Why it’s mathematically impossible to share fair

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!

as an Alabamian, I can confidently say our education system never forgave math for this and has actively scorned it ever since

The amount of joy on this man's face when he said "the united shapes" is enough for me.

2:40 Why is Circula so upset? You'd think he of all shapes would appreciate rounding.

28:06 Fun fact, the folks at Wikipedia have actually gone through the research and found that the original census actually miscounted a single county that had 450 people living in it. So, it actually isn't a transpose error where somebody flipped a digit. The original source is off by 450, and it happens by coincidence that 490 + 450 = 940. How wild.

You're really good at explaining complex math concepts. Thanks for letting me play along.

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

Speaking of clerical errors, you've got one in the video. At 16:45 the resulting values for =POP/DJ are being displayed using the final divisor, not the initial estimate 930. Which is also how I could tell that the excel/spreadsheet magic was just smoke and mirrors! Clever editors

“The united shapes” blindsided me like a freaking freight train. I should have seen it coming but I’m still giggling to myself

The cameo by Destin—I mean Alabama—really made my day. He obviously had a ton of fun recording those bits!

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!

Performance excel has to be perhaps my favourite thing going. I can't quite get my head around what you've done to make it look so slick other than manually updated everything to make it look like excel so I just wanted to say I appreciate the work that went into that!

I think this explains something I'd been wondering about for a while. In Australia the number of MPs is supposed to be approximately twice the number of senators - it's important to maintain a consistent ratio for the case of a joint sitting. I have often wondered why it's approximately rather than exactly two-to-one until now: the quota rule vs Alabama paradox only applies if the number of seats is fixed. If you have a bit of wiggle room to change the number of MPs (as is the case) you can avoid both issues!

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.

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.

I ran into a similar issue years ago at an engineering company. I wrote a program to generate a monthly report in nice, round dollars. The problem was that the numbers didn't add up do to roundoff and that really ticked off the accountants. They didn't care what it took to make that report balance. I considered choosing one of the totals and use it for the other side, but I figured if they ever added it up, the accountants would be even madder. The solution was to add up the numbers, and determine a roundoff that would make them balance. So one month, it might be rounding everything up from 40 cents and the next month it might be rounding down from 80 cents.

I loved this video! The concept of "fairness" is absolutely something we should all know more about. I was wondering if you could explore the same type of concept in compating types of voting? Thanks!

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!

But how many sides does an “Ore-gon” have?

Or alternatively, you drop the seat limit entirely and figure out the size of seat based on a divisor of the population of the smallest state, and multiply out. That way as populations change you get automatic switching and remain fairly consistent.