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Just because you want to be surprised about the shape of the universe because the shape of the earth was surprising, doesn't mean it actually is surprising.

i dont get it. wheres the connection between voting and the math?

I love youtube's algorithm

We don't.

I’m sure every US citizen is extremely happy about having to choose between sexual abusing geriatric and genocidal geriatric

This is beyond me.

How do you define what is one object? Everything is arguably a pile smaller things..

how does the math here make more sense than the wordS?

whats wrong with your tongue?

This has too many abstractions for me to follow your argument. Can you explain how this breaks in the case of pure proportional representation? I can't see the unanimity or anonymity constraints breaking, so it must be the continuity one, but how? Here in the Netherlands we have a nearly pure proportional system and I can only see small changes in the votes create small changes in the outcome.

MATH??

As soon as political parties form, the people inside it vote as a block, thusly skewing entirely the results of their election wildly in their favor. It doesn't take many people either. I found this out in 1st grade when 4 kids from a clic got in cohoots in a class of 23 and voted as a block and swept what was suppose to be a fair election. After a few elections of skewing the results this way, it becomes a simple matter to promote these to the rest of the voting public as the only candidates that can win, and thusly programmed from past history results, skewing the election even further. This is what we have in the United States. Political parties have subverted voting forever. That's what these kids in the class did for the next 11 years..

I think this is the first time I really regret not being able to give multiple votes through the like button :) What an excellent video! Funny but also interesting, I'm so glad to have stumbled upon this channel!

Regarding the discrete nature of preferences in practical applications, note that you can consider as valid outputs any convex combinations of preferences. For example, if Trump and Biden are the possible preferences, the combination 0.15 Biden + 0.85 Trump Explains how much you prefer one to the other. This is used in may contexts, e.g. in neural networks to allow categorical variables to be treated as continous variables. The categorical result is then extracted by taking the variable with higher coefficient, with a chosen convention when draws occur.

In the voting literature, most people explain Chichilnisky's theorem using the example of where to have a party. Imagine you and I live along a circular road, and each of us wants to have the party closer to home. A natural way to decide where the party should go is to pick the halfway point between our two homes (or, if we live together, to just have it there). But this rule leads to a discontinuous jump. Suppose I live at 12 o'clock and you live at 6:01, just slightly past the bottom of the circle going clockwise. Then the party will be way over on the left side of the circle (near 9 o'clock), since that's halfway between us. But if you were to move just slightly counter-clockwise -- say, to 5:59 -- the party would have to move way over to the right (near 3 o'clock). An arbitrarily tiny nudge to your preferences can lead to a big leap in our collectively preferred location. And this point generalizes to other anonymous rules that respect unanimity. Interestingly, there is a topological condition that will get us out of the problem. You can have an anonymous, continuous rule that respects unanimity so long as the space of preferences is contractible -- which in this case means a line rather than a circle. (BTW great video.)

The sound is AWESOME

But in reality, the options are discretized, so the continuity is anyways not well-defined...

Rubbish. There exist very clear understandings about why and how humans like music in the Eastern philosophies and musical disciplines. One is called Nada Yoga -- the study of sound vibrations within the mind-body complex and the physical universe. All very provable, and known for 3,000 years. Western science knows full well that every atom has a resonant frequency ... DUH. We can see sand patterns on glass in the visual firms of Yantras (geometric patterns. People thus have different frequencies in their bodies, hence harmony/disharmony arises when summed with conditioned upbringing (ie, psychological familiarity, likes/dislikes, in-utero exposure to different styles of music). It's all very, very simple. You really need to get out of your biased Western ignorance and stop making definitive, absolute pronouncements about things you just don't know. Just because YOU don't know something doesn't mean that someone else doesn't. And you hide behind this "WE" collective of Westerm science -- another example of arogant Western group think.

wow this explains those concepts so well but doesn't get enough attention while most brain-rot or TikTok videos got millions of views this channel is definitely underrated and also most of the educational channels as a CZcams creator, I started because I also wanted everyone to study so the world could be a better place but many kids my age keep watching Skibidy toilet things and I am trying to draw their attention by making cat memes and baiting them to study but it seems that it didn't work so well also, I'm broke and need to pay students depth :)) anyways sorry if my English sucks it's my 5th language

Great video on maths of social choice!

It's 2am here and I fucking CRAVE popcorn rn lol

Voting can't be continuous when you have so few parties (even in France where you can get 15+ president candidates) because every vote above a certain percentage become useless...

Neil Degrasse Tyson said that people don’t have an intuitive sense of exponential scales. Here’s a toy that gives you that!

10:07 is it just me or does the music sound like windows fail notification. I was scarred for a second thinking my mouse or something was breaking.

Everyone votes a number between 0 and 1. The end result will be the average of all votes. This seems to obey all 3 "demands" (continuity, anonymity, unanimity)

Omg. Why do scientists lose touch with reality. To get 100% popped kernels, it's as simple as: (1) not microwaving it in the first place, but frying it in butter in a saucepan with a lid; (2) shaking the saucepan near the endso the unpopped ones fall to the hot bottom and the popped ones don't burn. What a fkn waste of human intelligence you exhibited here.

1:20 except piecewise functions CAN be continuous with the Laplace

What a superb video :D

bro invented the rabbithole

I had those when I was younger. I lost them unfortunately

While an interesting topological result, violating continuity isn't that big of a deal. E.g. a simple normalized average of everyone's preferences only has a single discontinuity, at the point where all preferences exactly cancel each other out - for practical purposes that doesn't really matter (because it doesn't really happen).

I thought you were going to talk about why it's impossible to fairly vote with 3 or more options.

Continuity is definitely the one compromised because most votes are winner take all. So for example if the spectrum is Nuke Canada vs Don't Nuke Canada we don't nuke a % of Canada equal to the vote. Its part of the reason you see extremism in political candidates. Good guy Jerry with mild opinions isn't an option so people end up voting for whoever happens to be closest to them.

👍

The video ends with "and that's why democracy doesn't work"

I mean, continuity of results is kind of a lot to ask for a system where there is any sort of victor, and the victor is not predetermined ahead of time. In the case of u.s. politics, either the democrats win, or the republicans win. In order to have a system where the output is as continuous as the input, while still reflecting the preferences of the voters, you would need to do away with elected officials entirely, and just have every voter vote on every issue... which actually just pushes the continuity question downstream, since at some point, you get to the discontinuity of "do we do the thing, or do we not do the thing".

Okay I am ready for 4D Politics now

3:00 slight correction: you need a not gate and either an AND or an OR gate, due to being able to convert AND and OR gates with DeMorgan's Law

2:50 I don't understand what these function axis are supposed to represent. Do they represent # of cheese burgers compared to # of fries? It's not very specificied

if things didnt need to get bolted together, we wouldn't have to worry about this. why is stuff put together? damn this mad mad world.

A 2 dimensional creature living on a sphere would actually be extended into a third dimension, but just a little bit. How much it is warped depends on how big the sphere is. And the creature would be able to imagine the sphere it is living on if we are given a dimension of time. The creature wouldn't be able to imagine the sphere all at once, but in 2d slices which flow through its imagination.

I think the mistake is that in reality, you cannot vote against a party (except by only voting for the other ones). At 4:14, there is only one party, but you can still vote against. In reality, having only one party would have only one voting option. To fix this, we should only have a positive vote, creating a quarter circle (in 2D). A quarter circle doesn't wrap around, so I don't think realistic voting is a möbius strip.

Entropy

Seem your argument of representing it as a mobius strip based is build on that is it only two voters? It might still be true, but think you did a small jump over if this representation still holds with more voters. Interesting video regardless.

In a first-past-the-post system (terrible name btw) continuity is clearly not upheld, one person voting differently can result in a different party winning and getting basically all power. But it gets harder with proportional parliamentary systems, in the Netherlands the number of seats a party gets is equal to the number of votes they got divided by the total number of votes times the total number of seats. Voting is anonymous, if everyone votes for the same party that party gets all seats, and if voting habits change a little bit the seat arrangement only changes a little bit witch won't have massive effects on which parties form a coalition and which laws get accepted. The math in the video seems correct, but I wonder how it works on a proportional system.

Joe Birden

1:40 Ever learn Esperanto's word for "and", which is "kaj"? Dance ChaCha? Pet a cat named Kiki?

Your conclusion about continuity seems to me to be related to the concept of transitivity in economics. If a person likes oranges better than bananas, and bananas better than apples, doesn't imply that the person likes oranges better than apples. There's a discontinuity of transitivity. Humans are complicated.

How universe in the shape of some Klein Bottle variation would look like?

Why is continuity a requirement, that does not map to democracy at all, preferences can vary a lot one cicle to the next.