I'm getting my masters in PPE here in Germany, and the professor who is teaching this class is so impossible to understand, but listening to you was easy and the IIA made sense, finally. Thanks!
Dr. Hudgson: This is a really nice video. First of yours I watch. From a math professor to an economics professor: You are really good at explaining math.
Aside from the fact that I understood your discussion, I was indeed happy with the fact that you are using the characters in Harry Potter. Keep it up co-potterhead. Spread the knowledge through magic. Excellent explanation😊
Cool video. I could be mistaken, but I think you’re getting the Independence of Irrelevant Alternatives (IIA) condition required for Arrow's theorem mixed up with another condition of the same name. The IIA condition required for Arrow's theorem (`IIA-1') says that if two profiles contain exactly the same orderings regarding candidates x and y, then they must give the same final ordering of x relative to y. More intuitively: whether or not x is weakly preferred to y in the final ordering can depend only upon x and y's relative positions in the individual orderings, and not upon any other alternative, z. Whereas the IIA condition you’ve referred to says that you can’t change the final ranking (of x and y) by adding or taking away a non-contender to the set of candidates, X. A similar IIA condition which appears in the social choice literature (`IIA-2’) is the condition that Sen called `condition alpha’. It says that if x is weakly preferred to y in the final ranking given a set of candidates X, then x should be weakly preferred to y in the final ranking given a set of candidates X1 (which is a strict subset of X). However, this condition is not relevant to Arrow’s theorem, which concerns IIA-1. See Chapter 6 (p. 127) of Gerry Mackie’s `Democracy Defended’. (Again, happy to accept I’m wrong if I’m making a mistake).
I've been trying to understand the theorem by reading Steve Skiena's Data Science book, but your explanation cleared it all up. Keep going, your explanations are succinct and you deserve more views.
You just disproved that spoil candidates can exist but in the Borda count vote thus conflicting with the Independece of Irrelevant Alternatives. You didn't show other election systems like instant runoff voting that would conform with this
Thanks! Great video. I was convinced by the arguments in Pettit and List, 'Group Agency' that it's reasonable to relax some of these conditions, but I can't remember the details now.
Thanks! Yes, I think a good area for future research is to figure out which situations are least likely to be manipulated. That would involve probabilistic/statistical research, rather than "pure math" (as Arrow's is). I want to do a video on that eventually.
Amazing video. As a Latin American man, I can tell you with all certainty that the reason why the political system in Latin America countries is so frágil is precisely because of this. Practically all countries in Latin America have the system where if the 50% + 1 voting is not obtained by a candidate, then a 2nd round of voting will take place, where the candidate that obtained the less votes on the previous round will be eliminated. Then those votes will go towards the other “surviving candidates” from the 1st round. Then, an alliance occurs between the eliminated candidate and one candidate that did not win the 1st round, but with the addition of those new votes, eventually becomes the final winner after the 2nd round. Arrows Theorem is right on the money. On my humble opinion, the best voting system should be the one where whoever obtains the most votes (regardless of 50% + 1 or not), wins. No 2nd rounds or 3rd ones, just 1 election and that’s it.
So what would be the ideal voting system? And I would add that we need to keep in mind the fact that average people would need to vote using the system, and they would have to understand it to some significant/reasonable degree to accept it as being legitimate. This is to say a really complex voting system that may in theory be "ideal" wouldn't necessarily be accepted by the populace as legitimate if they cannot really understand how it works.
This is incorrect. Arrow's theorem isn't a proof that there's no "perfect" voting method, it's a proof that no *ranked voting method* (i.e. rank orders as opposed to cardinal ratings/scores) can satisfy a list of criteria including independence of irrelevant alternatives. It doesn't apply to cardinal methods like score voting and approval voting. More fundamentally, it's really relevant to social welfare functions, not voting methods. If you assess voter satisfaction efficiency (VSE) with a cardinal/utilitarian social welfare function, then the implications of Arrow's theorem are already accounted for and you can just do an apples-to-apples comparison of any arbitrary set of voting methods using utility efficiency.
So could you not narrow the field of candidates with a plurality vote, and then eliminate any candidate from the running that had less than some set percentage of the vote (like, 10-15%, I guess?)? Then do a Borda vote between those candidates. There would be no reason to remove any candidate after the fact, as none of the candidates would be irrelevant. Or am I not seeing how that could still be manipulated?
"In economics we like to talk about preferences an preference orderings" And this one of many reasons your field is an unsalvageable farce. You have no remotely coherent concept of utility, and very nearly everything you pretend to discuss immediately collapses on first principles.
All I know is that, the more people who vote for Dr Jill Stein or Howie Hawkins or Ralph Nader or any other Green Party candidate, for President of the USA or President of any country, or for any other political office, the more likely we will have more Greens in power. All voters must be assumed to have full responsibility for their vote: nobody forced them to vote a particular way.
That varies from one country to the next. In proportional-representation countries there usually greens in parlement. In the USA however, you have first-past-the-post - and nobody seems to campaign against it. I myself would prefer approval-voting or similar, not instant runoff
@@ronaldonmg not a lot of people look into Arrow's Impossibility Theorem but when I did I discovered that it has cullinaries that go 'yeah, not even alternative voting systems are only going to have the same problem'.
I'm getting my masters in PPE here in Germany, and the professor who is teaching this class is so impossible to understand, but listening to you was easy and the IIA made sense, finally. Thanks!
Dr. Hudgson: This is a really nice video. First of yours I watch. From a math professor to an economics professor: You are really good at explaining math.
This lady is a genius in explaining things and making things simple. Which I think is an indication of genius in general.
Aside from the fact that I understood your discussion, I was indeed happy with the fact that you are using the characters in Harry Potter. Keep it up co-potterhead. Spread the knowledge through magic. Excellent explanation😊
Cool video. I could be mistaken, but I think you’re getting the Independence of Irrelevant Alternatives (IIA) condition required for Arrow's theorem mixed up with another condition of the same name.
The IIA condition required for Arrow's theorem (`IIA-1') says that if two profiles contain exactly the same orderings regarding candidates x and y, then they must give the same final ordering of x relative to y. More intuitively: whether or not x is weakly preferred to y in the final ordering can depend only upon x and y's relative positions in the individual orderings, and not upon any other alternative, z.
Whereas the IIA condition you’ve referred to says that you can’t change the final ranking (of x and y) by adding or taking away a non-contender to the set of candidates, X. A similar IIA condition which appears in the social choice literature (`IIA-2’) is the condition that Sen called `condition alpha’. It says that if x is weakly preferred to y in the final ranking given a set of candidates X, then x should be weakly preferred to y in the final ranking given a set of candidates X1 (which is a strict subset of X). However, this condition is not relevant to Arrow’s theorem, which concerns IIA-1.
See Chapter 6 (p. 127) of Gerry Mackie’s `Democracy Defended’. (Again, happy to accept I’m wrong if I’m making a mistake).
I've been trying to understand the theorem by reading Steve Skiena's Data Science book, but your explanation cleared it all up. Keep going, your explanations are succinct and you deserve more views.
You explained this waaaaaay better than my professor! THANK YOU
thank u! i'm cramming for a comparative politics exam rn and this helped me grasp the theorem !
Fantastically explained.
You just disproved that spoil candidates can exist but in the Borda count vote thus conflicting with the Independece of Irrelevant Alternatives. You didn't show other election systems like instant runoff voting that would conform with this
Realy a great video and details Explanation abt Arrow's Impossibility theorem.Which will b definately helpful for research n learning both.
Thanks.
Thanks! Great video. I was convinced by the arguments in Pettit and List, 'Group Agency' that it's reasonable to relax some of these conditions, but I can't remember the details now.
Thanks! Yes, I think a good area for future research is to figure out which situations are least likely to be manipulated. That would involve probabilistic/statistical research, rather than "pure math" (as Arrow's is). I want to do a video on that eventually.
This more closely uses the form by which I was taught Arrow's, which was taught in a PPE class using the book by Gerald Gaus.
It helped a lot 🥰
Amazing video. As a Latin American man, I can tell you with all certainty that the reason why the political system in Latin America countries is so frágil is precisely because of this. Practically all countries in Latin America have the system where if the 50% + 1 voting is not obtained by a candidate, then a 2nd round of voting will take place, where the candidate that obtained the less votes on the previous round will be eliminated. Then those votes will go towards the other “surviving candidates” from the 1st round. Then, an alliance occurs between the eliminated candidate and one candidate that did not win the 1st round, but with the addition of those new votes, eventually becomes the final winner after the 2nd round. Arrows Theorem is right on the money. On my humble opinion, the best voting system should be the one where whoever obtains the most votes (regardless of 50% + 1 or not), wins. No 2nd rounds or 3rd ones, just 1 election and that’s it.
So what would be the ideal voting system?
And I would add that we need to keep in mind the fact that average people would need to vote using the system, and they would have to understand it to some significant/reasonable degree to accept it as being legitimate.
This is to say a really complex voting system that may in theory be "ideal" wouldn't necessarily be accepted by the populace as legitimate if they cannot really understand how it works.
My favourite HP character, Floor.
Ron definitely would put Fleur first though
Who was Freds vote
I am always down for some mathematically-based pro-monarchy videos.
Great video, but we all know Billy will choose Fleur over Dumbledore any day lol
No any other way this could be explained better than this.
This is incorrect. Arrow's theorem isn't a proof that there's no "perfect" voting method, it's a proof that no *ranked voting method* (i.e. rank orders as opposed to cardinal ratings/scores) can satisfy a list of criteria including independence of irrelevant alternatives. It doesn't apply to cardinal methods like score voting and approval voting. More fundamentally, it's really relevant to social welfare functions, not voting methods. If you assess voter satisfaction efficiency (VSE) with a cardinal/utilitarian social welfare function, then the implications of Arrow's theorem are already accounted for and you can just do an apples-to-apples comparison of any arbitrary set of voting methods using utility efficiency.
It should be noted that the cullinaries of this theorem prove that even cardinal methods won't work... yeah, this theorem has _cullinaries_ too.
So could you not narrow the field of candidates with a plurality vote, and then eliminate any candidate from the running that had less than some set percentage of the vote (like, 10-15%, I guess?)? Then do a Borda vote between those candidates. There would be no reason to remove any candidate after the fact, as none of the candidates would be irrelevant. Or am I not seeing how that could still be manipulated?
Fudges
This is basicly Godel theorem for politics
"In economics we like to talk about preferences an preference orderings"
And this one of many reasons your field is an unsalvageable farce. You have no remotely coherent concept of utility, and very nearly everything you pretend to discuss immediately collapses on first principles.
All I know is that, the more people who vote for Dr Jill Stein or Howie Hawkins or Ralph Nader or any other Green Party candidate, for President of the USA or President of any country, or for any other political office, the more likely we will have more Greens in power.
All voters must be assumed to have full responsibility for their vote: nobody forced them to vote a particular way.
That varies from one country to the next. In proportional-representation countries there usually greens in parlement. In the USA however, you have first-past-the-post - and nobody seems to campaign against it. I myself would prefer approval-voting or similar, not instant runoff
@@ronaldonmg not a lot of people look into Arrow's Impossibility Theorem but when I did I discovered that it has cullinaries that go 'yeah, not even alternative voting systems are only going to have the same problem'.
not good enough explanation in my opinion. get good.