> temp > à-trier > why-winner-takes-all-democracy-is-mathematically-impossible-veritasium

Why Democracy Is Mathematically Impossible

Veritasium - 2024-08-27

Democracy might be mathematically impossible – here’s why. Head to https://brilliant.org/veritasium to start your free 30-day trial and get 20% off an annual premium subscription.

If you’re looking for a molecular modeling kit, try Snatoms, a kit I invented where the atoms snap together magnetically. https://snatoms.com/
 
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Massive thanks to Prof. Eric Maskin for helping with the script. Thanks to Chris Dong for inspiring this video. Massive thanks to Latif Nasser for being part of this video. Massive thanks to Curtis Gilberts, and to Radiolab -- listen to their great episode on voting systems here https://radiolab.org/podcast/tweak-vote

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A few great proofs of Arrow’s impossibility theorem:
Yu, N. N. (2012). A one-shot proof of Arrow's impossibility theorem. Economic Theory, 523-525.- https://ve42.co/Yu2012 
Geanakoplos, J. (2005). Three brief proofs of Arrow’s impossibility theorem. Economic Theory, 26(1), 211-215. - https://ve42.co/Geanakoplos2005 

References:
Arrow, K. J. (2012). Social choice and individual values (Vol. 12). Yale university press. - https://ve42.co/Arrow2012 
Arrow, K. J. (1950). A Difficulty in the Concept of Social Welfare. Journal of Political Economy - https://ve42.co/Arrow1950 
Black, D. (1948). On the rationale of group decision-making. Journal of political economy, 56(1), 23-34. - https://ve42.co/Black1948 
Black, D. (1969). On Arrow's impossibility theorem. The Journal of Law and Economics, 12(2), 227-248. - https://ve42.co/Arrow1969 
Maskin, E., & Sen, A. (2014). The Arrow impossibility theorem. Columbia University Press. - https://ve42.co/Maskin2014 
Gehrlein, W. V., & Valognes, F. (2001). Condorcet efficiency: A preference for indifference. Social Choice and Welfare - https://ve42.co/Gehrlein2001 
Dardanoni, V. (2001). A pedagogical proof of Arrow's Impossibility Theorem. Social Choice and Welfare, 18(1), 107-112. - https://ve42.co/Dardanoni2001 
McCune, D., & Wilson, J. (2023). Ranked-choice voting and the spoiler effect. Public Choice, 196(1), 19-50. - https://ve42.co/McCune2023 
Santucci, J. (2021). Variants of ranked-choice voting from a strategic perspective. Politics and Governance, 9(2), 344-353. - https://ve42.co/Santucci2021 
Kaminski, M. M. (2018). Spoiler effects in proportional representation systems: evidence from eight Polish parliamentary elections, 1991–2015. Public Choice, 176(3), 441-460. - https://ve42.co/Kaminski2018 
Brams, S. J., & Fishburn, P. C. (1978). Approval voting. American Political Science Review, 72(3), 831-847. - https://ve42.co/Brams1978 

Other references and election results - https://ve42.co/IODRefs 

Images & Video:
Minneapolis 2013 Debate Images: https://ve42.co/Minn2013Debate 
4 Images from this article: https://ve42.co/MinnDebateMPR 
Arrow Nobel Prize Image from NYT Article: https://ve42.co/ArrowNYT 

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Special thanks to our Patreon supporters:
Adam Foreman, Anton Ragin, Balkrishna Heroor, Bertrand Serlet, Bill Linder, Blake Byers, Bruce, Burt Humburg, Dave Kircher, David Johnston, Evgeny Skvortsov, Garrett Mueller, Gnare, I. H., Jack Cuprill, John H. Austin, Jr., Josh Hibschman, Juan Benet, KeyWestr, Kyi, Lee Redden, Marinus Kuivenhoven, Matthias Wrobel, Meekay, Michael Krugman, Orlando Bassotto, Paul Peijzel, Richard Sundvall, TTST, Tj Steyn, Ubiquity Ventures, gpoly, john kiehl, meg noah, wolfee

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Directed by Petr Lebedev and Derek Muller
Written by Petr Lebedev and Derek Muller
Edited by Trenton Oliver
Animated by Fabio Albertelli, Jakub Misiek and Ivy Tello
Filmed by Derek Muller
Additional Research by Gabriel Strong
Produced by Petr Lebedev, Derek Muller, Gabriel Strong, Rob Beasley Spence, Emily Lazard, Luke Lewis
Thumbnail contributions by Jakub Misiek, Ren Hurley, Peter Sheppard
Additional video/photos supplied by Getty Images
Music from Epidemic Sound

#democracy #voting #mathematics

@ganeshmaganti-u6d - 2025-04-30

this is like math class, social class, history class all smashed together

@just_a_dude75 - 2025-06-12

life is that

@adamSmith_1723 - 2025-06-17

Yes Because it's all just biology. Humans are living things

@tokesalotta1521 - 2025-07-08

With a left-leaning biased like most things from academia and media

@Avlysh - 2025-07-13

@@tokesalotta1521 got a problem wizh that?

@tokesalotta1521 - 2025-07-13

​@@Avlyshit's not about me

@kentslocum - 2024-08-27

My city voted against STAR voting (a Rated Voting system) because the people who were lobbying against it were the ones in positions of political power--and they benefit from first-past-the-post voting. They knew that if we used STAR voting, their extreme views would be likely supplanted by more moderate candidates. 😢

@Irondragon1945 - 2024-08-27

STAAAAAAARS

@Feefa99 - 2024-08-27

@@kentslocum Class struggle continues

@johnreese7973 - 2024-08-27

RAAAAATS

@jerrygreenest - 2024-08-27

More moderate candidates is good isn't it? Why go extreme?

@justjay3750 - 2024-08-28

​@@Irondragon1945 resident evil nemesis??

@Creequ - 2024-09-05

The worst problem with FPTP is that the current two parties will forever block changing it.

@noddle045 - 2024-09-10

yep it's quite contradictory. how do you vote for a better voting system under a bad voting system?

@rasta77-x7o - 2024-09-11

Well in Australia the 2 party preferred system is worser that FPTP, the current dude only got 30% of the votes and got in.

@FilthyLogic - 2024-09-11

Exactly this.

@ccederlo - 2024-09-12

Support the Equal Vote Coalition and help us get past this challenge! Ballot initiatives, city council ordinances and pressure from citizens can make it happen.
The good thing is not all politicians staunchly align with their party. City council members understand the issues with FPTP and some are open to change.

@reecye - 2024-09-13

​@@rasta77-x7o You mean 30% of the FIRST PREFERENCE votes. Preferential voting will always be objectively better because it considers multiple candidates for individual votes. If you believe in a democratic society then you should not be rooting for fptp...

@Civics_Minded - 2025-05-30

There is nothing scarier than politicians coming together and singing kumbaya.

@shadowman8787 - 2025-06-08

Literally nothing, anywhere

@Tearsofsoil - 2025-06-23

😂😂 So True. But they are always Kumbaya in private while the voters fight among each other on streets and homes. I have seen families/relationships broken after Trump election this term and it was something i never expected to see that people will take politics and politcian words so seriously

@Thomas-s5d3u - 2025-06-27

I can think of something worse, lawyers doing the same.

@danajones7262 - 2025-06-30

Dream to nightmare

@BobMcBobJr - 2025-07-03

You graze a very interesting topic: Are we targeting the correct variable? The exact target of the video's analysis seems to be fairness, ensuring each vote counts identically. It is assumed that would lead to the actual goals, freedom, justice, prosperity, and happiness but whether that is true or not is up to debate. For a counter-example: in the US certain crimes disallow someone the vote. This is not fair but it does serve the interest of justice because it is logical that criminals would vote for crime.

Statement made, chaos ensues... =)

@Android480 - 2024-08-27

The pivotal voter thing doesn’t make sense, because it’s not actually an individual person. You shuffle up the votes, and one random ballot happens to be the pivotal voter. No one knows who it is ahead of time, and even more important, that vote being pivotal relies on all other voters having made a specific decision. Had they voted different, that would no longer be the pivotal vote.

@GardenGuy1942 - 2024-08-27

You don’t need one when it’s rigged…. Biden should be president for another 4 years. Long live King Joe.

@eleviathan4621 - 2024-08-27

Yeah, the "dictator" ends up being a random person, who doesn't even know they're the dictator for that election.

It's one of those math things that doesn't translate to real life as well. Having one determining vote is how voting works sometimes, that's why you always use an odd number of voters, so in the event of a tie, one vote will break that tie.

@rusMusDie - 2024-08-27

Why do you want to prove that dictator Trump is a way to go? Russians money again?

@StanAbelHU - 2024-08-27

In this field it's hard to make the explanations make sense intuitive, because the conclusions are sometimes not but also the terminology is confusing. Unfortunately Arrow's theorem does mean that it's not just a pivotal voter who is unknown before the election. It means that the rule of the election is "look at how this person voted, and say that is how society votes". Unless it is such a rule (the dictator can be selected randomly, but it's not just a coincidence, it is a pre determined person outside of the vote counting process) you cannot have both unanimity and independence of irrelevant alternatives. It's a looser rule in special cases, but no generalized ranked system passes.

@peterhoelder2652 - 2024-08-27

It does make sense, though it is difficult to highlight constructively. First you show that any 'dictatorship' (i.e., a voting system with a pivotal voter) satisfies the other 4 conditions. Then, you assume that a voting system satisfies all rules except potentially the non-dictatorship rule. You can then show rigorously (with the type of argument that was presented in the video) that there MUST be a pivotal voter. You can't know which person it is because you are making a general argument for all voting systems. But you did show that every such voting system must have a pivotal voter.

@dragonabsurda - 2024-08-27

I absolutely loathe the first-past-the-post voting. My entire life we've ended up with a system where everyone votes AGAINST the candidate they dislike the most rather than voting FOR the candidate they actually support the most. The amount of disinformation that has been spread when we've tried referendums to move to proportional representation or alternatives is infuriating.

@sammysalter - 2024-08-27

why is that a problem? Sometimes that's the choice you face as a country - it says more about the political climate in your country than your voting system. And arguably getting rid of the guy you don't want to be in charge is the single most important requirement of a voting system.

@GardenGuy1942 - 2024-08-27

Exactly, Biden should be president for another 4 years.

@GardenGuy1942 - 2024-08-27

Like this comment if you want a man in office

@taqoe6430 - 2024-08-27

US or UK?

@opensocietyenjoyer - 2024-08-27

you can only have one unified entity that is the administration. it can never be representative. so called representative systems are not representative at all, since there is coalition building that is entirely out of control of the voters.

@lifelover10o9 - 2024-08-27

Good video, now let’s watch it

@TheOleg1000 - 2024-08-27

😂

@EikichiOnizuka69 - 2024-08-27

Another banger by riot kassadin

@iVirtuall - 2024-08-27

🤣

@markgosline3986 - 2024-08-27

Not if I watch it first

@outsomnia - 2024-08-27

​@@EikichiOnizuka69 "The balance of power must be reserved" - Kassadin F. Kennedy

@creatimaginouissement2616 - 2025-04-24

As a mathematician working in decision making, I am happy that you make a video on such topics.
I also appreciate that you mention some of these better alternative systems (see also "Majority jugement" from Balinski & Laraki).
I believe it would be great that you spend some time to explain one of these alternative system in detail, and show their strength.

Now, there is on crucial thing you did not adress in your video: ensuring people actually deviate from the highly risky "first past the post" system.
If we keep presenting these only with example of presidential elections, it is likely that nobody will change our voting systems for a few more centuries.
But when you realize that the "first past the post" system is actually used everywhere, from family circle, friends, associations, companies, etc, you can understant the massive risk it creates on a societal scale. The moment a CEO understands the risks it takes by using the "simplest" system in a company, he/she will try something else: and at this point almost ever other system is better.
Indeed, since "first past the post" does worse than just possibly electing bad propositoin: it actively favors the most cleaving proposition. Hence imagine the massive risk this creates when applying this in a governing board ! (and most companies use it without even being aware of the risk)

Hence I humbly suggest you make another video, with other examples of decision, focusing on the risk of "first past the post" system, and discussing one concrete alternative in detail.
The idea, I believe is to first convince companies, associations, and people to stop using this crazy system in their collective decisions and use an alternative one. The moment they try an alternative, they win.
I'll be happy to further dicuss such points.

@hiriasbloodweaver8593 - 2025-05-29

that's all very unpractical in terms of government of countries because those models do not scale or scale badly. It is fundamentally not possible for everyone to become an expert on everything to make good decisions. A much better system historically is monarchy. One absolute ruler, which allows quick and extreme decisions if necessary due to war, famine or similar. And a bunch of aides who can give expert opinions on specific topics. No person can be an expert of everything, so just assemble experts of different fields and listen to them. Easy. We figured this out thousands of years ago and it worked in practice much better than democracy.

@CuriousCrow-mp4cx - 2025-05-31

​​@@hiriasbloodweaver8593Then what you say applies to you, and if you actually thought about wgat you wrote, you would realise it applies to you, as much as ut applies to Elon Musk. There is no such thing as a perfect decision. Why? Because decidion making is hard for all human beings, as their neurology evolved to be biased. And saying that ranked choice voting does scale, is just not true. It does scale, as people use ranked choice voting when deciding where to eat, what consumer goods to buy, and what mate to marry. So it disengenuous to argue it doesnt scale uo, when its in operation in democracies.

@hiriasbloodweaver8593 - 2025-05-31

@@CuriousCrow-mp4cx what you are saying is incoherent and missing the point entirely.

@KellenBedingfield - 2025-06-02

Okay, so you have feedback, but he can’t just make another video 😂. That’s not how YouTube/views rolls

@xseros7954 - 2025-06-03

​@@hiriasbloodweaver8593 This is assuming that said monarch listens to the experts, and that the experts give their expert opinion and are not influenced by anything else than that. There have been plenty of good monarchs in history, and even some good dictators, but any system giving a single individual supreme executive power is bound to fail. The reasons why monarchy worked is for a few reasons:

1. Social hierarchy: Until early-modern times most societies had a rigid social hierarchy. In Europe it was feudalism, in India it was the caste system and so on. Social mobility was not a possibility for the overwhelming majority. At the top was usually the monarch who via this hierarchy was righteous in their power. If we want equality in modern society social hierarchy of these levels are not acceptible, and the monarch would lose justification for their power.


2. Religion: Many monarchies claimed to be chosen by the God(s) of whatever religion the people adhered to, giving them further justification of their power. In a mostly secular western world that we live in this is not possible.

3. Mass media: Until the industrial revolution mass media was scarce. Newspapers existed but were generally only for the wealthy. This made democracy impossible for larger realms as there was no easy way to spread the information required to the general population, and also hard to collect, count, and transport votes. The examples of republics we see before this point were generally more city states or oligarchies such as early USA and the Netherlands.

Monarchies are by definition hereditary, and theres no way to ensure that a child of a good ruler is as good of a ruler as their father. What youre thinking of might be more of a meritocracy, where the ruler is chosen by how suited they are. But here we introduce some form of election in that case. Lets ponder. Candidates for ruler go through various tests of intellect, morality etc etc. These are subjective matters, and must thus be reviewed and compared by one, preferably multiple people to avoid corruption. Imagine that they are not unanimous. How will they choose the ruler? Likely by an election. And now we have made a big move toward democracy again, albeit in a very small group.

The other way to chose a ruler is if the current ruler chooses his next, but how does he know who is suited? how do we prevent tribalism, where only a certain demographic of the nation has the possibility to become ruler?

The third way is to quote Stalin; "The only real power comes from the barrel of a gun". But I think you can see why that is a bad idea.

To summarize. Monarchy does not work in our modern society, and any dictatorships thrive on oppression, nepotism and tribalism which are also not desireaable. Humans are not perfect, and thats why its better to trust a large number of humans with power to counteract this imperfectness, than to grant it to one imperfect human.

@ilovestitch - 2024-08-27

18:40 that pivotal voter isn't really a dictator though, because he requires all the other voters to set up the scenario in which he would become, unknowingly, the pivotal voter. That pivotal voter would never know or be able to abuse their dictatorial status in practice?

The grain of sand that tips the scale isn't a dictator. Edit: I understand that this question is largely philosophical and has little bearing on a scientific debate/discussion but I felt it's worth examining for the sake of the larger conversation about where autonomy of the voter ends.

@dkSilo - 2024-08-27

They become, mathematically, the dictator that changed the outcome for everyone.
Doesn't matter if there's only 2 choices, you'd never know who the pivotal vote would be, but with 3 or more choices you can construct scenarios where you can find the single ranking that influences the outcome (which is what is shown in the video, the position doesn't matter).

Doesn't mean it has to happen every time, heck the more voters there are, the less likely it will be. But if you can mathematically show the case can exists, the voting system isn't "perfect" enough to adhere to that condition.

@mufasafalldown8401 - 2024-08-27

​@yak-i4c this is exactly what I was thinking while watching. Ignoring the definition of "dictator" to prove that one exists.

@mufasafalldown8401 - 2024-08-27

I hope this comment gets more traction. Can't ignore the definition of dictator in order to prove that a dictator exists.

@disjustice - 2024-08-27

100% agree. One can only be a dictator with the foreknowledge that their vote is pivotal. If you can't leverage your "power", you have none. You're best off just voting your heart.

@taragnor - 2024-08-27

The pivotal voter only becomes a thing if there's discussion and negotiation where everyone knows how many votes they have (like what happens in Congress) versus just having an election day where everyone goes in and votes and nobody has any idea what the vote count is. Even in the first case, that only happens if only 1 voter is willing to negotiate and the others are immovable. But that's more a testament to how negotiating in politics can get you favors.

@BrandonMirrors - 2025-01-23

So when they say "we must protect our democracy" they're just referring to protecting the power they already have and suppressing anyone who tries to take that power away.

@julianj9830 - 2025-03-31

Anyone who says they are for democracy and uses deceptive practices are clearly not for democracy. So yes, you are probably correct.

@realityobservationalist7290 - 2025-04-07

Bingo! Anyone who unironically uses "our democracy" is fundamentally anti-democratic and anti-liberal... which is the entire modern left. They HATE democracy, but will virtue signal all day about how they're protecting it and how anyone who has a difference in opinion from them is threatening it. It is laughably absurd that this delusion (or malice) infects half the Western world. Certainly, a large percentage of them must know they're tyrants, yet they all put on the same act in lockstep... They don't consider it tyranny because they think they are better than those who dissent. It's nothing but righteous indignation and terrible ideas that will never work, check the history books.

In the end, when you strip it all down, leftism/collectivism is synonymous with totalitarianism. It doesn't matter what their utopian ideals are, leftism manifested in reality always descends into dysfunction and disorder, then corruption, then authoritarianism.

@realityobservationalist7290 - 2025-04-07

Modern Western "our democracy" enthusiasts - We care about "our democracy" so hard that when the political opposition becomes more popular than us, we will literally throw them in prison.

@BboySquidfoot - 2025-04-12

Spot on haha. I hate it here.

@masoneder6367 - 2025-04-15

He's learning

@caldodge - 2024-08-28

In Europe, with proportional voting, parties form coalitions after elections, because it's very rare for one party to win a majority of districts. In the US, coalitions are formed IN parties. That's an inevitable results of 'winner takes all' elections, and the fact that it's impossible to get a majority to agree on every significant issue.

@ClayShentrup - 2024-08-28

@@caldodgethis is a total myth. Even duverger himself noted that countries which use a top two runoff tend to escape duopoly. There's absolutely zero reason to expect single winner districts to produce a duopoly. What produces a duopoly is the plurality voting method.

@der.Schtefan - 2024-08-28

Plus the person put in charge is not voted for directly, but the coalition selects them. They can't go against the will of the government or people, and the government reflects the mix of the people in the country much better, even if the voting system would be slightly off.

@bjornherrstrom6077 - 2024-08-28

I was looking for the words but you summed up my thoughts perfectly.

I think the American perspective on democracy is culturally different from some of the Europe and prone to misunderstandings. It's complicated to explain every system and would probably take a lot of videos to cover I believe.

@sybrand2 - 2024-08-28

Who needs districts if your country is x times smaller than the average US state?😅🥳 Still, election results can go against the will of the majority, albeit partially. Forming a coalition can mean that the least liked party will be in government for example and the second most liked is not.

Speaking from experience, having no say in who becomes prime minister or who takes a seat in the senate can be a bit of a bummer as well.

Looking at our own version of MAGA-ism, even though our guy has been bothering our parliament for far longer than Trump, our version of democracy is definitely far from perfect at this moment. But that has more to do with the way people "do" politics these days and the ways people (don't (care to)) inform themselves i guess.

Now, can you guess where i'm from?😅

@TheXorionas - 2024-08-28

This. Everyone's vote is heard proportional to the number of people who voted for the party. It's only winner take all that is stupid.

@Mr.Ning12 - 2025-04-29

4:01 CGP Grey, Lol

@charleauxX - 2025-06-07

Hexagon is the Bestagon

@Botyourbuissness - 2025-07-05

I was gonna say 😂

@sweatyeti - 2024-08-31

14:13 Imagine being awarded a Nobel Prize for essentially saying, "Look everyone, I've mathematically proven why we can't have nice things."

@lukamiler5824 - 2024-09-01

Introducing 5 axioms, misinterpreting one of those axioms to show a contradiction and get a Nobel prize for it.

What a joke

@nardopolo101 - 2024-09-01

@@sweatyeti good summary of 20th century voting malaise? In any case, better tests are here…

@godcomplex3942 - 2024-09-01

​@@lukamiler5824 Could you explain the flaws in the theorem please?

@Luv_JaydenOfc - 2024-09-01

well his work did lead to us now understanding why rated voting systems are probably the only systems that work- it may not have been his intention but it was informative enough for us to avoid the slander that rated voting systems could have accumulated, people will criticise anything without any understanding of it just because it could inconvenience them. It is like how when you do a multiple choice question it may be easier to prove why everything else is wrong than to prove why the answer is right.

@Alkixkix - 2024-09-01

I too can raise my standards so high that I can then declare things hopeless.

@bennyboy5949 - 2024-08-28

Title: “Why Democracy is Impossible”
Video: “Why ranked choice voting only works 99% of the time”

@mehere8038 - 2024-08-28

and they actually left out a key potential issue with ranked choice too, in Australia a few years back a candidate with only 17 number 1 votes was elected to the senate due to preference deals. He served with honour, but that's the clearest actual real world problem with the system, preference deals between candidates

@MajorCoolD - 2024-08-28

My thoughts precisely. I mean YEAH there are SOME inaccuracies, but then again it's not like first pass the post system ACTUALLY reflects the will of the people.
Heck, make it simple: As many Candidates as people present themselves, every voter gets 3 choices. 1st Choice, 2nd Choice, 3rd Choice.
The one with the most points wins. Simple as that. Afterall while that person might not be the MOST favourite candidate, they ARE the candidate that most people are reasonably happy with.
Heck, give the people the choice to forgo their 2nd and 3rd choice, a la 'Bernie or Bust!' style if they REALLY want to.
But in that case they shouldnt be surprised if they end up with a candidate they dont like at all.

@mathiaschaves7604 - 2024-08-28

It's getting sad to see how greedness is affecting good science channels...

@-danR - 2024-08-28

Conclusion: Derek's cIickbait strategy works 99% of the time.

@jmhorange - 2024-08-28

I mean if you watch his videos, you know it's usually involves math or science. Thus his title makes sense within the context of his video. Mathematically a democracy would be something where it's free and fair every time. 99 percent free and fair would not make the mark of a democracy. He didn't even cover the peciluar way that the US elects its president. The electoral college works 93 percent of the time.

The truth is, in reality, all the methods he talked about are practiced by many different democracies we all recognize as democracies, whether they use first past the post, ranked choices, or an electoral college system. If you actually clicked on a Veritasium video and expected the host to make a political argument that democracy is impossible, you must have never seen any of his videos before. I knew when I clicked on the video he would make a mathematical argument why, not some actual political argument that democracy is impossible.

@arcane3943 - 2025-01-09

“Holding many elections is a hassle”
Bulgaria with their 8 or 9 elections in the last 4 years:Amateurs

@antal4s - 2025-06-26

The hassle is in consistently getting high enough turnout every time for the election to mean something, otherwise you can hold elections where the same 10 people vote every single month lol

@Mojo-Beans - 2025-05-24

This is why I don't have friends. Forget you guys, I'm getting tacos.

@lawrencetchen - 2024-08-30

We don't need perfection, we need improvement. An outcome more reflective of the will people will be better than the one that is less reflective.

@williamyoung9401 - 2024-08-31

In a time when voter confidence in our election system is at an all-time low, the title of this video is very irresponsible. "It's crooked, but it's the only game in town?" Why not just regurgitate everything Fox News says? 🙄 You're the Ralph Nader of this election.

@WarpedKarma6471 - 2024-08-31

at the very least I don't want my ballot to essentially be a true or false between two parties.

@mylittleparody2277 - 2024-08-31

Exactly this.
All problems with better way to vote are like "But imagine there is only 3 people voting, and they exactly line up with this or that!"
It never happens IRL. And in the so very unlikely even that it does, just redo the vote, people will change their mind. Heck, maybe even remove the least favorite one.
But, yeah, that's the problem with maths, they forget the real world application.
Country population are counted in millions, one person won't change a thing because such a huge number of people can't think the same thing.
And voting for one candidate only is really bad.
Even more if you have, like here in France, a two turn based election!
It's awful really.

@LakeLee-r1g - 2024-08-31

@@williamyoung9401 definetly

@doc1223 - 2024-08-31

​@@williamyoung9401 You leave MSNBC out of this!

@iamasquidinspace - 2024-09-06

As a European, I was patiently waiting the entire video for him to mention that of course, democracy can take completely different forms wherein you don't have to elimimate a list of individuals down to one final victor, so that democracy does not necessarily have to stand or fall with this issue, but I was sorely disappointed.

@keltzar1 - 2024-09-07

As an American how do things tend to work over in Europe?

@Olathaen - 2024-09-07

@@keltzar1 If party A gets 48% and party B and C gets 26% each, then party B and C can make a cooperative government and win, or if they cant agree, then Party A wins..

There will be alot more than 3 parties and there is alot of negotiation too see who will cooperate. If noone wants to cooperate, you might end up with a "minority government" wich would be is Party A ended up winning in the first example. Party B and C are not the rulers of the country, but they have a majority for votes and such, while the ruling party has a minority.

It can also happen that Party B and C cooperates, but decides to stop cooperating after a few years, then suddenly the winner is Party A.

All that being said.. I know nothing.. They teach us nothing in school, and what i believe i know i have deduced and infered from the elections i have voted in.

@skt453 - 2024-09-08

Thanks, that's 20min of my life I'm saving.

@Joel-y6m - 2024-09-08

@@keltzar1 Imagine there's 100 seats up for election. If I get 2% of the vote I get 2 seats. etc. So you end up with a much more diverse Parliament. This type of system also has its problems and critics and on occasion lead to pretty chaotic and unstable Governing.

@user-lo4me9oe9z - 2024-09-08

how anarcho syndicalist of you

@Olive_Gamer139 - 2024-08-28

3:39 I love that CGP Grey reference, perfectly fits with his voting videos. Great video!

@jgharston - 2024-10-12

Hexagons are perfectagons. :)

@mrtno24283 - 2025-06-11

7:40 I think there are two fallacies here:
1. why would Bohr's voters switch to Einstein if Curie, who is a moderate, is closer to Bohr's ideas than Einstein is. Shouldn't the majority of voters who switched their vote vote for Curie and not for Einstein?
2. From the moment that at the start Bohr had the majority of votes, he would have won anyways, even if he hadn't given the bad speech that made people change their mind and vote for Einstein. This means there's no such thing as being rewarded for doing bad in your electoral campaign.

Hope I explained myself, also hope that someone tells me what I am missing. Thank you

@Nysyarc - 2025-06-24

"why would Bohr's voters switch to Einstein if Curie, who is a moderate, is closer to Bohr's ideas than Einstein is"

It is a hypothetical example to show what could happen in that scenario. Yes, realistically it would be far more likely that a majority of voters leaving a left or right candidate would switch to a centrist candidate rather than swinging all the way over to the other side, but this example was just to show how much a single event could change the outcome of the vote in theory. A "perfect" voting system would not allow something like that to happen, even theoretically, that's what is being proposed here.

"From the moment that at the start Bohr had the majority of votes, he would have won anyways"

Not in the voting system being showcased in that example. In a first past the post system, yes he would have won, but the previous scenario at 7:20 shows why (in this hypothetical example) he wouldn't win. He never actually has a majority of all the votes (>50%), he only has 45% of the votes at most.

@Dungeoofpain - 2025-07-01

You could think of Bohr as someone who is very green and pro nuclear power and Einstein as very anti Nuclear power.
Chernobyl blows up.
Bohr still supports Nuclear power, while Einstein is even more vehemently against it.
Curie in this case might just be slightly against it. The people, listening to the fearmongering mostly swap from Bohr to Einstein in this hypothetical situation.

2. Bohr had the plurality of votes. Majority requires over 50%. Plurality is the largest group that is not over 50%. Out of 10 choices, you could have a plurality at 20%.

@johnmcdollar - 2025-07-15

@@Nysyarc this is just a way to disagree with a better system just because hypothetically (which is very rare in this case) we have an option that can do worst! This is just a talking point that doesn't makes sense and it just attention seeking! It is Veritasium trying to make a longer video to gain more purchase and not trying to solve the issue in hand. It is TH action that happens in a lobbyist economy to try to rob people of their vote and opinion to gain economical benefits

@teknolozik - 2024-11-07

3:40 I see CGP Grey there haha

@nominatively - 2025-02-14

of course a hexagon shape too

@Brr.18 - 2025-03-28

​@@nominatively😂

@alicewonderland9254 - 2025-07-04

His voting videos are so good!

@raiden24 - 2024-08-27

What's Mathematically Impossible is to have a winner-takes-all voting system that's representative of the electorate. If you want to represent the electorate accurately you have to let go of the winner-takes-all system and adopt a representative democracy where parties are awarded seats in parliament proportional to their vote share in a general election.

@wacobeer6469 - 2024-08-27

Yes. Imagine 100 candidates... A winner would then be determined by 1% + 1 vote. Clearly not the choice of the majority of the population.

@sillymesilly - 2024-08-27

United States is not a Democracy.

@Nonixification - 2024-08-27

Good idea BUT if there is no majority in parliament then none of the law can be pushed through

@tharealmb - 2024-08-27

@@Nonixificationthey could just push the laws that a majority does agree with. You know, like getting pizza, indian or Chinese food... You can still get a majority.

Lost of countries have systems that don't use the "winner takes all" system. And it also leads to less extreme choices. But it means that multiple parties will need to work together, and negotiate, to get something they all can somewhat agree on.

The "winner takes all" will always lead to a two-party system, and always to very bad politics IMHO.

@BlueHawkPictures17 - 2024-08-27

​@@Nonixification I really hope I am misunderstanding you here, because what you said is very silly

@lancewelsh638 - 2024-11-12

Thanks!

@manne8575 - 2025-02-03

You're welcome

@proxeroshi7624 - 2025-02-08

Thank me

@amongothers8555 - 2025-04-26

Thank you​@@proxeroshi7624

@phongnguyen7795 - 2025-06-15

Madi is absolutely crushing it! Love the content, but take rest don’t burn out.

@SimonLAylett1 - 2024-08-28

I was SO CLOSE to writing 'didn't CGP Grey do this topic already'?! and then I saw the graphic at 3:35 - well played sir! :D

@planecrashcorner7283 - 2024-08-27

Love the CGP Grey Cameo

@WarlordofWarren - 2024-08-27

"Hexagons are the bestagons"

@mphRagnarok - 2024-08-27

More like CCP Gay

@LUKA_911 - 2024-08-27

​@@mphRagnarokskibidi toilet

@Laiyo_1762 - 2024-08-27

@@mphRagnarokyou’re not sigma lil bro

@TotalVikingPower - 2024-08-27

Time stamp?

@nathanlee6654 - 2024-09-02

I liked the CGP Grey reference. His videos about voting systems are phenomenal. They’re quite simple, but I love how he talked about them. Good job Derek! This is a great video!

@albertratan - 2024-09-04

Glad that someone else noticed the reference!

@xm4366_ - 2024-09-05

Veritasium even made him a hexagon!

@eniza9747 - 2024-09-05

CGP Grey's video was the first thing that came to mind when I saw this on my home page and the reference made me so happy while watching!

@version365 - 2024-09-05

Not only the 'Hexagons are the bestagons' comment, but the hexagon having the similar glasses as Grey was nice touch.

@LuckySahu-gh2vf - 2025-05-08

timestamp??

@leelaprasad9916 - 2025-04-15

Actually in 7:35 you assume the Bohr voters would vote for Einstein and not Curie who is the more ideologically similar to them than Einstein.

@MercuryA2000 - 2025-04-24

There are some people who might. Even if Curie is moderate, Bohr's voters might have a negative view of her for whatever reason. Even if they don't agree with Einstein, they respect him more. There is a chance they might lean his way a bit.

There's also the fact that politics isn't just a 2 dimensional line. It might be that Curie is moderate on most policies, but there's one or two that she has a strong view on then Einstein. Depending on how important those policies are, it might be a deciding factor. Especially if that policy is related to why Bohr lost his voters.

And while it isn't a complete victory, there are scenarios where Bohr doing worse could be the difference between Einstein and Curie getting elected. Curie isn't as good as Bohr, but you could still argue him doing worse got him a better outcome.

These fluctuations are also a lot more likely to matter in a scenario where the votes are close. Yea, a whole 6% of Bohr's voters moving over to Einstein is unrealistic, but what if the difference between Einstein and Curie is only half a percent? A quarter? Sure the scenario isn't likely, but fringe cases like that are important to at least consider with something as big as an election.

@KellenBedingfield - 2025-06-02

In theory you’re right but somehow that never happens in our two party system

@Mikke-G - 2025-07-02

Imagine voting for a guy who married his cousin and snitched on Germany which lead to the Manhattan Project.

@Kodak-t7q - 2025-07-07

Well, people often don't vote for moderate candidates because they don't think anything will get done. So it's not too much of a stretch that people might want someone who will do some good things and some bad things instead of someone they don't think will do anything

@sprightly106 - 2024-09-28

love the CGP Grey references, he introduced voting systems to my mind sphere. Thanks Derek for further expanding on the topic, would love to see different scenarios for approval voting and +/-10 points voting

@justgaming1952 - 2024-11-10

STAR voting is a nice system of rated voting

@alfredgarrett5065 - 2024-11-12

But one man alone is going to destroy it

@intermedianguitarsguild4482 - 2024-11-14

or, just vote for any candidate you want. +10 and -10 adds complexity which isn't needed for approval voting

@danielzhang1916 - 2024-11-22

every scenario has problems, they want a winner not just several choices

@hannahMadden-s7u - 2025-04-29

CGP Grey is as crazy as this channel.
He just makes goofy cartoons, that play fast-and-loose with facts; and it fools the ignorant, because he's a con-artist.
Just like this video, which ignores that, BY LAW, democracy in the United States, is the VOTERS having supreme authority; while elected officials are their mere chosen DELEGATES, and the voters can OVERRULE them. That's how the Constitution was ratified, with each state's voters being their supreme national authority. And so, the voters in each state were their own supreme national rulers.
Unfortunately, usurpers seized power after that, claiming that the states were NEVER sovereign; and the rest is history.
So as William Feather said, "a single fact can often destroy a most interesting argument."

@evrimagaci - 2024-08-27

Cool, but doesn't this (especially Arrow's Impossibility Theorem) assume that the votes of the citizens are known ahead of time, so that the 'pivotal voter' can change the vote one way or the other? In reality, elections wouldn't actually hinge on a single voter, as they wouldn't be able to know how others ranked their choices exactly.

In the end, the problem with the current system is not really certain people affecting the vote more than others, but the outcome does not really represent the majority's wishes, especially when you consider the Electoral College and gerrymanderin in the US (Europe and other places luckily doesn't have Electoral College, but I believe gerrymandering is still a problem). Particularly with approval voting, both problems disappear mostly, but it is crystal clear that ANY ranked choice method is almost guaranteed to be better than (meaning, a more representative democracy than) what we have now. So it is INSANE to insist on the current system.

The only logical argument would be that it is 'easier to understand', and that makes this that much more insane! Hundreds of millions of people, afraid of primary school level maths and logic...

@lonestarr1490 - 2024-08-28

It's not about changing votes or outcomes (or actually exerting the power of a "dictator"). It's just about those 5 demands being mutually incompatible. There cannot exist a voting system that satisfied all of them. That's all.

@GCOSBenbow - 2024-08-28

No it becomes apparent after the fact (or rather during the counting).

A basic outline of the proof:
1. You assume you have a voting system where IIA and transitivity hold for any possible combination of votes.
2. You show that in this system, by transitivity and IIA, if every vote ranks B either at the top or the bottom, so must the social welfare function.
3. You show that given step 3, there is some “pivotal” voter that determines B’s ranking relative to AC. Note at this step, the “pivotal” voter is just a tipping point (point of no return), not a true dictator.
4. Now, you show that regardless of how every other voter ranks A relative to C, by assuming IIA the social welfare functions relative rank of A and C must mirror this pivotal voters relative rank of A and C. This shows that there is some voter that fully determines the relative rank between A and C, regardless of how anyone else votes (i.e. is a dictator over AC). Call this voter voter x.
5. By similar logic, there is some voter y that fully determines the relative rank between A and B, and some voter z that fully determines the relative rank between B and C.
6. Without loss of generality suppose voter y has A>B, voter z has B>C. Then the social welfare function has A>C by part 5. But this means that voter x is not a dictator over A and C, contradicting part 4. The only way to resolve this contradiction is that voter x is voter y and voter z. But this means that voter x is a relative dictator over AC, AB, and BC, making them a full dictator.

The dictator in this sense isn't consciously choosing to manipulate the voting, but their individual vote has more meaning than every single other vote which is against the common rules set out (that all votes are equal).

The video isn't a value proposition of FPTP vs RCV (and any other single winner election). Just that all of them are flawed whenever there are more than 2 choices.
Of course PR doesn't have any of these specific issues (but does have multiple other issues).

@ExtremusStupidus - 2024-08-28

nice to see you here

@dw620 - 2024-08-28

Why does it matter, anyhow?

Conflating "democracy" with "deciding who wins an election" is missing a major point when the politicians will just do whatever they want once elected regardless of "promises"...

@deyoloco3110 - 2024-08-28

The main issue with Ranked Choice Voting is that voters will not be able to make educated guesses of each candidate and the possible combinations of runners. Also, a lot of people will not rank more than two candidates, so there will be a faux majority, because others did rank more than 2.

@crowlsyong - 2024-08-31

Whoever does your animations, those pencil-looking drawing parts, great job

@corriejo3655 - 2025-04-03

6:29 that was therapeutic

@atlanticdaniel432 - 2025-04-23

That wasn't therapeutic it was PATHETIC!

@shalvpatil4631 - 2025-04-30

​@@atlanticdaniel432
The sound was pathetic, but the concept of opponents being nice to each other was therapeutic🙂

@ArtemiyS_ - 2024-11-21

1:17 I think you made a mistake by including Belarus here, as a Belarusian I can say that it is more a dictatorship. We had the same presidents for 30 years and it is not because everyone wanted him to stay, but because he wanted to stay and the majority didn’t.

@stfuswapnil - 2024-12-27

I have a friend from Belarus, an online friend whom I met on reddit. Her descriptions were errie, at least i felt that way for her as uni students are restricted by vile system, policies, and corrupt authorities.

I hope the situation becomes good in the upcoming time. Hare Krsna..

@andyjohnson9714 - 2025-01-02

In Belrus votes are not counted. You can vote for whoever but when votes are not counted all that is doesn’t matter.

@TigerVIIAustB - 2025-02-02

Бело-красно-белое либеральное дерьмо, спокуха.

@hopeful1817 - 2025-02-08

The problem is, every poll that was ever made shows that Lukashenko is head and shoulders above everyone else, so how do you know he isn't popular? Oh right, it's because of anecdotes, some of them are personal, others spread by MSM. Of course it works other way too, all of these polls are state controlled, so technically they could be manipulated.

As for 30 years in a row, given an opportunity, people tend to vote for the same president. In Finland we voted Kekkonen for 28 years. But this isn't an outlier, we always voted for the incumbent, it's just most of them pre 1991 term limit, didn't even run for the second term. But this status quo preference isn't mathematical.

Which elections are made up is a can of worms for a different video on entirely different channel, here he showed correctly what voting system are in use.

@sadfah69 - 2025-02-10

Boycott democracy voting system....only religion scholar should select the PM via consultation (shura)

@willcarter7079 - 2024-09-27

That approval voting actually excites me. When you started explaining it I started seeing a light at the end of the tunnel. That's pretty cool I would totally participate in that type of election

@intermedianguitarsguild4482 - 2024-11-14

exactly!

@jeyruff429 - 2025-01-27

@willcarter7079 (🤸 Like Approval? You Will do Carter -wheels for ⭐STAR! 😉)

I really hope you read this, even after 3 months. If Plurality, the way we vote now, is an F-minus (), Approval voting is a B+ or A-. There are still some ways it can be unfairly manipulated. However...

A better method, and a permanent solution to the USA's political issues, is ⭐ S.T.A.R. Voting! ✨ It's like this:
1) Rate as many or as few candidates you want out of all of them on a ballot, like a 5-star online review, from best (5) to worst (0, so actually 6 stars each on ballot 🙂), same rating is allowed;
2) Candidates with the 2 highest Score(s) Then Automatic(ally) Runoff (S.T.A.R.), with each ballot that rates a candidate higher than the other going to that candidate;
3) Most ballots wins!
Simple, Accurate, harder to cheat, harder for crazies to win. Less need for money & mudslinging. In fact, candidates that mudsling are more likely to lose, even more so than in Ranked Choice Voting (RCV).

Many more have heard of Ranked Choice Voting (RCV), but that only gets a "C", maybe even a "D". Still way better than the "F-" we have now with the "classic" First Person Plurality Voting (or First Past the Post, FPP/FPtP). STAR Voting gets the highest "A" I've seen of many other A & B grade voting methods, including approval.

All it takes is State law or Federal law, not necessarily both. Call your congress(wo)men!! Legally and respectfully demand The Truth about ⭐STAR Voting and other methods until you get it!! --J

@jeyruff429 - 2025-01-27

@willcarter7079 (🤸 Like Approval? You Will do Carter -wheels for ⭐STAR! 😉)

I really hope you read this, even after 3 months. If Plurality, the way we vote now, is an F-minus (), Approval voting is a B+ or A-. There are still some ways it can be unfairly manipulated. However...

A better method, and a permanent solution to the USA's political issues, is ⭐ S.T.A.R. Voting! ✨ It's like this:
1) Rate as many or as few candidates you want out of all of them on a ballot, like a 5-star online review, from best (5) to worst (0, so actually 6 stars each on ballot 🙂), same rating is allowed;
2) Candidates with the 2 highest Score(s) Then Automatic(ally) Runoff (S.T.A.R.), with each ballot that rates a candidate higher than the other going to that candidate;
3) Most ballots wins!
Simple, Accurate, harder to cheat, harder for crazies to win. Less need for money & mudslinging. In fact, candidates that mudsling are more likely to lose, even more so than in Ranked Choice Voting (RCV).

Many more have heard of Ranked Choice Voting (RCV), but that only gets a "C", maybe even a "D". Still way better than the "F-" we have now with the "classic" First Person Plurality Voting (or First Past the Post, FPP/FPtP). STAR Voting gets the highest "A" I've seen of many other A & B grade voting methods, including approval.

All it takes is State law or Federal law, not necessarily both. Call your congress(wo)men!! Legally and respectfully insist they explain why they either haven't heard of, or are willfully ignoring ⭐STAR Voting and other methods until they answer honestly!! --J

@onthemerits - 2025-04-30

Until you understand that Approval Voting can EASILY violate the Majority Fairness Criterion (which means that the person who gets a majority should win the election). (Borda Counts also can fail to satisfy the Majority Criterion.)

Derek didn't make this clear, and I think it was a mistake: Arrow's main result--and why it's worthy of a Nobel Prize--is that when it comes to voting (to use a Thomas Sowell phrase) "There are no solutions; only trade-offs."

This is a big deal, especially for mathematicians and engineers who are used to calculus-type optimization problems: there is no "best" system. It's an impossibility. The best you can hope for in voting is 1) trade-offs (what do you want to "give up", as Derek put it), and 2) procedural fairness (which is important, but not the same as mathematical fairness).

And Derek neglected to mention this, but parliamentary systems have their own mathematical impossibilities: Apportionment. Fair apportionment is also mathematically impossible. Matt Parker on Stand-up Maths has a great video explaining that problem.

I think Sowell's great insight is that the real world is more like voting theory & apportionment theory than Calculus: "There are no solutions (no optimization), only trade-offs."

@RGarella - 2025-07-08

@@onthemerits The arguments that I have seen saying that approval voting can violate the majority fairness criterion only show that it can lead to a different winner than FPTP or ranked choice — if certain very specific assumptions are made. These assumptions appear to cause the violation.

@Marco_Onyxheart - 2024-08-29

All this assumes that we are voting for a singular position to be filled by just one person. There is still proportionally representative voting.

@policeman1104 - 2024-08-30

could be different parties too tho

@npn8046 - 2024-08-30

Exactly, proportional representation is a proven and effective form of democracy. Unlike the winner-takes-all system, which often distorts the true will of the voters, proportional representation ensures that the distribution of seats in a legislature more accurately reflects the percentage of votes each party receives. This results in a more representative and inclusive government, where even smaller parties and minority voices have a chance to be heard. The winner-takes-all system, on the other hand, often leads to disproportional outcomes and can entrench a two-party system, stifling diversity in political representation. In contrast, proportional representation encourages a more balanced and fair political landscape, making it a far more democratic approach.

@kobyma2 - 2024-08-30

The thing about proportional representation is that proportional representation can also result in extremely disproportional effective power. In the extreme case you can end up with a small party and two large ones just shy of 50% of the seats, and despite this, the small party has the same amount if effective power as the large ones, as any combination of 2 parties has a majority, and no single party has. Now imagine the two big parties being opposides that barely agree on anything, and the small party representing some narrow interest group that only carss about that and nothing else, and you end up with a small "kingmaker" group with way more influence than it's proportional vote.

@npn8046 - 2024-08-30

@@kobyma2 In Denmark, the political landscape is both diverse and dynamic. There are approximately 14 political parties to choose from, at the moment, each offering a range of candidates that you can vote for personally. This personal voting system allows you to give your preferred candidate a significant boost, even if they are not at the top of the party list.

Coalitions in Denmark are highly flexible. If a party cannot secure the necessary mandates within its current coalition, it is free to seek support from other coalitions or parties. This flexibility encourages continuous negotiation and compromise, making the Danish political system both inclusive and representative.

@falafeldurum2095 - 2024-08-30

Isn't this all assuming that by voting for a party, you support all their stances on all political issues/topics at this exact percentage? A voter's opinion isn't represented correctly in the first place since you don't vote for each topic separately

@Jordanthecool7 - 2025-03-06

The irony of democracy is that it often works best in places which are very homogeneous when it comes to culture , ideals , and beliefs . Basically places where the people already think the same / very similar to each-other, since pretty much everyone agrees on a lot of thing’s , things simply are able to get done much faster and more efficiently . Places where people are very divided culturally and ideologically, it doesn’t work so well since there’s so much disagreement, often times barely anything if at all is able to get done due to constant fighting over issues. Regardless it’s still much better than other system’s though .

@xx5949 - 2025-06-28

That is why the Chinese and Indians are never fans of democracy but Japan can pull it off

@peachyjam9440 - 2024-09-05

My man said "It's the best thing we got and only game in town" after a whole video of showing how there are many different ways of doing democracy, the worst possible one is used in most places in the world and the best we could figure out is not used anywhere

@terrablaze3387 - 2024-09-16

He’s referring to democracy as a system.
Not the winner takes all nature of American politics

@terrablaze3387 - 2024-09-16

Democracy good because everything else not as good

@loslingos1232 - 2024-09-16

Exactly.. he was completely right with everything and then spat into the face of it at the end.
CLEARLY a better way is available but everyone just says “uhhh bad German man!1!!” without even looking into it.

@peachyjam9440 - 2024-09-16

@@loslingos1232 Not sure what you mean about the bad German. The video also hasn't mentioned direct democracy, referendums, council rule etc. Or anything about lobbying, media capture, manufacturing consent etc.

@BulentBasaran - 2024-09-18

The practical problem of a hierarchical democratic organization of the whole state (federal government at the top, then state governments, then local governments, then companies and large families, i.e., clans) is more interesting than these theoretical musings. let's hope we get another video on this topic. After all, in theory, theory and practice are the same. In practice, they are not.

@BFive_025 - 2024-09-20

Now lets introduce a term "coalition" to this video.

@atscub - 2024-09-22

I was going to mention that. It doesn’t has to be: winner takes all.
What if candidates get power in proportion to their vote? They can rule by consensus.
The real problem I see with Democracy is weakness against other powers ruled by Autocracy.

@shawnradke - 2024-09-23

@@atscub you are on the money! I vote for A because I like rules from A and no one else, likewise for people who voted B etc etc
OH WAIT that's called a free market, lets skip voting and just pay for goods/services from people who are servicing us the way we like

@bminecreeper - 2024-09-28

@@shawnradkeExcept then you immediately deny the principle of democracy by ceding power to people with the most money. Not to mention the free market fails at providing ideal choices all the time.

@fallendown8828 - 2024-10-02

​@@bminecreeperyeah and also monopolies exist, they will just bankrupt anyone trying to offer a service so they are the only one that people can purchase from

@divokyvlkgaming243 - 2024-10-02

ok yes that solves the parlament election problem but what about the presidental election? of course there can be a multiple round system but there are many problems with it which he talks about in the video

@djtmaga639 - 2025-03-25

I learned these concepts, including Arrow’s impossibility theorem and lot more, in a graduate course on social choice theory. It was offered by Nobel Laureate Alvin Roth who is an excellent teacher (rare for Nobel laureates). He taught these concepts so passionately and clearly that everyone was hooked.
Having said that, the video is also very well made and presents these concepts very well.
@veritasium: Please make a video on solving the “Marriage problem” in game theory. Will be entertaining and helpful.

@xyzxyzxyzxyzxyzxyz - 2024-08-27

Here is a better title: "Why Winner-takes-it-all Democracy is Mathematically Impossible".

The first theorem only applies if there is a single winner in every district.

Having actual proportional representation does not have these flaws.

@1ucasvb - 2024-08-27

Not quite true. The underlying problems still exists even with proportional representation, if based on rankings. It's just less noticeable because the PR "simulates" cardinal information in aggregate.

@wizardaka - 2024-08-27

I was thinking "Why democracy isn't an abstract, rational, mathematical problem, but if it was we'd have a problem"

@thecursed01 - 2024-08-27

JOIN THE FIGHT FOR SUPER EARTH AND MANAGED DEMOCRACY!

@jcreature11 - 2024-08-27

It’s not about that, humans are humans period. We have terrible traits as a species and those have been exploited for so long we are programmed to it.

@DmitryB-h4i - 2024-08-27

Less clickbaity you say?

@zzcool04 - 2024-08-27

This feels like a mathematical proof that suggests problems in edge, corner or point cases make an entire system unusable. I’ve never interpreted “impossible” to mean “it only works 99% of the time”.

@IlIlllIllIlIIIll - 2024-08-27

The recent 2022 Alaska special election had Palin spoil the election for Begich. There's not even any need to speculate about what voters would have done, since it's all in the voting data. Begich was preferred to both Palin and Peltola but Palin stole too many hardliner votes away from him.

@DavidRoberts - 2024-08-28

It's more that real-life voters are not accurately modeled by the assumptions of the theorem. People act illogically!

@lonestarr1490 - 2024-08-28

​@@DavidRoberts The theorem makes no assumptions on how people act. It's only concerned with showing that 5 random demands are mutually incompatible.

@kamikeserpentail3778 - 2024-08-28

When it comes to first past the post, it's looking like the whole thing is edge.

@averywhitaker3513 - 2024-08-28

Veritasium makes rage-bait to help people click and engage. It sucks, is probably very effective, and I hate it and him on every level for it

@justalilfella - 2024-08-27

7:55 idk if I agree with this. Cuz if bohr gives a bad speech and gets less votes, presumably a portion of curies voters would also be dissuaded from voting bohr as second choice due to the bad speech. That is to say, I don't think it'd be a 50/50 split of curies votes in round 2

@h.f.2823 - 2024-08-28

Well i think it would make sense to assume that before bohrs speech the second choice of curie voters was distributed 25:45 (Same as the initial ratio of first votes between Einstein and Bohr) and after the terrible speech it was closer to 50:50 (Like the Einstein Bohr First Vote Ratio after the speech). So while you're right that some Curie voters switched their second Vote from bohr to einstein it still makes perfect sense as long as the second votes of curie voters are similarly distributed as the First votes between Einstein and bohr

@paulscherz3680 - 2024-08-30

Maybe I'm missing something, but I definitely disagree with what is presented in the video. "Clearly this isn't something we want in a voting system"...? I don't see this as clear at all. Thats kind of the whole point in RCV, even if you're not the people's first choice, you are more closely aligned to how people want you to govern.

It also seems like the example has two first rounds of voting. No one would know what the numbers are before Bohr gave his bad speech or whatever.

@xybersurfer - 2024-08-31

i'm also not buying the example. the voters had 2 rounds to move away from Bohr

@garion046 - 2024-09-01

Also, why are Bohrs voters going to Einstein and not the more moderate Curie? If a candidate performs poorly, voters tend to go to their 2nd choice, which tends to be close to their political position. This example assumes voters swing all the way to the other side which makes no sense.

@randomyoutubebrowser5217 - 2024-09-02

I disagree with that example also. Why did those voters who were turned off by Bohr's speech all go over to Einstein (who was vastly more unpopular overall) and none go to Curie? Even if just a third of the switching voters went to the centre, Curie would have still won.

@A1BASE - 2025-04-24

Love the CGP Grey nod with the bestagons!
He did videos on this specific issue years ago.

@Reoh0z - 2024-08-28

The funny thing about voting is that most of the time we don't get to pick the options we're voting on, rather we're delivered a curated selection of options and are left to choose the one we find most palatable.

@TheKingWhoWins - 2024-08-28

The establishment wins no matter what. All the "options" you get to "choose" from help them regardless

@chrisdiboll2256 - 2024-08-28

Then join the body that curates the options?

For example, here in the UK, join your local party. Then you’re one of the ones picking the candidates. In fact, since we have a lot of safe seats, joining the local branch of the party that controls your seat effectively makes you one of the few dozen or so people in that constituency whose vote counts for anything.

I’m sure there are similar possibilities in the US and other places.

@xyz-je2wx - 2024-08-28

You can just stand in the election and wala u picked a choice

@Shadow0fd3ath24 - 2024-08-28

we do though, its just every finds the 2 big ones and never even try to support the others, especially in the west and even more in the US

@wasdwasdedsf - 2024-08-28

"The funny thing about voting is that most of the time we don't get to pick the options we're voting on, rather we're delivered a curated selection of options and are left to choose the one we find most palatable."
and the ones who arent curated are smeared endlessly by the establishment and the media, so to th extent that they often become the most hated people in the country

@creeper7444 - 2024-09-02

I find it interesting that every problem presented relies either on the premise that the voters need to elect only one winner or on the idea that a candidate who wasn't anyone's first choice but was everyone's second choice isn't a good compromise. These things are just presented as facts without establishing why this should be necessary.

@deco90014 - 2024-09-03

I hoped that in the end, Michael reflect how this theory could really represent real elections struggles. And how power dynamics fumbles with the math principles in the "fairness"

@shredded_lettuce - 2024-09-04

It also makes a huge assumption that “democracy = elections with voting” and excludes any other form of collective decision making, of which there have been many throughout history (like lots of indigenous societies in the Americas, or the Catalonian Anarcho-Syndicalists who used systems of mandated recallable delegates, or a variety of activist groups who use some form of modified consensus, etc)

@Lindsay_Quo_Vadis - 2024-09-04

@@shredded_lettuce The drawback of these other forms of democracy is that they even further empower the masses and disempower the individual. Democracy was a bad word until the rise of mass society in the 19th century. What we need to work toward is a world without "the masses." In mass democratic society there will always be a tyranny that manipulates social reality to guarantee its hold on power. People who live and think locally are free to organize themselves however they please. Most of the time, it turns out this is some combination of monarchy and aristocracy. Everyone in such a local world exists in an organic matrix of direct obligations and privileges, duties and benefits. It's how families have always operated. I would dare call it the natural mode of human organization.

@lemiureelemiur3997 - 2024-09-04

​@@shredded_lettucehe's either clueless, or more likely, pretending to be so he can get views by making people outraged that democracy is actually "mathematically impossible" when it isn’t. It's perhaps his weakest video yet, certainly the most repugnant.

@garethkalum8297 - 2024-09-04

​@@shredded_lettuce if it was used by indigenous americans, its probably worthless then.
Maybe a defeated and crushed people arent the one to take advice from.

@murpledeer - 2024-08-27

3:54 I love the CGP Grey nod in a video he definitely has covered some of the topics of, and also love how you put your own spin on these videos

@Dvinuz - 2024-08-28

I love the "Hexagons are the bestagons" :D

@Lizard_Ri - 2024-08-28

Hexagon is the bestagon :p

@VincentVonDudler - 2024-08-29

CGPGrey has done so much damage to voting reform selling Ranked Choice Voting.
This video does his best to undo that damage by asserting that Ordinal methods are trash.
CGPGrey also has an Approval video but insinuates it's only good for picking lunch.
imho STAR Voting is best. If I can't have STAR then Approval is best.

@Lascarnn - 2025-05-13

It's not Marie-Curie, it's Maria Skłodowska-Curie! The Polish part of her name was actually more important for her, yet people want to show her as French which she was not.

@qripuest - 2025-06-30

Thank you, thought no one commented that ❤

@anvilsvs - 2025-07-19

Remember Maria Antonia? The Austrian princess who frenchified her name to Marie Antoinette?

@BenKickert - 2024-08-27

I live in a "first past the post" country that forces a two-party system and penalizes voting your conscience unless it aligns with one of those parties. While there may be flaws in Ranked Choice Voting that could emerge in fringe cases, it is so obviously superior to our current system that it is hard for me to worry too much about the nuance of how it might not be 100% perfect 100% of the time. Any (democratic) system is better than what we have now.

@some-online-dude - 2024-08-27

The rated voting system sounds even better imo

@scopeguy - 2024-08-27

The US has had first past the post for over 250 years and only had a "forced" two party system for fewer than 100. Coincidentally the prevalence of the "two party system" began around the time universal suffrage was introduced.

@1ucasvb - 2024-08-27

RCV solves the spoiler problem, but it does not solve the representativeness problem. It just makes smaller parties inoffensive to the "big two". It actually performs terribly and erratically when more than two parties are competitive, which is exactly the scenario where you would want a better voting system to matter.

@latbil - 2024-08-27

@@scopeguywhat do you mean by this? With very few exceptions, we’ve only ever had two parties really in contention for races.

Third parties have EXISTED, sure, but their main effects have been bringing new ideas to the two major parties’ discussions, and splitting the vote between more moderate and more extreme members of the same “side” of political thought

@龱 - 2024-08-27

What’s the country?

@poems35 - 2024-09-18

I am an engineer, not a mathematician. Let's not make practical the enemy of perfection. We should use the method with the least chance of undesired results. After all, little in life is perfect.

@evanpereira3555 - 2024-09-19

Exaclty, especially when we don't even agree on which necessary/sufficient conditions.

@DelaneAtalanta - 2024-09-22

The least one with undesirable results? Tell me, how is democracy helping White people to secure their borders, any of them for that matter, on all of our countries. How is it the fertility rate? Happiness? Health? The safety of our families? It would be one thing if we just stopped having almost any children, but we are bombarded with legal and illegal immigrants across the whole of the West. We are 7% of the human population world wide, we are the minority and we are closing in to 0% in a 100 years, or becoming a tiny r4ce of sl4ves for 100's of years more. I don't understand this cheap, weak and cowardly 3rd rate philosophy which older men cling on to. You are leaving us with nothing but D3ATH.

@hyleg666 - 2024-09-22

So we don't Even try to make better things? I'm also an engineer, and I think that things that can be improved should be.

@DelaneAtalanta - 2024-09-22

The least one with undesirable results? Tell me, how is democracy helping White people to secure their borders, any of them for that matter, on all of our countries. How is it the fertility rate? Happiness? Health? The safety of our families? It would be one thing if we just stopped having almost any children, but we are b0mbarded with legal and illegal immigrants across the whole of the West. We are 7% of the human population world wide, we are the minority and we are closing in to 0% in a 100 years, or becoming a tiny race of sl4v3s for 100's of years more. I don't understand this cheap, weak and cowardly 3rd rate philosophy which older men cling on to. You are leaving us with nothing but D34TH.

@DelaneAtalanta - 2024-09-22

The least one with undesirable results? Tell me, how is democracy helping White people to secure their borders, any of them for that matter, on all of our countries. How is it the fertility rate? Happiness? Health? The safety of our families? It would be one thing if we just stopped having almost any children, but we are b0mbarded with legal and illegal immigr4nts across the whole of the West. We are 7% of the human population world wide, we are the minority and we are closing in to 0% in a 100 years, or becoming a tiny race of sl4v3s for 100's of years more. I don't understand this cheap, weak and cowardly 3rd rate philosophy which older men cling on to. You are leaving us with nothing but D34TH.

@blew319 - 2024-08-28

15:45 I don’t understand? By changing position of A and C such that all A are below C, aren’t you either not changing A at all or making all A worse than B by a larger margin or narrowing the margin such that A is now only slightly preferable to B?

To me, the clear winner is C; they have first choice on half and never last choice. Meanwhile B and A both have last choice for half with A never having first choice. C > B > A. Because half say B>>A. And half say A>B. Half say C>>B and half say B>C.

Please somebody explain differently?

@Stepantc - 2024-09-11

The video is just stupid

@marcovisentin2077 - 2024-10-13

It’d work as you said if you were using a Broda-like ranked system (point based - where the “distance” matters). They are using the Condorcet method where you only look at the head-to-head matchups. I agree here it’d feel more fair and natural to use the former here.

@Fearabbit - 2024-11-01

Thank you, I'm not insane. The example doesn't work. He arbitrarily puts the final ranking as A-B-C, but then the voting on the left shows a pattern that would only allow for C-B-A. And if you change the final ranking to that, then there is no contradiction.

@indigo4208 - 2024-12-19

So glad I found this comment this was driving me crazy 😂😂. It’s clearly just ranked C B A there’s no contradiction

@awangardowakukurydza1598 - 2025-02-18

I spent an 1h rewatching this part and trying to figure out what I'm missing, thinking I was crazy. Thank you.