The paradox of democracy: Arrow impossibility explained

[@ganondorfchampin]

So it looks like it's something similar to non-transitive dice.

[@spencerantoniomarlen-starr3069]

That's because it literally is showing nontransitivity lol

[@UncleJamie]

Downvoted for the following reasons: 1. As many other commenters have pointed out, this is a pairwise/Condorcet problem, not Arrow's theorem. You should have checked the details with someone in the University of Leeds' political science department. 2. The video is too short to ever get into the details of something like this, but if you're going to use it as an advert to your course you really need to get your facts right. 3. You fail to mention that score voting systems beat Arrow's so-called 'paradox', and are therefore the basis of any genuinely democratic voting system (ranked voting systems are also anti-democratic by comparison). This might seem like a minor point here but it goes to the heart of the ethics of voting systems - as shown by Arrow and many others, ranked voting systems are fundamentally unethical and should therefore never be used.

[@mydogskips2]

As an ignoramus who has never heard of any of this stuff until now, I would ask, if "ranked voting systems are fundamentally unethical and should therefore never be used," what voting system should we use? You mention "score voting" systems, so I would ask, what are they, how do they work, and how are they different from "ranked voting" systems?

[@UncleJamie]

@@mydogskips2 I just wrote out a detailed answer but it seems to have disappeared. Basically have a look at the Center for Election Science's website (mainly in the Library pages) and at their KZbin channel. Cheers.

[@mydogskips2]

@@UncleJamie Okay, thanks.

[@Sem-yi1ry]

This is called the Condorcet paradox, named after a French mathematician Marquis de Condorcet, who first formalized this paradox. Arrow's impossibility theorem is a corollary of this problem.

[@matthewvicendese1896]

It isn't saying that democracy is bad. It is saying that we don't have a fair voting system. There are better systems than others. You analogy with litter and global warming was bizarre. Empower the populace and see them more engaged and informed. Most people are not these days because we're powerless.

[@janeknox3036]

This explanation would have been much better had the three people been named Larry, Moe, and Curly.

[@alfieking1293]

how is this different from the condorcet cycle. anyone?

[@alphamikeomega5728]

It's not - but what's explained here is also much simpler than a proof of Arrow's impossibility theorem.

[@BigDBrian]

The only thing you showed is that democracy is a complex game of rock paper scissors. I had to use knowledge of a more abstract version from another video to even understand how this leads to a problem. That's because the important premises weren't even presented!

[@alvaro92]

You didn't even finish your

[@BigDBrian]

Alvaroho I did though

[@alvaro92]

mind = blown

[@owlnyc666]

Ranked Choice Voting-Democracy?🤔😉😏

[@ElectoraleHervorming]

This theory is valid while n=3 but in normal elections the amount of voters is much bigger. So the chances of a draw are next to zero.

[@SKyrim190]

The title is completely misleading as the video talks about another subject!

[@GigasnailGaming]

uh thats condorcet's paradox not arrows impossibility theorem.

[@cyg7655]

Aren't they basically the same?

[@MrAaronvee]

@@cyg7655 No. Condorcet is an essential ingredient of Arrow's proof, but was discovered hundreds of years earlier. Arrow died only recently. A truly simple proof of Arrow's theorem could destroy society; lucky that 99.99999% of the population would not comprehend Arrow's original 'ultrafilter' proof.

[@Mathsaurus]

I have made a video on Arrow's theorem here that gives a proof kzbin.info/www/bejne/mJ3XhKKed9Fpmq8

[@studyeducation7875]

Sir, A, B and C can be voted in 6 different ways (I.e. 3!). But in the video only three cases are taken. If you consider all 6 cases then you will find A> C in three cases and C>A in remaining three cases. So A = C. Similarly we can prove A=B=C which is normal hence no paradox 😁 Or If as per video, A>C and C>A then A = C Maybe 😅

[@salvador.garcia]

Is a paradox cause you need to have 1 preference with democracy. What the Arrow's impossibily shows is the democracy doesn't work to obtein preferences; is the paradox of democracy, is democracy the one that is mathematically imposible.

[@jstrider47]

Glad I live in a republic, as it is a democratic 'republic'.

[@hgdln]

Great soundtrack

[@stevealexander8010]

The obvious fallacy is in assuming that preference is a strict ordering; a>b & b>c does NOT imply that a>c ( where '>' is majoritarian preference order).

[@moixxoi2658]

It does, have you even taken a game theory class? This is the rule of rationality. Its something you learn week 1 or 2 of a game theory or economic rationality class in uni... LOL

[@avinashg3516]

well explained..Thankyou

[@bekahmyers2206]

nice, but the music is too loud and distracts

[@davidnagy8956]

Why do you make a video on something you have clue about? This not Arrow's theorem. And this is a uni prof...

[@noneofyourbusiness6269]

Yeah the video isn't great, on the other hand if we relax the unrestricted domain axiom in Arrow's theorem to only single-peaked preferences (which is also a solution to the Condorcet paradox) then we can solve Arrow's theorem

[@CruxCalix]

more like University of misleeds

[@LucasFS_]

There is no paradox. A > C is a fallacy, this does not derive from A > B and B > C. This is just a draw.

[@MrAaronvee]

So try to draw a diagram which demonstrates that. And how can it ever be a 'draw' if you have not allowed for indifference? By the way, it was a previous neglect of transistivity which forced physicists belatedly to introduce a new law of thermodynamics: the zeroth law.

[@LucasFS_]

@@MrAaronvee First. By paradox, I meant something that we cannot understand even if we are respecting the laws of logic. Please, note that the symbols < and > in the video means preference, not quantitatively in the same way that we treat numbers. Therefore, I can't see a clear meaning to (Aa. Sorry that you couldn't understand why it was a draw, I haven't enough skills to show you that it was a draw.

[@MrAaronvee]

@@LucasFS_ I have been studying voting paradoxes for a quarter of a century. I have never seen such an argument as yours advanced and, as you cannot even offer a proof, it all seems a bit irrelevant.

[@isaacdarche7103]

50%+1 is always fair, regardless of the magnitude. All the votes are morally equal, even if the outcome is decided by 1 vote. Arrow was wrong.

[@Matt-gd4vo]

Is it? If an election determined that 50%+1 decided to enslave the other 49.9999...% and permanently revoke their voting rights, would you consider that fair?

[@noneofyourbusiness6269]

The dictator in Arrow's theorem isn't 50%+1 (a poor definition of simple majority by the way), it's literally one single voter whose individual preference ranking dictates exactly the collective preference ranking regardless of anyone else's ranking

[@jimsmid8229]

50% +1 is correct if all cast their vote equally unaware of the others. The one vote could be anyone's. Even though ALMOST half the people will be disappointed it is still fair by majority of the voters. BTW if the vote is 51-49, there are bigger problems to be solved than just voting. Order of preference in voting? You can vote multiple candidates for positions but not preference. What am I missing?

[@منوبيالفلسطي]

Islam is the unique solution for all problems of humanity..

[@alphaicedragon137]

No

[@fozerockz6945]

@@alphaicedragon137yes. Why not?