the one negative. Either of these would work: "the divisor loses some of its strict meaning" OR "the divisor ceases to have some of its strict meaning".
- Sorry, at 16:47 column D is wrong. These are different numbers using 880 but the values over in E use the correct 930. It's just a display issue and does not change the results (despite being a bit confusing!). Spotted by a few people including Thomas Klemm and AverageJon.
- Let me know if you spot anything else.

Filming and editing by Alex Genn-Bash
Animations by William Marler wmad.co.uk/
Voice work by Ben Moor and Destin Sandlin. Yes, it was Destin. Well done on scrolling all the way down here to check.
SUM Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b...

Hep Cats by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. creativecommons.org/licenses/...
Source: incompetech.com/music/royalty-... Artist: incompetech.com/

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24 Nov 2021

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Comentários 3 347
Stand-up Maths
Stand-up Maths Mês atrás
Yes, I turned every Patreon name into a fake state name. If you cannot find yours: I'll start a post and look them up as requested. patreon.com/standupmaths And do check out brilliant.org/standupmaths to learn how to do things like this!
Tomáš Růžička
Tomáš Růžička 7 dias atrás
I feel like the first method with sorting was the most fair. The randomness is just a perceptional paradox to me. If you increase the number of seats, you increase the resolution with which you can distribute power to states. The reason a state loses a seat whe number of seats gets increased is because it had too much seats in the first place and when you increase resolution you got better result in which that state should have had worse result. It's like increasing resolution of pixelated line (lets say line by graph y = (pi-2)*x). If you aim to preserve the rule that with bigger resolution, no part of the line gets lower. You get skewd line with increased resolution. I think. Not verified.
Actually It Is Rocket Science
This comment should be those corrections. I shouldn't have to search for it.
Nick Farinacci
Nick Farinacci 17 dias atrás
@Stand-up Maths I think i noticed an error in the video! @ 16:44 in the video we round down the number gotten by =pop/DJ. new triangle rounds from 24.8614 to 23 rather than 24, circular rounds down from 11.0375 the 10 rather than 11, and then squaryland, octiana, and rhombus island round down properly.
Nico Ocin
Nico Ocin 22 dias atrás
Countin´ cookies is TIGHT tho, bro...(((;
Nico Ocin
Nico Ocin 22 dias atrás
Hi Matt! The math to this problem is ACTUALLY SUPEREASY, barely an inconvenience: just shovel ALL cookies to the supersquare dis-tract of ColumbIA which -ODDly enough- isn´t EVEN part of the US corp. Like 666...lol Welcome & cheers
SmarterEveryDay
SmarterEveryDay Mês atrás
You're really good at explaining complex math concepts. Thanks for letting me play along.
kur1tan
kur1tan 23 dias atrás
In the video, you're the voice of Alabama... Run for office and you can be the voice of the USA. Destin 2040! (Gives you and the kids more time to get older).
Oliver Dreyer
Oliver Dreyer 26 dias atrás
Not sure if you read these, but you got my girlfriend and I together ahaha
wherp
wherp 27 dias atrás
Oh wait, are you Alabama?! Lol, I knew my Spidey senses were tingling. 🤣
Maadhawk
Maadhawk Mês atrás
LOLOL I thought I recognized your voice at the end there Destin! I scrolled down to get ready to make a comment asking if that was you and here you are!
Collin Schofield
Collin Schofield Mês atrás
I had a feeling that was you! Especially after finishing up the most recent Supersonic Cannon video and coming here!
Sarah S
Sarah S Mês atrás
I really liked how you showed Excell commands and functions in a more friendly way. It's nicer to be able to follow along to.
Tedula1134
Tedula1134 29 dias atrás
The amount of joy on this man's face when he said "the united shapes" is enough for me.
Danikov
Danikov Mês atrás
The problem, of course, is integer representatives. But you don’t have to solve that issue by chopping up representatives, instead you could fractionalise the power of their vote to match the size of their representation. This then causes problems with voting because the votes are no longer equal, but it could be argued that’s the only way to be truly fair with integer representation.
Michael Sandy
Michael Sandy 2 dias atrás
Chopping up representatives is not a solution. ;)
Kyle Johns
Kyle Johns 5 dias atrás
Apportionment is not meant to be fair it is meant to help the smaller states have representation as a way to force compromise
Sci Entia
Sci Entia 17 dias atrás
i had the same thought about "fractional seats". you can still keep the rule of "at least one seat per state" because that seems sensible but i'm not sure how relevant that is (was there ever a US state who had less than 1% population?). but either way you would then always end up with a number of seats of around 100. is there a reason why the number of seats gets determined seemingly arbitrarily - sorry i'm pretty clueless about the US gov system : / any info on this much appreciated, though. on the other hand i don't see that much of a problem with the resulting "unequal quote". i think that by integer representatives you already shift the power dynamic, don't you? e.g. a small country getting a "round up" rep, would gain more influence per capita, or am i getting this wrong?
nacoran
nacoran 24 dias atrás
I was thinking of that too, but you still have a weird problem where one representative might have won 90% of the vote and another got 50.1%. My fix? A combination of an instant runoff and seating the top two vote getters- basically you pick the top two vote getters but anyone who got votes but wasn't seated could pledge their votes to one of the two candidates who did get seated for the duration of the term. That would give you a House that most closely represented the will of the voter.
derkylos
derkylos 24 dias atrás
@Derek Eastman Yeah, well, obviously you would have to account for that in some fashion. The most obvious problem with fair electoral reform is it usually disempowers those that implement it
Ken Surrency
Ken Surrency Mês atrás
I love his naked honesty. It’s a breath of pure, fresh air in the atmosphere of bad YT content. I had no real concept of how complicated it is to create and maintain a fair system of governance. (And it’s a shame that recently we don’t seem to care much for fairness.) Also, I like history.
FU meCK
FU meCK Dia atrás
@Ilyak1986 “we have absolutely no way of assessing knowledge” and ‘the least educated populaces shouldn’t have a right to vote’. Despite your contradiction, it sounds like you’d support slavery, Germany, and be against giving minorities representation, let alone 3/5. “crumble overnight” - the system they're advocating for is the system we have. And we’re still here over 200 years later; if you believe only the intelligent should have a voice, you’re shooting yourself in the foot. “Supported slavery”: How you support killing the Earth: You use modern transportation (cars, trains, trucks) for food/work/live, so you support the destruction of the environment. Just because you happen to live in a time when society necessitates you to use fossil fuels, is no excuse, just like the founding fathers during slavery. (Also you know slavery is happening right now in other countries, non-western countries, specifically Africa, Asia, South America. Why aren’t you being an ally to those disenfranchised slaves by spreading awareness?) Hoping you’re just miseducated, please read/watch some of the alt-right white supremacist views of Thomas Sowell.
Hopefulone
Hopefulone 13 dias atrás
@Ilyak1986 Yes, those are all good examples of the attitude which produced President Trump. Everyone is convinced they're so obviously right only a moron would disagree with them. As a result they justify tyranny such as you're describing even as you criticize Republicans for doing the same thing with gerrymandering and voting laws violations. Both of which, by the way, Democrats only care about because they believe their voting bloc's are adversely effected. If it was the other way around they'd be defending those same actions.
Ilyak1986
Ilyak1986 13 dias atrás
@Hopefulone the founding fathers also advocated slavery, and didn't live in a time in which an orange turd of a carnival barker can spread propaganda across the internet to the utterly inane. If most institutions and/or businesses ran like what you allegedly advocate our democracy would run like, by counting the vote of any rank and file idiot identically to that of those with knowledge, those institutions would crumble overnight. Heck, just look at any of the orange turd's businesses. Furthermore, most people *aren't* getting it wrong--the republicans in the senate represent something like 30% of the population. Add the issues of gerrymandering, obvious voting laws meant to disenfranchise minorities, horrible voting logistics (E.G. 10 hour lines in some parts of cities), and it's clear we're far from even so much as representing the average voter. Furthermore, there are a huge chunk of people too far gone to Fixed Noise. Anyone that advocates for those imbeciles having a say in economic, foreign, or climate policy, well, do they want the U.S. ending up like Trump Steaks, Trump Water, or Trump University?
Hopefulone
Hopefulone 13 dias atrás
@Ilyak1986 You're advocating for the type of governance which the founding fathers specifically avoided. Namely, that privileged elites hold all of the power while the general populace struggles in silence. For better or for worse everyone in the US has a voice. If you think most people are getting it wrong then your responsibility is to figure out how to convince them of your position not imply they're of lesser value. People like Donald Trump are an inevitable outcome when ideas like yours become mainstream so, while he was voted into office by conservatives, he was created by liberals.
Ken Surrency
Ken Surrency 13 dias atrás
@Ilyak1986 don’t forget this is the same system that got us the Princeton turd Wilson. The 1910’s were the end of the republic. It was a good idea but we just can’t have nice things. (Universal citizen voting rights were not granted by the constitution - they assumed that elections would only work if the electorate was educated and informed and that excludes most of us)
Snorkl FPV
Snorkl FPV Mês atrás
Doesn't all these complications come from the fact that we are trying to allocate a fixed number of seats? Why not just round (up/down/nearest), apply the 30.000-rule and change the number of seats to whatever comes out?
Zraknul
Zraknul 4 dias atrás
If you round up, you solve the always having at least 1 rep problem. Changes to limit are set into the future so they're harder to game. The Census was 2020, the house sitting from 2021 to the end of 2022 is responsible for setting the divisor to be applied after the 2030 Census. Number needs to be 1 digit followed by zeros. Ie: The present debate would be over say 900,000 vs 1,000,000, or keep the current divisor. Now the states have at least 8 years to grow themselves for the chance of gaining a seat.
politepain
politepain 8 dias atrás
@keeperMLT That's pretty similar to what's called the Wyoming rule
politepain
politepain 8 dias atrás
@Mihai The problem there (other than the fact that it's probably unconstitutional) is that minorities within each state would receive no representation whatsoever, making the House as a whole incredibly disproportionate.
Zachary George
Zachary George 11 dias atrás
@John E Evans For a brief time between states being added and the next apportionment occurring after the following census representatives can increase past 435. For example Alaska and Hawaii joined as states in 1959, the census occurred in 1960, and the following apportionment in 1963. So between 1959 and 1963 there were 437 representatives so that Hawaii and Alaska would be represented. But the system is set to automatically reduce back to 435. With a fixed 435, the Alabama Paradox only comes in effect when states are added, but then it’s not truly an Alabama Paradox as the additional seats are given to the new states. And later the seats are redistributed by population. So with the current U.S. constitution limiting seats to 435, the Hamilton method seems that it could both be simpler and more fair (if you can get around the divisor language)
Jim Goodwin
Jim Goodwin 16 dias atrás
@Good Morning Gent the 30,000 limit is the other direction. You can't have a rep with fewer than 30,000 constituents.
David Guthary
David Guthary Mês atrás
I know it's not really related to methods of apportionment, but I can't help but wonder how the Wyoming Rule would play into all of this: setting the total number of representatives so that the average population per representative in each state is equal to that of the least populous state (currently Wyoming).
Tesla Falcon
Tesla Falcon Mês atrás
That whole problem stems from trying to squeeze between 2 rigid rules: divisor & max seats. If we left the divisor uniform & the max seats flexible, it works fine. In the beginning, the divisor was 30,000. The populations round naturally up or down, except when the result is
Tesla Falcon
Tesla Falcon Mês atrás
@Taripar If we're talking over the Internet, then why have the layers? Leave the reps @ 1:30,000. They stay in their respective districts. All voting is online. 1:state physically verifies the votes and tallies but have no actual voting power similar to the actual election process. Once passed, the bill proceeds as normal w the Senate being there to debate/discuss in-person. The only reps who might need to be in DC physically are the Speaker & Minority Leader.
Taripar
Taripar Mês atrás
@Tesla Falcon Yeah, if that was an actual body, I think I would agree. However, my vision was more like a representation funnel rather than a fixed thing. All meetings in the "lower" House would be to tell the Federal House Rep what to vote for and nothing else. If we keep 435 as the Federal Representation Limit, then each Federal Rep would represent about 25 State-Federal Reps. So those 25 lower reps would be the sole constituents of the upper reps. And the upper reps would mandatorily vote for what their 25 reps vote for. Does that make sense? It's sorta like an electoral college for the US House of Representatives. The electors (Fed-Fed Reps in this case) are beholden to their state legislatures (the St-Fed in this case). I think if that system were in place, there would be no need to recalibrate the Senate. And I don't think the logistics would muddle up lawmaking too much. Since each Washington Rep would only need to hold a small meeting with his 25 Local Reps to get their votes. And this could easily be done over the internet nowadays so the Federal Rep wouldn't need to leave Washington in a time of crisis.
Tesla Falcon
Tesla Falcon Mês atrás
@Taripar Considering the current state of the country, I doubt such a split would be amicable. However, if it had been planned for a split from the beginning, it might have worked better. We almost had it in the 1860s w/o planning. Your idea mirrored my original thought: geographic regional governments between state & federal. The main problem is checks & balances between regional vs federal vs state. If the House alone was regional, it would effectively split the House into x separate Houses. Any bill would need to pass all x to pass the House. W 11,000 reps, legislation would effectively STOP being passed. (Not that that would always be a bad thing.) But it would be of little difference than running the bill by each state house individually. Reconciliation would take forever.
Taripar
Taripar Mês atrás
The solution is rather simple: Empires are not meant to be as big as the U.S. is. If the divisor is too big, the nation becomes an elective oligarchy, and if the divisor stays the same, government is no better than a small mob because there are too many people to make effective decisions. Easy solution: the country needs to split so that the people and representatives can stay as balanced as possible. This won't happen, for obvious reasons, but it is probably the healthiest solution. Either that or we have tiered representation. Keep 30K. For each 1500ish of the ~11K reps apportion a Mega Rep that represents the representatives at the Federal Level. You would basically end up with "Local Federal" representatives that meet in your State and send your "Federal Federal" representatives to Washington, D.C. The Senate wouldn't need to change, since it already ignores the population mechanic.
Tesla Falcon
Tesla Falcon Mês atrás
@IHateUniqueUsernames I agree it could fall into a range of values, but physical limitations would produce a hard upper limit. I am also wondering how to handle the excessively high divisor issue. 750,000:1 seems a bit excessive to me.
Arieh Jacobson
Arieh Jacobson Mês atrás
Wow, the production quality of these videos is rocketing up faster than New Triangles fraction under the Jefferson method! Even the little things, like sharing a cleaned up spreadsheet without all the grid lines and the whole UI up top adds so much to the visual clarity of the math itself. Keep it up Matt!
Brendan Hall
Brendan Hall Mês atrás
@Robert Cousins yes. It has been described in detail in the doobly do
Robert Cousins
Robert Cousins Mês atrás
@Brendan Hall except the values are incorrect around 16:33
Brendan Hall
Brendan Hall Mês atrás
I would very much like this fancy spreadsheet and skills to boot, thanks in advance
akoisme
akoisme Mês atrás
stop it, scambot, anyway yep, i agree with you makes it so much more appealing and motivating to watch the whole thing!
Jonathan Poole
Jonathan Poole 9 dias atrás
I instinctively think what's more important is how much error each state has rather than the Alabama paradox or the quota rule. That is, I think we should allocate seats to whichever state has the highest error error is their actual seat divisor. I _think_ this is very similar to what the Hill method is doing but maybe the squaring helps with small vs. large states.
KJ Driver
KJ Driver Mês atrás
While this is a great explanation of an interesting math concept, there is an issue with U.S. House of Representatives example. The size of the House should not be finite as it should be determined by the number of seats required as dictated by the census and the Constitution. In other words, each state's number of representatives should be determined first then the total of all the states' representatives is the size of the House versus the House's number of representatives being divided up among the states. This would eliminate the Alabama Paradox altogether as one state gaining or losing a seat would have no impact on the number of seats in another state. If this is not how we actually do it, then we are doing it wrong.
Claus Jensby Madsen
Claus Jensby Madsen 5 dias atrás
I'd choose the quota rule every time. I'm fine with random fluctuations as long as everyone is close to the true ratio.
Joran Martijn
Joran Martijn Mês atrás
Awesome video! What if, hypothetically, you would change the number of representatives and or seats after every census, and pick a number that minimises the total "unfairness" over all states? I imagine the more seats there are to distribute, the smaller the total remainder is after dividing population by seats. But maybe you don't need to increase the number of seats that much to get a significant improvement in fairness
Snekz
Snekz Mês atrás
At 16:33, you've claimed that POP(New Triangle) / D_Jeff(930) = 24.8614, rather than the correct ~23.5247. Notably, in your next column, you've fixed the issue with the rounding down correctly recommending 23 seats, but it's still a very baffling error if you don't get out a calculator and do the division yourself. The error also carries over for Circula, where you've listed the incorrect value of 11.0375 rather than the correct 10.4441, though your floor function still works. Actually, looking a little closer, that whole column appears to be in error, as though you used a divisor other than 930. It's simply that New Triangle and Circula end up being off by a whole seat, so when you fix the equation in the next column that also takes the floor of each number, it's readily apparent for them.
SamorZo
SamorZo 7 dias atrás
couldn't tell if I was being a dumbass or not when I noticed this thanks g
Olliert
Olliert 24 dias atrás
If only we had someone very interested in why people make mistakes in maths to get to the bottom of why he got it wrong...
Alice Teague
Alice Teague 27 dias atrás
Yes, I was very confused by that
fabnie
fabnie Mês atrás
@bkrphon true - but I doubt it'd be possible today unless some major clash happened somehow. not to say that I wouldn't love to see that happening (some with integrity, not me personally though)
Kevin Adams
Kevin Adams Mês atrás
@Brendan Maas It looks like he acknowledged the error in the description of the video and said that it doesn't change his final results.
Immudzen
Immudzen Mês atrás
What would happen if you used an optimization method to have the lowest difference between their actual representation and their ideal representation? If you took your column where you just divided population/reps and figured out how many reps each state gets and then look at rounding each of them up or down with the lowest residual.
James Watson
James Watson Mês atrás
I work in accounting and we have some financial statements that work this way. Auditors want whole-dollar amounts for some values, but when you add a large number of normally-rounded values, you usually end up with a rounded total that doesn’t match the value of the rounded actual total. Simple example… 3 values, $1.95, $1.45, $1.20, total = $4.60. The auditors want to see $2, $1, $1, and that adds to $4 but the actual total ($4.60) would round to $5. A dollar has disappeared. The way we have to handle it, since we’re dealing with much larger numbers where a few dollars isn’t “material”, is just dumping the cumulative rounding error into the largest value to make the totals match.
Bryan Yurasits
Bryan Yurasits Mês atrás
Matt, I like your idea of “what if states rounded to halfs and time-shared an extra seat” -I’ll add that each state’s “buddy” options are restricted to their adjacent states with an available half seat. (Also… time-share or vote-share? If they can’t agree they don’t get the extra vote)
Tesla Falcon
Tesla Falcon Mês atrás
@witiwap86 Had to look it up but it was a conversation started by my comment. 1) Do you trust that the Reps are reading & understanding every bill now? 2) I suggested NO changes in how they are elected, NOT assigned. The only difference is WHERE they live & work from & HOW they vote on said bills. The process of passing the bill doesn't change. Most are voting as a block per party instructions anyhow w precious few breaking for it in both directions. 3) Your initial comment on the influence of lobbyists would be mitigated. Right now, the collection of politicians in DC makes lobbying that much easier to do. Studies done have shown the swampy nature of DC and how easy it is to be corrupted in that hive of scum & villainy. Maybe if the Rep stays in their district more, they'd stay more true to their campaign promises.
witiwap86
witiwap86 Mês atrás
@Tesla Falcon While I can see the merit to that, there are also some huge limiting factors. There are a lot of bills to be voted on. Every one of those ~11k reps would have to read and understand each bill. I honestly don't have that much faith in people. The other problem would be allocating reps to their constituents. Some voting districts would only be a couple square blocks if they were allocated geographically. If you split it alphabetically or something like that it would basically remove the voting power of any rural residents because of the concentration of people in large cities. If it's done geographically it would be extremely difficult to jerrymander but if you combined geographic and alphabetical it would make it much easier. A large part of the reasoning with the number they chose was to not have large population centers control too much of congress. The more seats the greater the proportion of votes go to high density areas. Though I guess the number of seats is assigned just to the state so it would be state-level reps who decide how those seats are allocated to the population. But that also makes it easier for each state to jerrymander. I guess this comment would be better in the thread you mentioned. Who's the OP for it?
Tesla Falcon
Tesla Falcon Mês atrás
@witiwap86 In a different thread here, we discussed leaving the representation @ 1:30,000 which, at current population, would be ~11k representatives. While this is a very unwieldy number if all need to be physically present to vote (hence the current ratio of 1:750,000), it would be more workable if the reps stayed at home in their districts to stay connected to local issues and voted online or some other remote method. Only a small fraction of this number would be physically needed in person in DC. Further, it would make lobbying more difficult w so many scattered so far apart.
witiwap86
witiwap86 Mês atrás
Politicians already spend little enough time on actual policy compared to the time they spend campaigning to keep their seats. It would be better that they spend that little time directly on what people want. You could argue it's better for them to do nothing at all due to the corporate influenced corruption but in that case it would be better to change the elective process rather than trying to prevent congress from doing anything. Or make stipulations/requirements on how much influence corporations and lobbyists can access and/or influence the politicians with each of their possible activities (which would be my preferred method.)
Muhilan
Muhilan Mês atrás
this would be so chaotic lmao
cushmanproductions
cushmanproductions Mês atrás
I find the idea of states sharing representatives hilarious. But then I thought about metro areas that cross state lines, like Kansas City, that could much more reasonably share a representative. But then I remembered how we draw districts, completely ignoring city and county lines anyways...
David Scheel
David Scheel 25 dias atrás
This is awesome, I have looked into this the past 2 months, and it was great at throwing me back to the big picture, and looking at the fundamentals, instead of getting stuck in 3d models covered in dots, that each represents a seat. If I had seen this 2 months ago, you would probably have saved me a month of free time research. This video is great for anyone curious about this.
Starlite Lemming
Starlite Lemming Mês atrás
Love this! My first thought, early in the video, was effectively to normalise before ranking the fractions. If I weren't ADHD, I'd be setting that up in a spreadsheet right now -- but I have so many other things to procrastinate on! :D
Kapil E
Kapil E Mês atrás
This was amazing! I love that it was a tour through history, using real nitty gritty math. Something like this would be so valuable as a high school lesson, because it teaches A) how math can/was used in the real world, B) how small choices like this can have big real world impacts, C) how important it is to understand math and do this analysis *so that* you can understand those impacts, and most importantly D) that math isn't just a bunch of equations to plug and chug, it's actually created for logical reasons, and if you follow the history of how the complexity was built, you can understand it I want to take it on as a side project to distill this all down to a short lesson plan that guides the student through this historical story, with some math problems thrown in along the way. But also, I won't have a lot of time and I'm not a teacher skilled at making lesson plans, so if someo else is inspired, please take on the charge!
Kapil E
Kapil E Mês atrás
@Andy Harris That's great, I'd love to be in that class :)
Andy Harris
Andy Harris Mês atrás
@Kapil E the class is based on a book by Peter Tannenbaum. It does a full unit on voting and sharing. We then do units on graph theory, growth, shapes, and fractals. It's a lot of fun.
Kapil E
Kapil E Mês atrás
@Andy Harris that's awesome!! I'd love to hear more about the lesson. It sounds like an absolute ton of fun
Andy Harris
Andy Harris Mês atrás
I do teach this in a dual credit high school / college math class. It is one of my favorite lessons.
picassodilly
picassodilly Mês atrás
I understand this doesn’t work in many general “apportionment” situations- but it seems to me like just giving each state one representative per x population (round up so each state gets at least one) and making the total that gives the total number of representatives would avoid the quota problem, as well as any Alabama paradox equivalent (The Alabama paradox requires a fixed number of reps, so it wouldn’t fit this situation- but I don’t believe there would be a situation where lowering the x-population per rep mysteriously takes reps away from some state).
Steven Glowacki
Steven Glowacki Mês atrás
The best answer to this is to break from the concept of "one representative, one vote" to "one voter in the election for the legislator, one vote in the legislature". Cut the number of districts in half and then send the top two vote getters in each district as representatives with the weight of their votes in the legislature determined by how many people voted for them.
Flan
Flan Mês atrás
2:10 I love the proud smile on his face when he says “United Shapes” and thinks about how funny of a joke it is
Ira Sanchez
Ira Sanchez 27 dias atrás
I cackled I must admit
R Barreiros
R Barreiros Mês atrás
Missed the name "United Shapes of Arithmetica", but love the joke anyway heh
Vigilant Cosmic Penguin
He's not wrong.
Al Quinn
Al Quinn Mês atrás
the United Shapes aren't so great due to all of the Squareymandering going on
Lucarr10
Lucarr10 Mês atrás
It's 2 minutes in and it's already started
Lee Shallis
Lee Shallis Mês atrás
17:08, personally I would've gone with the "=POP/D" method, rounded down, set the left over seats as ignored and made all the used seats as "=SEATS/(POP/D)" or something that split the fractional value into relative vote worth, in other words each seat would always be worth 1.X with any leftover seats from a round down ignored or worth 0, the resources remain the same but like currency it changes in worth **Edit:** For an example let's take the 1st example in new triangle 23.47483, 1st they get 23 seats, no question, however each seat becomes worth 1 + (0.47483 / 23), it remains fair and the final result of votes can still be TOTAL_SEATS/(STATE_SEATS * STATE_WORTH), STATE_WORTH being that 1.X
Master of None
Master of None Mês atrás
Yeah, for fairness this wins. Issue being slightly more complex, but I like it
Sam Leonard
Sam Leonard Mês atrás
I've loved fairness theory since I took a class in college. This is great!
Jaime Warlock
Jaime Warlock Mês atrás
I always thought there should be just one or two representatives per state, but adjust the number of votes they get according to their population. This would also reduce federal government expense. Better yet, do like I read in a SF novel once. Select a national representative when you vote. The top 100 winners get votes proportional to the number of votes they received. So instead of representing geographical areas, a representative would represent groups.
UnknownDane
UnknownDane 8 dias atrás
I hope you'll do a lot more in this Excel style, I use it for work, so I'd love to learn more math in it.
QuantumHistorian
QuantumHistorian Mês atrás
Some years ago I was writing code and I came across this exact problem in a different context. I didn't want to spend too long thinking about it, so came up with Hamilton's method and wrote a quick and dirty implementation of it. I remember at the time thinking that there must be a proper mathematical solution somewhere, but that it wasn't important enough here to waste time on. I'm surprised to learn that not only is there no "fair" solution that always works, but also that the US Federal government took the same bodge-it approach I did!
Derek Eastman
Derek Eastman 25 dias atrás
@hypofixations. back in the first years of the constitution they clearly cared a lot more than our politicians do today.
ain92ru
ain92ru Mês atrás
@Katrina Bryce It's the Jefferson method actually, just put in other words and called with a different name
Katrina Bryce
Katrina Bryce Mês atrás
​@Gregory Morse The other common method in use is the De-Hont method. Divide each population by (number of seats already allocated + 1). Allocate a seat to the population with the highest number from the previous step, and repeat until all the seats have been allocated.
Micó Papp
Micó Papp Mês atrás
I faced this problem too like a year ago and didn't know how to find the math behind this. I came up with distribute the whole numbers only, then the remainder seats at random one by one.
bluerizlagirl
bluerizlagirl Mês atrás
There really isn't much else you can do, though when you can't apportion things perfectly. Somebody always gets more than they deserve and somebody else always gets less than they deserve. If you have ten cookies and three people, somebody will end up with 2/3 of a cookie more than they should have, and two people will end up with 1/3 of a cookie less than they should have. All you can do in that situation is keep a record of who has had how many cookies and when; and then next time you bake cookies, give the fourth one to somebody who only had three last time. By the time the third batch is baked, two people have had already had seven cookies; 7 + 3 = 7 + 3 = 6 + 4, and now everybody has had an equal share. And when batch four is ready, the extra cookie goes to the person who had it the first time and by now has waited the longest for it.
Jan S.
Jan S. 24 dias atrás
Awesome presentation! Bonus question: How about the Sainte-Laguë method, as it is used in Germany and - slightly modified - Sweden? It's supposed to neither favor bigger nor smaller populations; but how does that really fare in comparison?
WJS
WJS 18 dias atrás
That's just another name for the Webster method. It favours smaller states/parties and when used for elections can lead to situations where one party gets over 50% of the votes cast but gets less than half of the seats.
Holger Forsberg
Holger Forsberg Mês atrás
With your idea about rounding to half a representative, it reminded me of how differently some elections are done. Like, here in Denmark we've just had our local elections and the mayors are picked (same goes for the prime minister btw) not by winner takes all, but by the party who can get backing from more than half of the seats granted to the partie, by making agreements with other parties to get their backing.
Ben McKenna
Ben McKenna Mês atrás
This was so interesting. I love how you use excell commands to help us understand what you are doing.
KpxUrz5745
KpxUrz5745 Mês atrás
One of my favorite youtube experiences is to see bright mathematicians excited to bring us into their world of understanding.
Allan McPherson
Allan McPherson Mês atrás
The cameo by Destin-I mean Alabama-really made my day. He obviously had a ton of fun recording those bits!
Addison Miller
Addison Miller Mês atrás
Please tell that they used the take where Matt just asked him how he was feeling. That was such an awesome cameo.
Vigilant Cosmic Penguin
I thought it was him; I'd recognize that Alabama drawl anywhere. I'm feeling pretty good about that cameo!
he we
he we Mês atrás
@needamuffin that's where I first noticed as well.
needamuffin
needamuffin Mês atrás
@Martin Veselý I heard a bit of him in "Alright, I'm feeling pretty good!"
MacGyver III
MacGyver III Mês atrás
I didn't pick up on that until the end of the video--I feel ashamed.
Christopher Verdery
On the one hand, this is something I've been curious about because it affects an Excel spreadsheet that I made to calculate speed ramping for video editing, which requires whole numbers of frames. Which brings me to my next point, did you have someone animate working on an Excel spreadsheet? 'Cause I respect that.
James Jackson
James Jackson 7 dias atrás
This was great 👍. The more I delve into election theory the crazier it gets. Paradoxes and trade off's everywhere. Don't believe this video applies in Australia as we follow the quota rule but are happy to have more seats (or less seats but this doesn't happen in practice as a quirk of the territories not counting in the population divisor) than the targeted number
Servbot 40
Servbot 40 Mês atrás
37:19 The hill method favoring smaller states, has a compounding effect on electoral votes, and makes, individual votes more impactful in smaller states. Maybe switching back to the Hamiltonian method would balance this. Not sure you were up to doing this, but maybe you can see how these methods would affect close elections.
Burke McCabe
Burke McCabe Mês atrás
I really liked the excel type of explanation. Also, the Alabama thing was super interesting, I love little surprising paradoxes like that! Thank you!
Emily H
Emily H Mês atrás
as an Alabamian, I can confidently say our education system never forgave math for this and has actively scorned it ever since
D L
D L 5 dias atrás
@ElectromagNick Some private Schools are good and some are bad Nick. That's why it's great that you can avoid funding the bad ones. In fact, it is morally reprehensible to force you to fund bad Schools. That's why Public Schools are so hideous. They are based on the forced extraction of money through taxes. If a Public School does evil, even if you don't approve they will take your money. Public Schools *must be abolished!* your example proves that Schools must be accountable! Public Schools are fundamentally unaccountable and evil.
KMichelle Argus
KMichelle Argus 5 dias atrás
ha.
Derek Eastman
Derek Eastman 25 dias atrás
@ElectromagNick to be fair, most public schools would give the same response. Punishment for bad behavior in schools has more or less gone out the window.
ElectromagNick
ElectromagNick Mês atrás
@D L Yeah, I went to a private school for a bit, and the teachers' response to one of the students threatening to stab me with a knife was "Well, he probably won't go through with it." Also they disavowed the moon landings and climate change. Private schools ain't the answer, chief.
D L
D L Mês atrás
@Grim Affiliations I propose that taxes are significantly reduced to ensure that Parents can better afford to send their children to Private Schools. The average cost per student at Public Schools is 93% higher than the Median Private School Tuition. The way to reduce taxes is to Abolish the Public Schools that extract so much money from the people of America through Sales, Property, and Income tax.
BlackOak
BlackOak 11 dias atrás
I've recently gone from floor level warehousing/logistics to a more administrative role and I've been stunned by what I've found. Where you can face disciplinary action(depending on the company) for a minor mistake when you are handling the products and maybe cost the company tens of dollars, the number of transposing errors in documentation at the administrative level is absolutely appalling and can regularly cost a company thousands of dollars, or even hundreds of thousands depending on the company and specific issue. You can loose an entire order because someone between purchasing at your company, sales at the other company, data input, resource allocation, production runs, packaging, warehousing, shipping, to a carrier's receiving, warehousing and shipping transposes or drops 1 number. Or worse, someone gets a little happy with copy and paste and repeats a number
Sander Bouwhuis
Sander Bouwhuis Mês atrás
Thank you for doing things properly! Doing things quick'n'dirty is maybe 10% of the work. I hope you know that many people will really appreciate your effort!
Aiden Losh
Aiden Losh 3 dias atrás
you see this whole problem could have been avoided had we just apportioned each state independently from the others. if each state just rounded their population down to the nearest 30k there would be no argument on who gets the extra votes since you wouldn't be trying to share from a predetermined pool, but instead drew the pool from the needs of each state.
H
H Mês atrás
When I went to share a cookie or say brownie with my brother, I always made sure that I ate an even amount from both so the two halves were as close to even as possible. In fact, I was so devoted to getting the two halves as close as possible, that often there was nothing left at the end, which in a mathematical sense left perfect numeric equality. Sadly, my brother was not as mathematically inclined as I was to understand.
W L
W L Mês atrás
This was super interesting to see historic real-world consequences of math.
Vigilant Cosmic Penguin
I was not expecting the history nerd in me and the math nerd in me to both get so excited together.
Neil Wilson
Neil Wilson Mês atrás
Maths. Both of them.
Eric D
Eric D Mês atrás
I like your timeshare idea for half representatives at the end there, it would never actually get changed to be like that but it would make for a bit more cooperation between states at least, which we really need in the house of reps.
Mats Hansen
Mats Hansen 5 dias atrás
To me breaking the quota rule seems much more "unfair", than the Alabama paradox. This really bothered me for some reason.
Years-Strange
Years-Strange 12 dias atrás
Can confirm the "poor mathematician" thought process 🤣 Beautiful video though, and very well done on all accounts.
Nome
Nome Mês atrás
To prevent any states from losing representatives when new seats are added, wouldn't we be able to say "you will never lose seats?" Or does it not always work either
geekehUK
geekehUK Mês atrás
My thought was virtual representatives. Any time a significant amount of rounding has to be applied you give every member an extra fake representative then the impacted member their +1/-1. Eventually count up the difference between actual and virtual reps, and aportion voting power accordingly, you can't have fractions of votes so you just multiply it out. Alabama needs 1.5 votes, so now they get 3 and everyone else 2 etc. Yes that could get to the ridiculousness of say each rep getting 12 votes or something other than where it's specifically different but in practice it wouldn't really change how votes were cast and stuff. All I'm really doing here is taking the long way around to suggest that in situations where you have to divide up a limited resource and for whatever reason can't give anyone half a cookie, you can often improve the effective granularity by looking at the working parts or what factors are actually being represented. Here we're talking about State's participation in the federal government. Why do we have a finite limit on the number of representatives? Why not 1000 members of congress, or 100,000? Because it has to be a functional machine, reps need time to be heard, they need to lobby the government and be lobbied, they each have to be paid and they have to campaign for and win elections. Also the more representatives each state has, the closer and more often that the representatives for that State will trend toward being 50/50 split on any issue and decisions will be carried with ever smaller margins. So that's why there's a functional upper limit, why the lower limit? Why not just give every state 1 representative with a number of votes according to their population? Well because they are supposed to be a representative of the people. How much face time is the average Californian going to get when they're trying to raise an issue. Okay so we can see why the numbers are where they are, we can see that there is some advantage beyond simply an extra vote, to a state getting another representative, as it literally reduces the number of citizens per in that State, so each citizen has slightly better access to representation. But we can also see that's a fairly minor effect vs the amount of influence they can wield over federal policy. And so there seems to be an obvious, reasonable solution. Increase the amount of votes per representative say 10x and you improve the granularity 10 fold, meaning you reduce the potential unfair advantage or disadvantage given to a state whenever the number of seats cannot be divided perfectly equally.
Jared Cosby
Jared Cosby 17 dias atrás
Thank you for everything! Awesome content and explanation
Saverio Trioni
Saverio Trioni Mês atrás
Super nice video, I knew the Jefferson method as D'Hondt rule, and I really thought it was fair. It would have been nice to see and actual proof that there is no fair apportionment method :)
Byron Igoe
Byron Igoe Mês atrás
A great alternative for the House of Reps is to not have the total number of seats be fixed. Have the "target" be defined, then round normally. The resulting total might be higher or lower than the target, but that's fine.
LowellMorgan
LowellMorgan Mês atrás
The 3/5's clause was about slaveowners not being able to buy more representation. The free states didn't think the slaveowners should get more representation just for keeping more slaves who couldn't themselves vote or leave. The southern states obviously thought slaves should count as part of the population, not because they believed slaves were entitled to rights or dignity, but because it meant they'd have disproportionate political power.
Sean Taft
Sean Taft 10 dias atrás
This entire debate on the 3/5th Compromise misses a lot of the historical points: 1. Like MANY things in the Constitution, there were heated debated, arguments, and *legit* fights over it. People forget that the Constitution was written with a lot of compromises in it to keep the fragile alliance of the Colonies together (as the Articles of Confederation didn't help that at all). The abolitionists wanted slaves to not count so anti-slave states would have more power and could immediately ban slavery; pro-slavery states wanted a slave to count as 1 each so they could guarantee slavery would be legal. 2. The compromise, as stated, was political in order to keep the Colonies together. The men who wrote the Constitution knew that they couldn't last separated so they HAD to find middle ground. It wasn't easy, and they didn't enter and leave as friends but they knew they had a job to do. 3. Abolitionists and those in more northern states who already had some of the early benefits of the Industrial Revolution knew that technology would make slavery unnecessary. It's why, at the end, they adopted the 3/5th Compromise; it just took longer for technology to get ahold down South than they hoped.
Tuhljin Tampergauge
@Paul One of the original points in the Declaration of Independence was that Britain was forcing slavery in the colonies despite it being illegal in Britain proper. The king was very harshly called out as supporting slavery while hypocritically abhorring it at home. You can see it in the original draft, but it was taken out because the slave colonies objected and defeating the British in war was already a long shot as is even with their support. Despite the writer owning slaves, he was clearly disgusted by the practice, yet legally couldn't free most of them until his death. There are legal and economic nuances people miss when they discuss the topic. Anyway, the main point is, Britain encouraged slavery at the time and forced it to be legal in all the colonies, including the ones that didn't want it, and the colonies that would become free states had that as one of the chief motivations for independence. This is _quite the opposite_ of the narrative certain people want to paint - the same people who like to talk about the 3/5 clause as being eeeevil. They're history revisionists, and I don't need to point out which political faction they're in, do I?
grieske
grieske Mês atrás
@mrmimeisfunny According to the 13th amendment, there can legally be slavery in the USA.
Thanny
Thanny Mês atrás
@Gregor Hodson No, you're looking at it entirely incorrectly. It has nothing whatsoever to do with viewing slaves as less than human. It has to do with reducing the political power of slave states.
Herbie Goes Bananas
@Lyle Goodwin "giving a space for harmful ideas can allow them to grow" is antithetical to what actually happens. First, slavery didn't grow as a result of the compromise. It was already flourishing. Second, hiding, ignoring, or censoring harmful ideas allows them to grow unabated. One must constantly battle harmful ideas with reason and truth. Allow harmful ideas to be seen and point out why they're so harmful.
Neil Googe
Neil Googe 17 dias atrás
I would love to know, how the difference between methods, and so the way seats have swung, may have affected the outcome of history in a very real way. So by any one state getting an "unfair" seat, or a state "unfairly" losing a seat, it affected the outcome of any important decision that then affected the course of history in any significant way... At least in America. Was a fascinating look at a problem, that affects a potentially very important real world issues... Or did it. How many cookies a state may or may not get doesn't really matter, the voting power of a state, even by one seat, could potentially lead to some very real differences in history... But sadly, that is beyond my ability to figure out, even with the help of brilliant :) Great video as always...
crisis8v88
crisis8v88 Mês atrás
I loved the sensitivity analysis that you did for each method.
Noah
Noah Mês atrás
Your whole rant on primary sources is very relatable. I always try to look for primary sources and it sucks when that's difficult to find. I even found a myth surrounding a famous computer worm that apparently had it's origins in Wikipedia.
Matt Allder
Matt Allder Mês atrás
this brings up my question or problem is that with some of this paradoxes and in particular the quota break it feels like the number of seats changing would be the way to get a better even shake. like the number of seats should be matched to the divisor for the individual state rather than trying to fit the states to the number of allocated seats. but I am happy with how well Hill seems to work
Graham Asher
Graham Asher Mês atrás
A very similar problem comes up in typesetting when splitting lines evenly into a paragraph. A native solution tries to minimise the total divergence of spaces between words from the average, but that can result in one line being very bad (for example, two words on the line with a massive space between them) while all the others are okay. The fix is to minimise the average of the squares of the divergence; I believe that’s what Don Knuth’s TeX system does (I worked with it back in the 90s, so forgive me if my recall is bad). There are also strange Alabama-like paradoxes caused by the fact that although spaces can be stretched and shrunk smoothly, words do not normally stretch or shrink and jump from one line to another unpredictably as wrap width changes or new text is inserted. I spent a happy but confusing 9 years working on typesetting software and have scars to prove it.
ecoista
ecoista Mês atrás
It would be easier just to split the word.
Armin Samii
Armin Samii Mês atrás
"badness 10000"
John E Evans
John E Evans Mês atrás
There are potentially all kinds of paradoxes in computer science, such as certain scenarios where disk performance decreases when increasing the number of available buffers.
Robert Keddie
Robert Keddie Mês atrás
When I was a student on placement back in the eighties I built graphics hardware to interpolate pixels in live video by averaging the neighbours horizontally. It failed to work, because rounding meant the gap between pixels was often two wide. It looked really bad because averaging white and black gave medium grey, which looked almost the same as black when next to white. I only worked on this for a week and was unable to solve that problem.
139
139 Mês atrás
Lawrence Table of contents should be ragged. Makes no sense to justify them.
ca-ke
ca-ke 4 dias atrás
Looking into sources and citations can be extremely frustrating. Partially I think its because people just cite whatever at face value without really digging into what the primary source actually said. Its like a long range game of telephone, and one wrong source in the line can cause so many more publications to have the wrong number or concept.
The Terran Informed
Really fun!!! Researching obscure topics in general can sometimes be very difficult! (inconsistencies!!!) Also I like your idea at the end of the video for shared representatives!
David McGill
David McGill Mês atrás
Apparently I had rediscovered this Hamilton method when I had to distribute available points in a game to whole numbers. I know I had searched for a process to do such a thing but had no luck finding the right terms to search for it. Not finding anything, it seems I ended up coming up with this method on my own.
Thedoctor133
Thedoctor133 5 dias atrás
Something to point out, the House of Representatives has had it's members capped for over 100 years. This means that no more errors can be created from increasing the size of the House, and therefore an error created by increasing the number of available seats is not going to happen at all.
lolmaker777
lolmaker777 Mês atrás
Another interesting thing to look at I think is, what if we don't require an exact number of representatives. What if we just use that number as a target number and if it deviates slightly after rounding (up/down/closest integer) we just have a few empty or extra seats until the next census?
Tomorrow Vi
Tomorrow Vi Mês atrás
@Alexandre Zani their rescue funds came from the rest of the USA and printing money
Alexandre Zani
Alexandre Zani Mês atrás
@Tomorrow Vi California and New York are both running large budget surpluses.
Tomorrow Vi
Tomorrow Vi Mês atrás
@Alexandre Zani are you joking ? Their taxes are subsidizing the failed democrat run cities . Especially those running up huge debts from locking down excessively
Alexandre Zani
Alexandre Zani Mês atrás
@Tomorrow Vi Because of the immense economic benefits they get from free trade and the large transfer payments they get from larger richer states to start with.
Tomorrow Vi
Tomorrow Vi Mês atrás
@Alexandre Zani then why would the smaller states even be a part of it ?
Elijah White
Elijah White Mês atrás
Try this: no rounding at all. If the remainder is .5, or greater, a "junior" representative with exactly that portion of a vote is elected. If the remainder is less than .5, the remainder is given to the "senior" representative (seniority can be determined in many ways, including by another vote, time in the house, or dance-off.) So, for example, if a state's initial apportionment is 3.72, they would get 3 normal reps and 1 junior rep with .72 of a vote. Meanwhile if a state were to be apportioned 12.2, it would get 11 normal representatives and 1 senior rep with 1.2 votes.
Peter Samuelson
Peter Samuelson Mês atrás
Who gets to live in those shrunken Congressional districts, though? I would be a bit miffed if I happened to live in a district where my representative had only 0.72 of a vote.
LetTheTunesFlow
LetTheTunesFlow 17 dias atrás
You are really killing it with the quality of your videos and humour these days! Congrats! You just get better and better with each video you make! You should be damn proud of how far you have come! I just love seeing when someone who has been making videos for years, has gone from quick and dirty videos, to an excellent and professionally looking show! I’m also so glad that with the improvements you have made to your skills, that you still haven’t lost what makes your videos great! Your ridiculous humour is on point! I genuinely laugh more often than maybe I should watching your videos! Your videos make me excited to learn something weird/interesting/silly/etc… Without triggering my very traumatic memories and experiences with math(s) in high school. It’s such a shame that my experience was unimaginably terrible! I’m just so lucky to have been introduced to you, and many other infectiously passionate teachers on BRvid! You have encouraged me to see the amazing utility, and ability for math(s) to help explain all the infinitely interesting problems that the world often presents us with! I have learned it isn’t as hard as I thought to have a go at solving questions I may have with a little math(s)! Thank you!!! You don’t know just how important of a moment it was to me, when I realized I could start to understand and use math(s) to solve or just ponder potential solutions to problems! I’m unbelievably thankful to you for curing the mental and emotional damage I had from some pretty awful math(s) teachers. One teacher physically cornered me in the hallway after I had just gotten out of the hospital, due to some severe health issues I had at the time. He was turning red screaming at me for “always being sick on test day”, and other nonsense…He also would often call me “an idiot who just couldn’t get it, and I was just calling in sick to purposely miss his class”, and he should “just fail me regardless anyways, for missing a few exams…”. Yeah he had doctors notes explaining that I was in the hospital and still said those things to me… So yeah, apparently notes from the hospital were not good enough for him… So you may be able to identify where my “I suck at math(s)”, problem arose… So thank you so much for changing my view of math(s) and my potential future abilities, if I continue to learn and work at it! I’m just so thankful that you have replaced that false mental perception I had, because of one terrible teacher, and a couple others who were not so great either!
ItsReef
ItsReef Mês atrás
I've seen the Musical "Hamilton" and I can assure you they discussed allocations very thoroughly
andrew cobb
andrew cobb Mês atrás
The transposition of numbers behaves like stable mutations. I have seen this in book references - Chapter 10, page 5 going to Chapter 5, page 10 - and then quoted and requoted in all subsequent publications, proving noone read the source. An account of sleep paralysis in Hemingway's "Snows of Kilamanjaro" is an example . Old UK duffer here, enjoying the ride :)
AverageJon
AverageJon Mês atrás
16:34 - your POP/DJ figures are out here! Although weirdly column E rounds down ‘correctly’ using what should have generated. Did you input Jeff’s divisor as 880 as a test at some point? 🤔 Edit: ah, 880 comes later! Another Edit: Adams’ POP/DA figures for all states except New Triangle, all jump straight to your 960 conclusion on first entry, same issue.
Mike Nichols
Mike Nichols Mês atrás
@Daniel Kinal I agree. I've paused and rewound this video a LOT as I'm following along with everything. When he rounded down 24.86 to 23 I was like... Wait, what??? I didn't think to check his division on POP/DJ before coming to the comments. If I had watched far enough forward I might have caught the error that caused my confusion. But I think this video deserves to be edited to correct the issue or at least add a text note pointing out the error. As my physics professor used to say, getting the right answer doesn't matter if you can't properly show me how you arrived at it.
Daniel Kinal
Daniel Kinal Mês atrás
@Tissue Cat Thanks. Not being a BRvidr, I didn't realise this limitation. Bummer.
Robert B
Robert B Mês atrás
@Stand-up Maths my apologies for overstepping, but there is more than one thing wrong in that part of the animation: First, 21878/930 ≠ 24.86.. but 23.52…, and I see in your reply you comment that those numbers represent the 880 divisor of Jeff (DJ) which is correct. Second, at the stage of the 900 DJ there is another blooper, which gives Octiana 4.6133 instead of 3.6133 but the seat count is the correct 3… For a “math” channel, I would be embarrassed 😬🤭 to post a video with so many careless mistakes in one segment🤨. I would suggest adding text comments at the places where the mistakes are made or redoing the video correctly 😉 Other than that, a very interesting and educational video 👍
Karthik T
Karthik T Mês atrás
The kicker is 19:50 :D "Did you spot it, something funky going on with the numbers?" :D
Karthik T
Karthik T Mês atrás
Haha glad to see I wasnt going mad..
Ilya Gromovikov
Ilya Gromovikov Mês atrás
26:39 as a historian with some maths education who tries to dig in data, this hit so close to home
injart
injart Mês atrás
I just want to say how much I appreciate the bench shot. It's so perfect in so many ways.
Zeyev
Zeyev 26 dias atrás
Thanks for a discussion of one more aspect of the messy system of governance in the USA. I live in the non-voting District of Columbia and have lived in Alabama (twice), California (many times), North Dakota, Texas (twice), and Virginia so I understand the perspective of all of these areas. I have been reading that we need to add many more seats in the House of Representatives to achieve any sort of fairness, even if the problem of allocation has already been fixed. Perhaps the Congress should call you and other mathematicians to figure out all of this. PS The States (except the small ones) are now drawing boundaries for their districts in the House. Some are trying to be nonpartisan and others are going whole hog into gerrymandering. Lawsuits will ensue.
MSc Bijles
MSc Bijles Mês atrás
Wow love the suggestion at the end. States should indeed buddy up with others for halve seats. Maybe that should actually be much more of a thing. To promote dialogue again in US politics!
Alexander Sanchez
Alexander Sanchez Mês atrás
I always thought the "Alabama paradox" was when you went back in time to meet a distant ancestor, but--in a dramatic twist--it turned out that actually that relative was always you, so you have to stay in the past and fill the role to prevent yourself from disappearing.
Alexander Sanchez
Alexander Sanchez Mês atrás
@Gregory Morse I haven't edited since shortly after initially posting, and only to fix a typo that made the grammatical structure of the sentence completely opaque. I'm glad you were able to recognize my feeble humor as such upon second reading, though.
Gregory Morse
Gregory Morse Mês atrás
@Alexander Sanchez lol well now that you edited it, you have succeeded. It didnt read as humor before I suppose. Normal issue with text banter on the web, hard to gauge the tone.
Alexander Sanchez
Alexander Sanchez Mês atrás
@Gregory Morse Chill, bruh. I tried to write this as a PC incest joke about Alabama that wouldn't upset anybody; sorry if I stuck a nerve.
Brundin Grabe
Brundin Grabe Mês atrás
@JNCressey Your nonsense doesn’t actually make an argument. He would already have the genes that would have resulted from his being his own ancestor. The loop is not recursive.
JNCressey
JNCressey Mês atrás
@Brundin Grabe, a single unchanging stable timeline lends itself to all the paradoxes associated with time travel.
William Hilton
William Hilton 10 dias atrás
But what if instead of keeping the total number of representatives fixed, we're allowed to vary it based on the census data in order to create the "most fair" apportionment? What would we do then?
Soggy In Seattle
Soggy In Seattle 12 dias atrás
This was enlightening and entertaining. Well done. ⭐️⭐️⭐️⭐️⭐️
moestietabarnak
moestietabarnak 24 dias atrás
Instead of rounding up/down with a ad-hoc divisor, I'd use the % of representation and redistribute the extra from the highest state to the lowest state... I mean, if the biggest state get 23.6% of representation, you give them as many rep UNDER that value then give the rest (population to the other state) because a state with 40 rep can lose 1 and just lose 1/40 of power ..while the ones with 2-3 rep losing one mean a LOT, and giving one extra to the lower does not imbalance the division of power noticeably..
Just A Guy
Just A Guy 14 dias atrás
I like the idea of fractional votes. If you have 2.75 seats and another state has 8.25, you each get an extra representative but one holds 0.75 votes worth of power and the other only has 0.25. Combined, their agreement would be worth one whole vote
Clikcer Productions
I actually don't think there is an issue with rounding large numbers up by more than one, the system should be based logarithmically and thus 22.5 is closer to 24 than 1.5 is to 2
Clikcer Productions
Clikcer Productions 25 dias atrás
@Cooper Gates Thats actually really cool to know! I think the Quota rule is one of those things that to us seems to make sense, since we're usually raised to think arithmetically, but doesn't really lead to anything elegant or optimal in practice
Cooper Gates
Cooper Gates 26 dias atrás
@Clikcer Productions Matt discusses after his session on the reflection bench additional methods, including the variant of Jefferson and Adams with 'normal' rounding. I would use ceiling (float - 1/2) for fun. It's quite a bit more elegant than the method which is actually used now, and I expect if there are quota rule violations, they'd only happen to the big numbers, so your logarithmic argument would stand, e.g. 22.75 to 24.
Clikcer Productions
@ShadowZero27 It's all good, I should've given my full thoughts in my original comment, because as it is it leads to assumptions
ShadowZero27
ShadowZero27 Mês atrás
@Clikcer Productions i assumed incorrectly that you meant that the extra representatives or delegates should go automatically to the states that would occupy a logarithmic spike if this would be low populations or high populations, not for rounding after initial distribution
Clikcer Productions
@ShadowZero27 The ROUDNING should be logarithmically based, i.e. the system should be designed to be the closest to the exact numbers but that closeness should be logarithmic, in a lot of cases it would be more reasonable to round a large number by 2 than a small number by 1 as the amount of change in terms of a ratio would be lower, nothing I have said would even slightly lead to one party having total rule, what are you talking about?
rantingrodent416
rantingrodent416 Mês atrás
Couldn't you build a pretty fair system by handing out half of your representatives using the Jefferson method and half using the Adams method? Each method preferentially uses vote counts in larger states to correct errors, but has an opposing bias.
CubaKing
CubaKing Mês atrás
I feel like the solution here is to uncap the number of seats (aka technically infinite) and do the following for every x population of a given state/province/etc, that state/province/etc *adds* 1 rep. We worry about the number of seats after calculations.
Bruce Pollock
Bruce Pollock Mês atrás
On your mention of the electoral college, I feel we should break the connection between the number of electoral college votes and the number of House of Representatives members. There is no need to be limited in the number of votes simply because we limited the size of the House. It works in the House because it limits the number of voices that need to be mediated. In the electoral college, it should simply be a vote tally.
Bruce Pollock
Bruce Pollock Mês atrás
@Anton Lindequist Ariens If you want to get "technical" the populous doesn't vote for president. It votes for a party that assigns electors, who then vote for the president, almost exclusively along party lines. When the electors deviate from the popular vote of their state they are called faithless electors. Only a handful of states don't assign electors by a winner takes all method, which means large portions of the popular vote are thrown out because of arbitrary state lines. The number of electoral votes has always been tied to the number of congressmen and that number was fixed at 435 in 1911. This causes a vote in more scarcely populated states to be more pivotal than a more densely populated one. The electoral college does provide for an elected president to begin a transition before being officially elected, and allow a party to course correct if something drastic happens between Election day and when the electors vote in December. It also has a small balance for smaller states, guaranteeing three electoral votes each that a straight popular vote would not provide. Technically, none of this is any reason why the number of electoral college voters need be locked at 435.
Anton Lindequist Ariens
Well technically the electoral collage consists of people called electors, who actually elect the POTUS. In actuality the entire concept of the electoral college is antiquated and should be abolished.
Fredrik Wendt
Fredrik Wendt Mês atrás
If there is there one thing that I'm gonna take away from this, it's the fact that I NEED a reflection bench. The potential for insights and reflections seems off the chart! Love the format of the video in general though, calm reflective, and with a dry sense of humor!
Qlmmb2086
Qlmmb2086 Mês atrás
This reminds me of a similar problem I ran into when writing an RPG engine back in high school (circa 2003 I believe). I was treating character level as a percentage scalar to total attribute values but wanted to distribute attribute increases consistently at every level, so rather than do each attribute individually I decided to increase the total attribute pool itself, then distribute that pool proportional to each attribute's base value. So, for instance, the initial pool was 20 points per character with a 20% increase per level, meaning I wanted 4 new attributes to be automatically distributed with each level up. The problem I quickly ran into was that using the Hamilton method (without knowing that's what it was; it was just the first solution I stumbled upon), was that the 20% increases led to beat frequencies where occasionally the fourth and fifth highest remainders could be **ties** from attributes with identical bases, meaning no exactly-4 increase was possible with that method. In the end I just scrapped it for a round-down approach that had increment spikes on the beat frequencies, since I felt having every 5th level be the one where **every** attribute increases made for a better RPG style "milestone" feel anyhow.
Qlmmb2086
Qlmmb2086 Mês atrás
@Pockeywn Sticks For certain definitions of "finished!" I got it to a fully playable state and then kept adding onto it here and there whenever I got ideas on how to extend it. It was more of a self-teaching project than anything though, so it never left the family PC and wasn't ever "released" since I was a kid just figuring things out on my own and had no idea how to build websites, just basic applications.
Gregory Morse
Gregory Morse Mês atrás
@HesderOleh I'm talking about k-folds cross validation. So k equal partitions of a dataset. This means you can just divide out the remaining ones by fractional % which are all the same anyway. But the fact is you take the rounded down amount and just assign up to 1 more as needed to get the closest to an even partitioning as possible without discarding data
Pockeywn Sticks
Pockeywn Sticks Mês atrás
now did you ever FINISH that game? (yes this is a personal attack on you as a game developer)
Vigilant Cosmic Penguin
Now, if Hamilton had been designing an RPG, he would've figured this out in the first place.
HesderOleh
HesderOleh Mês atrás
@Gregory Morse why hailton and not hamiltons-hill?
Kenai Kuskokwim
Kenai Kuskokwim 24 dias atrás
Washington had spent years as a surveyor, dealing with math(s) and jealous landowners. He'd have been the first one to smoke out such problems!
Steve Jones
Steve Jones Mês atrás
As someone who works (in IT, not a political capacity) at the US House, I can tell you this is a pain.. Lots of stuff to rename and reorganize every 10 years.. This was a fantastic description of how this works behind the scenes, and I had no idea of these details! I'll definitely pass this video link around the office - I'm sure it's gonna get some views!!
Ian Mills
Ian Mills Mês atrás
When the 2020 Census results were first published I wrote a very simple excel macro that iterates through this process and tracks a bunch data about each state. Super interesting -- for me, anyways
Greg Pettigrew
Greg Pettigrew 12 dias atrás
In competitive gaming tournament matching systems, sometimes a player that benefits from rounding errors in iteration 1 gets pushed to the back of the line for benefitting from rounding in iteration 2. So, if the 2010 Census says the State of Rhombus gets 43.5 seats and it went up to 44, then in 2020 it would default to rounding down.
Lee Yung Hei
Lee Yung Hei Mês atrás
at the timing of 16:48, the rounddown() function seems to have the wrong column as rounddown(24.8614)=23.
Riccardo D'Ambrosio
I originally thought the same, but then noticed that when DJ value changed the relative POP/DJ changed accordingly and rounddown() correctly displayed the right value. Point is, the whole POP/DJ column at the very beginning appears to have been divided by a complete different value of DJ (POP/DJ and POP/D values should have been pretty close, as DJ and D were almost identical). To be precise, 880 instead of 930 shown on screen.
Mark McAdie
Mark McAdie Mês atrás
Because “fair” is not a mathematical concept, it is a philosophical one…
TFogs75
TFogs75 10 dias atrás
This was a fantastic video to keep my mind working during a quarantine
Brendan Luttrell
Brendan Luttrell Mês atrás
A few points..... 1.) I admire your commitment to accuracy and fact-based reporting. You don't find that often in the world, let alone in the midst of a youtube content creator. 2.) I'd like to know where you came about your reflection bench. I need one of those. 3.) How in the world did you pass yourself the plate of cookies while both of your hands were on screen? Obviously there is no other existing human in the world of your videos...
Chris Herrick
Chris Herrick Mês atrás
What about assigning according to the correct divisor (using rounding down), then assigning the left-overs randomly (but only allowing the left-overs go to someone who hasn't already received a left-over)?
Anthony Meek
Anthony Meek Mês atrás
I loved the amount of work in this video. My only issue it that the House must always have an odd number, so I'm curious what data would've looked like therein. Again, great video and I can't believe the headache that went into it haha. Keep it up
Peter Samuelson
Peter Samuelson Mês atrás
Why must the House always have an odd number? Is that enshrined in law somewhere? I presume these thought experiments don't take current legal restrictions into account.
Bill Carlson
Bill Carlson Mês atrás
This is something I've thought a bit about - and here's my solution... Stop using whole numbers, and start using real numbers. At least when possible. It makes the 'round down, regular, or up' issue go away. Take the population divided by the seats - let's say you get 3.4. Great, you get 3 'seats', but each of those seats has the voting power of 3.4/3. (or 1.13). OR, round up, and you get 4 seats, but each one's vote is only 3.4/4 (0.85).
WWLinkMasterX
WWLinkMasterX Mês atrás
Very cool! Do you think you could make a video breaking down the halocost numbers, so that we can show up the deniers once and for all?
Don Reid
Don Reid Mês atrás
One option is to remove a constraint. Divide all states by the "ideal" value and round normally. Then that is the total number of actual representatives. There is no reason it has to be exactly some predetermined value.
Pengochan
Pengochan Mês atrás
27:50 had that problem with scientific data (tables of materials properties) recently, when i was looking up a citable source for data used for a publication. Apparently the table from the original publication of those who did the experiment was transcribed with several typos for a publication of a compilation of several materials properties, then that table was adopted by some manufacturers association and widely circulated as service to their customers. Of course those tables are now still widely used although there is newer, and better experimental data.
V Blaas
V Blaas Mês atrás
@Adarsh Mohapatra Systematic (linearly progressing) errors I suppose? Within the statistical method or equipment itself?
Adarsh Mohapatra
Adarsh Mohapatra Mês atrás
@Tighe Lutz I think what he means is that the code in the instruments used in CERN account for the mistakes that arise in the statistical method they use.
Tighe Lutz
Tighe Lutz Mês atrás
@Tobias Wilhelmi Would you mind rephrasing that for me? Seems like it's probably a neat and interesting comment but I'm trying to figure out what you mean and I can't figure it out and I'd really like to understand what you're talking about (I know what statistical methods are, I know what CERN is, but I'm definitely still missing something!).
Tobias Wilhelmi
Tobias Wilhelmi Mês atrás
As far as I know the statistical methods used in CERN counter in mistakes within the code of the instruments.
Stand-up Maths
Stand-up Maths Mês atrás
I feel you!
Stu Lora
Stu Lora Mês atrás
@Matt, Please have a look at the German system for translating votes to seats in the Bundestag (i.e. Federal Parliament). Afaiu, it's one of the most complicated, but also one of the fairest. Needless to say, it leads to other problems, e.g., a potential increase of seats with all the statistical problems that come along with it, etc.
DividedByZero
DividedByZero Mês atrás
It feels like a lot of the headache can be removed by making the number of seats dynamic and add more temporary seats from the norm to allow better seat allocation overall after every census.
SkellyBobs
SkellyBobs 12 dias atrás
I vaguely remember this argument within the my social studies in school, it's nice to get more context two decades later.
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