The flaw in every voting system
2024 ж. 9 Мам.
413 422 Рет қаралды
#some3
0:00 Intro
3:11 Definitions
6:44 Proof
11:39 Arrow's theorem
13:25 Approval voting
17:03 Outro
Blog post: vasekrozhon.wordpress.com/202...
Github: github.com/polylog-cs/voting-...
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Thumbnail by Alžběta Volhejnová
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Comparison of voting systems: en.wikipedia.org/wiki/Compari...
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This is not a flaw in every voting system. It's a flaw in every voting system that has only one winner. In a country like Finland we have 200 seats in the parliament. We could fill all the seats based on how many votes each party got. Any party that got more that 0.5% of votes would get at least one member into the parliament. Problem solved. No reason to just have one seat like the presidential election. This is not the middle ages anymore.
If you don't think you're party will get 0.5% of votes you'd vote for someone else. Or if there's an independent candidate, any ballot above the 0.5% is wasted. And there can only be 1 prime minister anyways
@@LightPink True. But this voting system diminishes the problem by 100 times. There is a threshold but it's not impenetrable like in the US where there can only be two parties in power. No new party will ever topple them. It is technically possible but the chances are near zero. You would need major upheaval close to a civil war to achieve that. For the second part. Yeah. There's only one prime minister. There's also only one heath care minister, education minister and foreign minister. The power can be diluted. One person doesn't have to hold all of it. The US system where the president holds massive power is actually the exception, not the norm. We too have a president but he only does foreign diplomacy and doesn't meddle with our country's internal affairs.
Oh have I got news for you (namely that that creates an entirely different voting issue called the apportionment problem) kzhead.info/sun/erqhdqatoYKiiac/bejne.html (btw your country uses "Jefferson's Method" except instead of states it's political parties)
I also like parliaments! But even in Finland, you may want to decide with your class on which film to go to, or use top 100 movie lists etc.
And how will the 200 members of parliament vote? Say, about who gets to represent Finland on the international stage.
In my Swedish municipality we have public digital “suggestion box” for political ideas. An idea requires 100 citizen votes to be debated by the council. There is no negative voting however, which makes the system unreliable. There was a case (replace some car roads with parks) that got 100+ votes, but an anti-case (do not replace roads with parks) got over 3000 votes. Both had to be debated as separate topics in the council, which the media found hilarious.
The swedish democracy is one of the most fucked one in the world by strategic voting. The 4 % parties that can sway the results on who will govern (right or left) gets an insane amount of power in proportion to how many voted for them...
How bot (fake votes) protection work there?
What even was a point of an anti-suggestion? If it’s just a non-binding suggestion and people are against it, it will not pass. I just don’t understand why would you suggest to not do something that is not planned.
@@kaltziferYT Sweden have "BankID" which is a government authentication service to verify an individual. This is used to make fake votes less of an isssue.
@@snowmanscz1011To show the council that there was opposition would be my guess. Not everyone has the time/ability necessary to show up to the meeting, Ando governments have made bad/unpopular decisions under the false impression it was popular.
So many people are unaware of the very existence of voting theory (aka social choice). This should be taught in school because our entire society relies on how much trust people put on election results. And this trust is eroding very fast
People aren't distrusting voting systems because of tactical voting, they are distrusting voting systems due to attacks on the integrity of the government, from both within and without.
It’s a subtopic of game theory, which is already rarely taught in schools. For most people, they’ll never know about it, and even for those who do learn some, the most they’ll get is the Prisoner’s Dilemma. This isn’t exactly an easy topic to cover and I don’t expect it to be except at the most abstracted and babied-down level in a government class.
We are taught that "voting = freedom" and many can't think past that indoctrination.
Yeah that wont happen because the ruling class would never teach people about politics or they might stop making profit and capitalist propaganda wouldnt be as effective
Yeah, but even in the first example you must assume that banana votes for coconut 1;1 for it to hold true (in the two part section). That is never honestly true, and was just generalized and moved past. Even if you are talking about ranked, or star, or whatever ranking system, a run off is not guaranteed to produce those outcomes unless only one ballot can be cast at the beginning of the election. Then it wouldn't really be a runoff, just a consensus win. If people understand that going into the process it will change their calculus and the example still falls apart. Not everyone will use all of the lines... Unless it's mandated, and then it's not really a choice now is it...
thankfully, voting methods like approval voting, score voting, and star voting are extremely resistant to strategy. this is explained in the excellent book "gaming the vote" by william poundstone.
I agree these are good systems! Another class of great voting systems are so-called Condorcet methods. With approval voting, you sometimes still see a game of chicken, but with star voting I really find it hard to imagine how that can lead to strategic voting.
@@PolylogCS Seems to me the runoff round of STAR brings you directly into the scenario described at the start of the video? That is, if there's a condorcet cycle, you do NOT want the final runoff to be a matchup between your favorite and the choice that beats your favorite, even if that means keeping your favorite out of the running to prevent that scenario.
@@PolylogCS Every consensus-seeking voting method that allows voters to support multiple candidates simultaneously suffers from that "game of chicken scenario". It's not exactly a flaw, it's a risk. Cooperation between potentially allied factions is a desirable thing, but trying to eliminate potential betrayals generally (see below) means you have to eliminate cooperation altogether. This the idea behind Instant-Runoff Voting (AKA Ranked Choice Voting): you assume every single voter is as strategic as possible by default, only supporting their current favorite and nobody else until that candidate is removed by force. This is why this voting method is often claimed to be "resistant to strategy", but the reality is that it just forces everyone to be as strategical as possible by default (given the motivation of strategy under other voting methods, that's what it is). So there's no "chicken dilemma" because there's no cooperation at all. The only counter-example I know of to the above concerns is "Reciprocal Score Voting", which is a proof-of-concept system I created explicitly to exemplify these ideas. It rewards mutual cooperation between factions, and penalizes factions which betray one another. So you mostly deal with the "chicken dilemma", because betrayal is pointless. Factions that are true opponents are unaffected. But it's a complex system, not intended for real-world use.
@@PolylogCS Star voting can quite easily lead to strategic voting. Say before your vote the top 3 candidates are A, B and C. A is your first preference, B is your second and C is your third. If you give 5 points to A, 4 points to B and 3 points to C, then A and B goes to the final round and B wins. But if you instead give 0 points to B, then A and C go to the final round and A wins. This could also work the other way where if C goes to the final round then C wins. If it is just A and B then B wins. So you are incentivised to drop your vote from C down from 3 to 0 to keep it out of the final round. Possibly even changing your preference between A and B to make sure they go in.
Approval voting, score voting, and star voting are extremely rubbish at indicating disapproval.
I love how the US electoral college does not satisfy these requirements to be considered a "reasonable voting system."
Yeah, even actual reasonable systems like Borda count don't satisfy it, our definition of "reasonable voting system" frankly sucks :). You can check out our blog post that discusses it.
The electoral college is actually a good thing. Pure majority rule is horrible.
The error introduced by the electoral college is what, 1 or 2%? The error result of plurality or runoff voting is an order of magnitude greater.
@@massimo4307I hate how much I can believe that.
@@massimo4307 Minority rule is even worse! The biggest real effect of the EC is to give massive power to a minority of swing state voters. Marginal votes in Pennsylvania are tens of thousands of times more valuable than votes in Wyoming, according to voter power indices, so presidential candidates campaign in PA (and other swing states) and make promises to swing state voters, ignoring other voters, and this affects national policy. That's why the US seems to care more about rust belt fracking than the fires and droughts in CA or the plight of the deep south. Under popular vote, everyone in the country would be equally important to appeal to (whether in rural or city, swing state and not), and power would still switch back and forth between the two parties, if that's what you're worried about, because candidates would shift their strategy to appeal to the most votes, until voters are split roughly 50/50 again as they are now.
This should be taught on high school math, so everybody knows about the flaws of voting systems
Thanks, I also think this should be common knowledge.
that would make a great cross topic set of lesson. Start is social studies, go over to math and tie it back to history.
You vastly overestimate how many people would actually understand or care about it.
Which is why it will never even be hinted at in the education systems of those countries on the List of Shame
It's not that voting systems are flawed, it's that humans vote on stuff in the first place, just let those who are good at leading, do the leading and, let the sheep follow in their tracks. Dictatorships are always the best political systems after all, be them military dictatorships, instated by the US... Chile and Pinochet's Junta for example, don't mind the human rights violations.. they were sponsored by taxes after all and the US War Machine... or Absolute Monarchies, like Saudi-Arabia, don't worry about human rights, we got oil, and you want it, here's an idea... Let's shut down nuclear power plants and turn to wind and solar and hydro, and then as these are shite useless technology that has no use at all, people would need to buy more oil, coal and gas, which means we can line our pockets deeper, while extorting the general populace. Ah history, anyways, time for more modern stuff, let's put an Oil Company in power over an entire African nation and it's government and military. Shell PLC perhaps... It's interesting how far bribes can get you... Or you could rig an election, I mean you could have 247% voter turnout, you could do some ballot harvesting and other illegal stuff, then when the opposition questions how you got all them votes, call them conspiracy theorists, then take them to court in Georgia, and accusing them of racketeering for some reason. Because one can't deal with the opposition with the good old means of the past, it would rouse too much suspicions about it... Ain't want another CIA Presidential Assassination... 1 JFK is enough. Ah, politics, the worst thing that has happened to mankind ever, it was better in the good old day, when you just removed the unwanted from societal participation via less than amiable means. It was a lot better for societal cohesion as well.
One problem with these mathematical approaches is that they assume voters have a ranked preference. In reality, voters typically do not have that. The average voter might classify their candidates in 3 tiers: preferred, acceptable and objectionable, with little differentiation within the categories. Any further ordering is basically random (or noise, from an information point of view). This is why systems like approval voting have an advantage: they more closely capture voter preference.
It also assumes that each voter is motivated “towards” each item in the preference ordering, and some are just preferred higher. In practice many voters will instead be motivated “away” from certain items. A voter that ranks ABC for preference when all three are positively considered, but C is just the least positive, is different to ABC when C is absolutely hated in all circumstances. In the latter there is an incentive towards a different strategic behaviour, partly touched on (although not expanded upon) by this video.
@@kelly4187 agreed, that's what I call the objectionable category. Approval voting allows voters to indicate which candidates they positively approve of, and the rest are negative. The winner is then the candidate which is agreeable to the largest group.
@@kelly4187 I made a comment in the blog: What about something like STAR but with fibbonaci sequence (1, 1, 2, 3, 5, 8) and negatives half the size of the sequence (-1, -1, -2) and where you can't give the same score to multiple candidates? This way you can punish (being bad will make you worse than being unknown), but not to a huge degree (you can't give everyone a negative). Of course there could still be some strategic voting (voting 5 instead of 8) but it would be quite diminished. Under this system, say there are some more candidates, DE that nobody cares about. The first voter would vote A(8) B(5) C(3) D(0) E(0), the second would vote A(8) B(5) D(0) E(0) C(-2).
As for ties, the winner is the one with more points in the best positive category (8), if that is also a tie, the one with least points in the last negative category (-2), if also a tie, the one the second best category (5), then second last (-1), etc. It's only a true tie if they have the exact same number of votes in all categories.
In case of a true tie the candidates face each other in a all-vs-all no quarters hunger games competition :D
To be fair, the random voting system was used in one of the longest lasting voting systems ever used: the venetian voting system.
Apparently the randomness existed to hide corruption...
@@eyescreamcakeor prevent it. You can't bribe a voter unless you know which voter is the one that matters.
@@rsm3t Bribe all the voters. Push policies which sound good on paper but actually keep them poor. Work with your political rivals; Let them be villains for those voting for you, and you a villain for those voting for them. Keep the audience caught in the emotion, the rivalries, the "Sport" of politics - Not the policies. Better yet, if something really bad happens and no-one can be the fall guy, just blame it on the 'bad luck' the system enables. Worst case scenario; Nobody needs to be at fault. Some randomly selected elements nobody could possibly account for throwing a wrench in your totally good natured plans ¯\_(ツ)_/¯ Make the voters easier to bribe and dependent on your "help" , but they never actually receive what they want or need due to your 'rivals' and 'bad luck'
@@TheGaboom It's expensive to bribe all the voters.
Sortition is the method by which we pick juries for trials in the United States and, while there can be flaws in the jury system, it's pretty solid over all.
Actually, Arrow’s Theorem only applies to ordinal voting systems (where voters can only express their order of preference). Cardinal voting systems (where you can also say how much you like and dislike any given option) are a different matter. And indeed, price formation in an ideal market can be considered a cardinal voting system.
We said that in the video, right? Also, price formation in markets is a bit more complicated mechanism because everybody has a different amount of money, but I like how you are drawing the connection -- voting theory is just a special case of mechanism design!
That’s just what I was about to comment on, only your explanation is better stated. :) For example in either score voting or STAR voting I would give avacado 0 points , banana 5 points, and coconut 4 points because I would be happy with either a banana or a cononut with a slight preference for a banana but I _really_ don’t like avacados.
@@PolylogCSyou implied it, but never specified what kinds of systems G-S applies to where Arrow’s doesn’t.
@@trevinbeattie4888 Sounds like you are not voting optimally, you should give coconut and banana both 5 to get the best chance of avoiding avocado since that is your main priority. This is my problem with cardinal voting proponents, they don't acknowledge that in practice cardinal voting requires more strategy than ordinal (and disenfranchises voters who don't understand the strategy, unlike condorcet ordinal systems where strategy is only relevant in extreme edge cases)
@@oliverwilson11 STAR has that runoff round where your vote gets ignored if you gave both finalists the same score, so there's some reason to use the 4 and 1 numbers there.
I want to see an analysis of an up or down voting system. Each voter gets exactly one vote. They can either choose to vote for a candidate they like increasing the candidate's vote total by one, an up vote, or vote against a candidate that they dislike and decrease that candidate's vote total by one, a down vote. Inspired by the common complaint of people feeling like they must vote for the lesser of two evils, this instead gives the option to vote against the greater evil and gives candidates that people truly believe in to rise up.
Intresting idea. Some general observations: in a two candidate system this is identical to FPTP. If there are more than two candidates a down vote acts as an up vote for all other candidates. Due to this, this voting system might tend towards a W shaped curve, where either centrists or very obscure candidates get elected due to the lack of down votes for them.
@Glass-vf8il yes, giving third party candidates a real chance a victory is one of the things I see as an advantage to the system.
@@Harkmagic As a Centrist Moderate Independent, I vote up.
@@Glass-vf8il We did not mention it, but if you have just two candidates, FPTP is kind of the only reasonable thing to do, so every reasonable system should reduce to FPTP there.
This idea reminds me of this method en.wikipedia.org/wiki/D21_%E2%80%93_Jane%C4%8Dek_method that is trying to do something similar, while keeping that you are supposed to give more positive than negative votes.
"This was supposed to be a random fruit, not banana" got me :D
My sisters and I took turns picking ice cream flavors. I loved mint and chip but I never chose it because I knew my sister would, so I always got black cherry. I got my favorites twice.
What happens if you ask everyone to vote not knowing what the voting system is, and then randomly select a reasonable voting system after all the ballots are cast?
Then you become GOD as you can ultimately decide the winner in anything resembling a close race.
because you are the only person who matters (dictator) because based on what voting system you choose could completely change the result
Would a random choice from a set of reasonable voting systems with different methods of distributing spent votes constitute a reasonable voting system? It looks like one of the axioms for the law is that voters can predict how votes are distributed by the system. If you violate this axiom, it seems like the law no longer holds.
@@zen_tewmbs That's why it's random
That's why it's random@@Cheasle2
I saw the title real fast and thought it said "vomiting" and quickly made up my mind about this being a video explaining how we evolved vomiting as primates and how that helped us evolve
Saw this again on my feed two months later and my brain read "Strategic Vomiting" AGAIN
and you clicked on the video 😂😭
@@weeb6316 twice
Idea: use a voting system which is simply a culmination of the results of 10 or more established voting systems. collect a ranked list of a select number of fruits and convert that into every voting system’s input. Then, use ANOTHER voting system on those results until a winner is found. The only downside is all the confusion and red tape!😁
xD
if each voting system comes up with a different winner, which voting system do you use to determine the winner?
@@jonathanodude6660 The one who won the most voting systems
@@geenkaas6380 you’re seriously going to use first past the post to determine the winner after all that? 😭
@@jonathanodude6660 No I am personaly a fan of a system wich works as that there are 150 seats in parlement and if you get enough votes for 1 seat you get 1 seat in the parlement
The problem lies in thinking that a single winner-takes-all vote can comprise the entirety of democracy. There's a reason voting is considered the minimum responsibility of a citizen.
I never vote. They end up making the same garbage decisions no mater who gets elected. Voting is pointless. Just look at the US, who switches between two sides every 4th year. Does it really matter which 4 years are to one side and which 4 years are to the other side? The reason they keep voting for the opposite side is that they both suck, and they want to get rid of what is currently there. Apparently they never realize that what they get instead is not better.
Simplicity is _not_ a flaw. It's a form of transparency that allows people of all levels of intelligence to feel confident the outcome of a vote is legitimate. This is a challenge with so many alternative voting systems, if it adds any sort of complexity it begins to feel like the system is being gamed to harm one group or another. Unfortunately, the people who feel harmed are also the most likely to get very angry and frustrated. I love the idea of instant-run off voting but I see most people I know uncomfortable with this "new fangled" idea because it is way more complicated relative to first-past the post. The only reasonable choice I've been able to come up with that preserves legitimacy while granting better results is a combination system: ranked-choice primaries but two candidate run-offs for the final, separate, vote. *You cannot underestimate the importance* of having a system that *feels* legitimate because it is transparent and easy to understand. And I think most people would prefer to have the cost of multiple-round voting to feel, in their bones, that the system is legitimate.
If you can't understand instant run-off voting you're not intelligent or knowledgable enough to vote at all. Its not very complicated at all
It’s also a flaw to cater to lowest common denominator so to speak
@@Speedster___I agree so much with this but there is nuance here. I don't think this is catering or pandering. It's confidence building. And it has the virtue of keeping people focused on who the leaders are and what they actually did or not do instead of trying to assail the system that elected them. We shouldn't ignore those benefits.
@@x--. even without multiple voting systems you still get cranks. Makes me think speed accuracy and transparency matter way more for confidence then system used
The fact that the avocado monkeys voted for their known second choice to avoid their third is a good thing. They are sacrificing their favorite so that their second favorite wins, and the most voters are happy (7 vs 2)
I like how you are implicitly questioning whether we should care about strategic voting. We are discussing it a bit in the blog post.
@@PolylogCS The key factor on if Strategic Voting is good or not is the motivation. Like if you strategically vote in a way that would get a terrible choice as the winner, because you think it is funny.
Sorry if i'm misunderstanding something here but wouldn't that be very similar to approval voting in that sense that the metric is most people happy(ish) the avocado mokeys would also approve of banans which would make bananas win 7 vs 2
@@ebentually Exactly. But what happens if everyone voted strategically? Or worse, voted for their least favorite option as a gag?
@@ebentually The coconut monkeys could then strategically not approve of avocados, even if they tolerate them, so their first choice, coconuts, wins. Approval voting has the issue that if you approve all or disapprove of all candidates that have a chance of winning, then you wasted your vote. This incentives you to strategically either not approve of a candidate you like, because you like his opposition slightly less or to approve of a candidate you don't like because you hate their opposition slightly more.
One thing that I can't just wrap my head around is why all the voters for any first choice share the same secondary choice. It feels like an assumption that works backwards towards the end desired goal
For this very simple example, it was working backwards for a desired goal. The example in the video had to be simplified so there weren't too many combinations of monkey preferences. In a real election, the same holds, but it would just be different voters angry when some can vote strategically or have a dictator determining an election outcome depending on the combination of rankings any particular voter used.
@@pace1195 but there's the crux of it. The second choice is always harder to predict. Heck the first choice is hard to predict. Trying to mind game these systems feels more like an effort in futility
3:18 And thus I found out once again that my ideas are not unique. Yet, I'm all the happier to learn this concept isn't so unheard of.
Excluding situations where a Condorcet paradox exists (which I think would be very unlikely in a vote with millions of ballots), to me it seems like the Condorcet method is the best system because strategic voting is usually unlikely to be helpful
It's also nice because it tends to elect moderate candidates that everyone is at least okay with, and does so in an obvious way. Imagine how much happier Republicans in the US would be if Bernie Sanders was also an option in the 2020 general election, and they ranked Biden over Bernie, and they were successful in keeping Bernie out of the presidency. Having a winner who most people see as "not the worst" is a powerful thing.
I was watching this going "I hope he mentions the Approval Voting system..." and you did! I live in Scotland, and yes, I really wish we could throw out the disastrous FPTP for our UK parliament elections, but at least we get AMS for our devolved parliament, and STV for our local elections. But we cling on to it for many reasons (the big parties have no incentive to change, ignorance about how voting works, belief that it gives better outcomes etc.). Glad to see it's just as disliked by voting theory experts.
I recall the UK had a referendum on ranked voting in 2011 and voters soundly rejected the proposal. This also wasn't a regional thing as Scotland itself rejected it in a landslide.
There's only one thing I dislike about Scotland, and that is the haughty English that live next door. My least favorite people. Keep the faith brothers, it's about to get good.
Ok, here’s one that may be worth looking into: “Negative elimination voting”. You have a ranked choice and you eliminate the candidate who is at bottom of the most rankings, then you move all choices up and repeat. This should give you the choice that is the least hated. If you try to strategically vote for your second choice over your first, then you’re going to get your second choice instead of your first. And if you vote your third choice as your second choice then you’re more likely to get your third choice, not your first.
I think it should be immediately clear about a handful of different ways that one could strategically vote in this system
@@Laotzu.Goldbug after looking at it for a while I did find 1 that would be “successful strategic voting” but only the one. It would require the banana monkeys to list bananas as their least favorite, coconuts as most favored, and avocado as neutral. Which makes the avocado lose and the coconut win. Any other strategic voting causes the least preferred choice to win. However, I still think that it has potential as a system.
This reminds me of those forum games where you find the best football team/Pokémon/whatever by having people take points from the one they dislike and give the points to the one they like. And every one of those that I've seen ends with a winner that was just too bland to have any haters. Which isn't the worst thing, but I imagine it would leave most people feeling disappointed.
@@brandonm949 Considering that the current system is rapidly careening towards violent armed conflict, bland and disappointing seems like a step in the right direction.
Very very nicely done, and very nice animations!
my undergrad thesis presentation was about strategic voting, and its been a topic which has fascinated me since. great video
Thanks!
Thank you for the work you put into this! Very good explanation, even of the proof.
Great video! I thought it was really well done, and nicely made the point that theorems aren't always the whole picture. Personally I think STAR Voting would be the best option, but I really like approval voting as well
Really cool video with good explanations. Thanks mate
I really like the last part! Considering the intensity by which people will argue over how probability distributions should be sampled in path tracing algorithms, I can only imagine what the the arguments (or civil wars) would be like when the fate of the nation depends on it!
Awesome video! I'd lovw to build a website where people can play around with setting up different inputs, and try different voting systems
At first I thought the thumbnail said “strategic vomiting”. I then proceeded to have a conversation in my head, debating the likelihood of vomiting after eating a banana and an avocado.
What if every monkey wrote their favorite fruit and we randomly selected a ballot to be the winner POV: I didn't watch the entire video before commenting
That would be a schocastic version of first past the post. It would also eliminate the abililty to represent second preferences
@@gregoryfenn1462Although it superficially resembles first past the post, it has NONE of FPTP's downsides, and has some different downsides of its own. The fact that it becomes completely unnecessary to represent second preferences is actually one of its upsides!
One of biggest downsides: You get total psycho elected cause 1 monkey out of 1000 voted for him
@@koteghe7600 I feel like that is a better problem than most people have right now.
Thank you so much, I have had my PhD in statistics for over a decade now and you've finally made it clear to me how it works. Well to be perfectly honest, in my humble opinion, of course without offending anyone who thinks differently from my point of view, but also by looking into this matter in a different perspective and without being condemning of one's view's and by trying to make it objectified, and by considering each and every one's valid opinion, I honestly believe that I completely forgot what I was going to say.
Apparently they give out PhDs to just anyone
PhD confirmed
the scientists should have ranked the voting systems several times. every time using a different voting system :D
In reality, the two round system indeed can get stuck (with a very small probability). But capturing that in a definition of a voting system makes stuff clumsy, hence see 4:17
@@PolylogCS I think this answer belongs to a different comment?
Hey! This video is really wonderful! ❤❤ congratulations for the great work!🎉🎉🎉
What if we used science to take the candidates and construct a randomised monster candidate based on a ratio of all votes? Avonananut? Bacocodo? Cocadona?
I think a "no confidence" vote should always be on the list. If it wins we send every candidate home and get new ones.
Combined approval voting with a clause that says "no candidate with a negative score will be elected" will have the same effect. CAV is where each ballot scores each candidate "for/approve" (+1), "neutral/unscored" (+0), or "against/disapprove" (-1), and the candidates scores are the sum of the ballots, then rank them by their score and choose the top N candidates. It is a voting system that strongly emphasizes consensus building rather than catering to any extremes, and as such it is no good for proportional representation (though it would still be a significant improvement over plurality voting for district-based representation).
More generally, the concept you're looking to integrate into a voting system is called "negative voting".
@@k98killer you don't want to exceed voters' tolerance for complexity. Ranked choice is plenty.
The actual name of this concept is "NOTA", or "None of the Above". I agree, every ballot should have this.
@@ardentdrops ranked choice is often the most complex system to implement. A voter needs to be able to reason about how the election works to be able to vote, and the process needs to be auditable for integrity. Try implementing RCV in code sometime; it is convoluted as hell. CAV takes only a few dozen lines of code and is simple and easy to calculate and audit. If your voter base is assumed to be too stupid to understand how to vote "for" and/or "against" any number of candidates, then your society is already an unmitigated failure.
The solution is to vote your fruit into an assembly where the number of seats for each fruit are apportioned by the number of votes, and then whichever fruits build a multi-fruit coalition of over 50% of the seats win! In more direct terms, the monkeys talk to each other and are incentivized to form alliances larger than 50% of the total. This alliance then decides who their leader is!
Well produced video. Great explanations.
Thanks!
imagine discord polls having a better voting system than all countries
There's no political incentive for discord polls.
@@sam5992 nor is money typically involved in those
@@elpsykoongro5379... for neither voters or candidates.
A neighbor country of ours just had presidential primaries where the guy with the most votes ended up being someone who is, in his own words, an "anarcho-capitalist." I really think it's in huge part due to "protest voting," which is similar to strategic voting. Half-way through the video so far and I find the whole thing very interesting.
Argentina?
Thank god, there is finally a country that is definitely more stupid than the United States. What is your neighbor country's name, so I can use it as an example?
Awesome guy
Or maybe, just maybe.Most people aren't alienated anime avatar urbanites that vote different shades of progressivism and are more intelligent than the university educated avant-garde / bureaucrat class of this country believes them to be. In other words, we know both parties are a sham and we understand Argentina issues are mostly related to monetary policies and lack of fiscal responsibility. We don't want the european recipe of identity politics that muds the real, cold hard problems.
@@-pat-9429lmao: "we need better fiscal policies" *votes for anarchocapitalism* yeah alright that makes sense
The first problem with approval voting is that different voters get different numbers of votes. In order to maximize your voting power (if you have no polling results) you must approve of half of the candidates and disapprove of half of the candidates. (If there are polling results, then it's half of the candidates who could win within the margin of error of the polls and the others are irrelevant). If you assume a population of electors who is knowledgeable enough to not throw their voting power away and adheres to this, then approval voting is not Independent from Irrelevant Alternatives. The second problem is the gigantic game of chicken where if a supporter of a candidate A suspects that the candidate A approvers will be a subset (or nearly) of the candidate B approvers (A and B are very similar politically) then there is no way for candidate A to win unless a significant number of A's voters withhold their votes from B. But if this is taken to the natural conclusion then candidate B approvers will be a subset of candidate A voters, and so they will have to withhold their votes from A if they want B to stand a chance. But now it is quite likely that neither A nor B are approved of enough to win, so they both loose. However if candidate A were to drop out, then B could win and vice versa. So in practice approval voting is not Independent of irrelevant alternatives, and in fact appears to be a malicious choice of election on paper, coaxing uninformed voters to waste their voting power, and creating large political incentives for so called "spoiler" candidates to drop out ahead of elections.
I agree that approval voting is not ideal and can lead to a game of chicken! My favorite voting system is STAR voting that kind of solves this problem. Regarding your first point, I don't think approval voting forces you to approve exactly half of the candidates.
@@PolylogCS Consider an approval vote with for example 10 candidates and no knowledge of their relative standings, there are 45 different pairwise elections in play. A winner will be the person who has the more points when compared to anyone else. If you approve of all (or equivalently no) candidates, then you make no difference in any of those pairwise standings. If you approve of 2 (or 8) candidates then you make a difference in 16 of the 45 pairwise standings. And if you approve of 5 of the candidates then you make a difference in 25 of the 45 standings. So a ballot approving of 2 (or 8) of the candidates can only carry 64% of the decisive ability of a ballot approving of 5 of the 10 candidates. As to star voting, anyone not voting with just 1's and 5's is throwing away some of their voting power in the first round (there may be some situations where a small number of 2's and 4's are reasonable in preparation for the second round). And roughly half of the top contenders should be given a 5 and half a 1 for the most effect (as in approval voting) Jim Crow era Georgia is an excellent example of why we shouldn't use runoff elections between two candidates (two round system, TRS) where a divided majority is allowed to unite around their singular common interest of oppressing a unified minority. Ultimately star voting is better, but only marginally better, than either approval voting or TRS individually.
why would a voter want to maximize their voting power tho? You'd be trying to get candidates you like elected, not to get as much influence on the election as possible...
Ultimately in an approval vote there is going to be a candidate with the most votes and the candidate with the second most votes. If you approve of both of them, or disapprove of both of them, then you might as well have not voted at all, your opinion between them doesn't matter. So what you're really trying to do is to maximize your chance of making a difference between any particular pair of candidates.@@decare696
On the first point, voters do not "get different numbers of votes." They each get exactly one vote per candidate, with the choices being "approve" or "not approve." The "game of chicken" exists for every voting system, STAR included.
What an amazing channel! Would love to see more computer science applications ❤️
It's not always a flaw to have lots of strategic voters, since FPTP (Plurality) gives _better_ results with strategic votes than honest votes, in simulations measuring bayesian regret (voter satisfaction). When everyone is voting honestly, everyone spoilers everyone else, and the winner ends up being a cult leader. It's really the spoiler effect that is the problem, and the high amount of strategic voting is saving us from its worst aspects.
Another defense of FPTP: Say you have two entrenched parties, with an evenly divided electorate. The D's always vote for the D candidate, and the R's always vote for the R candidate. But in a particular election cycle, one or both of these nominees are shown to be seriously corrupt, or insane, or incompetent (even though ideologically loyal), and therefore likely to lose support. So one or more "spoiler" candidates decides to enter the race, either a single neutral candidate, or else one each D-ish and R-ish minor candidate. In the election, the minor candidate or candidates naturally draw votes away from the more compromised major candidate, tilting the race in the opposite direction. In this case a spoiler could be said to have improved the outcome by weeding out sick and weak.o I think this is a point in favor of FPTP in favor of alternative methods that eliminate most spoilers but don't adequately handle multicandidate elections. I'm thinking of top-two or RCV here.
@@captsorghum Oh, my post wasn't intended as a defense of FPTP so much as a defense of encouraging widespread strategic voting under FPTP. It doesn't just trivially help oneself to vote strategically, you get better results if everyone does, which is the opposite of what is normally the case. Normally, voting systems work better when everyone is honest. FPTP is unusual in that it works best when everyone is trying to game it. In that sense, it is "resistant" to strategy. Approval vote, score voting, STAR, etc. are all still better than FPTP across the board, with or without strategic voting, and they all produce higher expected voter satisfaction than FPTP.
Thanks for pointing out the alternative perspective, I was looking just for that! IMHO: It's a "feature, not a flaw"!! Life's not black&white, yes/no, 1||0... It's not about winning but choice... so I prefer 75% happy with a suboptimal result, than most UNhappy because 40% were just 'united'...
Yes, this is why RCV is actually worse than FPTP. Under FPTP everyone knows to vote tactically, which works around some of its problems, but RCV is non-monotonic, making it difficult to vote tactically, so it works out worse on average.
@@eyescreamcake Going by equalvote's accuracy chart, (RCV-with-honest-votes) is better than (FPTP-with-tactical-votes) is better than (RCV-with-tactical-votes) is better than (FPTP-with-honest-votes). FPTP does better the more tactical voting there is, while RCV does worse. If everyone is voting tactically, then FPTP is better than RCV. It's tough to say whether RCV makes an improvement or not. It's going to depend on how voters treat the system. That's why I prefer Approval or Score voting.
17:02 Germany also uses FPTP voting. Everyone has two votes, one, FPTP where it determines who from your district goes to the Bundestag and a second vote that determines the % of how the rest of the seats in the Bundestag are filled.
I've been obsessed with this topic recently so nice to see a high quality video about it. One idea I considered was that for any 3 voters that form a cycle, remove all 3 votes.
This makes a lot of sense to me if there are just three candidates, though I guess it will be hard to generalize to more than 3 candidates.
That idea sounds fairly similar to the "Ranked Pairs" Condorcet method. It's phrased differently ("If there's a cycle, resolve the cycle by discarding the matchup that wins by the smallest margin"), but I think it comes to the same thing.
Well done! You researched the topic much more than I did. I am happy to inspire such a nice video. If it doesn't win, it is for sure the flaw of the voting system ;-).
Thanks :)
Good stuff! Gotta love Manim too :)
I live in Australia, which has preferential voting. And yes, i strategically voted last election. I will admit though, that few people in Australia do vote strategically, even though we have compulsory voting. i would estimate that most of the time, when the vote is not closely tied, the vote is a genuine representation of the people. The rare exception is when people choose one option rather than multiple as it allows the nominee to direct their vote to another at their discretion, something the government discourages (primarily because independents use it to their advantage).
On that last point: that has never been a thing in lower house elections and has been abolished in most upper houses (except Victoria).
The missing vote is the informal, it can be used so no candidate gets a quoter so no one can be elected. I have yet to see it in practice but the first ACT election came close.
At least in federal elections, if you only choose one candidate your vote is invalid. I know also in nsw if you choose one candidate your vote just goes to them with no preferences given to any other candidate should your chosen one be eliminated.
"The rare exception is when people choose one option rather than multiple as it allows the nominee to direct their vote to another at their discretion, something the government discourages (primarily because independents use it to their advantage)." that's not how preference deals work, and that you're still spreading that lie is kinda bad. preference deals are explicitly about the useless little pamphlets that political parties hand out near election booths. they would affect literally nothing, except there's a population% that's so useless, that they can't think outside what their preferred party will tell them, on what to vote for, and what order
@@CH-bd6jg Not quite correct, but close - it varies by jurisdiction. :( The overriding principle is a vote is valid as long as the intention is clear. One interesting consequence is it can allow voters to 'null' an election by giving no candidate a quota - if enough people put in blank ballots. At lest in federal elections.
What if you make randomised voting a multi-round elimination voting system? So, the problem with random voting is that we have a small sample, which is generally prone to giving chaotic outcomes. If we make a larger sample, I'd bet we could get more stable results. Current (well, not current, but you get the point) system is »choose one, eliminate the rest« and I wonder if »choose half, eliminate the rest« and »choose one, eliminate the one« would be beneficial. Also, what would you say about squaring and normalising results? It would skew the votes towards the most popular candidate either way. IF you consider the definition of »reasonable system« reasonable. (I'd say we should gather not only the rankings, but some absolute values to, if that makes sense: I'd like to know, if the candidate is the least bad or the best)
To vote tactically you need: 1. To understand the way the system will work 2. To know how everyone else will/has voted 3. What result you want and what result you are willing to accept. I'm not convinced most of any public (electorate) are this well informed insightful or self aware.
The only part of the electorate that needs to figure it out is partisan media outlets. They'll tell the voters what the best strategy is.
Very interesting video! A delightful watch.
Glad you enjoyed it!
I really like the summer of math exposition, to see so many video on interesting topics from aspiring creators is amazing
Thanks! We love SoME too.
Well, the answer is no assuming that the winner is a deterministic function of the votes. But if you allow randomness, then you can use sortition (have everyone vote, then select a random voter, and whoever that voter voted for, wins). Edit: Though, this probably typically isn’t practically a practical idea? Edit 2: oh, you mention at the end Edit 3: personally, the one I prefer to cite wrt strategic voting, is “Gibbard’s 1978 theorem”, showing that the only “straightforward games” (potentially randomized functions from combinations of an action of each player, to an overall result, such that no matter what the preferences a player has over outcomes, their best strategy doesn’t depend at all on how the other players will behave) must be equivalent to a probability mixture between things of the form “outcome X happens (regardless of actions of players)”, “whatever outcome player p indicated, happens”, or “there is a vote between outcomes X any Y, optionally just amongst subset Q of the players, optionally with one of X and Y having an advantage of some number of extra votes” (I left out the “serial dictatorship” variation on “player picks an outcome”)
17:11
@@danielyuan9862 see “edit 2” (which I made before your reply)
People don't vote randomly.
@@aminulhussain2277 the randomness is in the function from ballot combinations to values
@@aminulhussain2277 What do you mean?
Because of how awesome this video is, I present my sacrifice to the algorithm. Let’s hope it uses approval.
-It is worth noting that approval voting was the only cardinal voting system on the displayed list.- Approval voting is the simplest form of range/score voting. A slightly improved version is combined approval voting, which also allows you to vote against any candidates without necessarily voting for all the other candidates. Edit: unpaused and immediately saw "range voting" on the list.
I wouldn't call that "slightly improved". It has the brand-new problem that the lowest possible score is less than the default score, which creates a risk of just randomly electing a total unknown (because everyone known got a negative total score, but the unknowns were just left blank). Should we be randomly electing total unknowns? Well... idk, it has its charm, but a lot of people aren't really cool with the risk there.
@@TzizenorecThat could be remediated by requiring a follow-up election if the winning candidate did not receive a threshold score, e.g. >=10% of the number of ballots. But by definition, in that scenario, all the known candidates were hated by the majority, so it is correct that someone else be selected over them. Even if it is a relatively less known candidate, it still provides continuity without electing a well-known scumbag, which I think most people in the US would prefer over the current system that always elects a scumbag.
@@Tzizenorec I agree, it's not an improvement over "clean" approval voting.
@@captsorghum Why not? Is it not just a psychological crutch to hide the negative sentiments of the populace regarding a candidate? Why is it preferable for a shitty candidate that most people hate to have a positive score?
Strategizing by voting for your second (or 3rd, etc.) favorite isn't a flaw, it's called compromise which isn't a bad thing.
you might enjoy the blog post that describes in which sense strategy voting is a flaw.
@@PolylogCS You could've explain it in the video, instead of talking about it as if it's self evident I don't see how that's a flaw either
the reason we evolved complex language is precisely so we could *avoid* all the shenanigans around strategic voting and stuff. elections have their place, but discussions are more able to reflect people's actual interests, which is why not a single society today runs entirely without discussions at the helm. be they in a parlaiment, war room, or a board of directors for some dictatorship.
Can you analyze star voting as well?
I'm an engineer. I've been exposed to all sorts of math and stats during my education, but this is absolutely foreign to me. Could anyone tell me what this entire class of theorems is called, what field does this fall in, and how can I learn more?
Probably discrete mathematics and game theory
Social Choice Theory
"An election is supposed to be a way of finding common ground, not a strategic game between voters." I would love to hear how you arrived at either of those beliefs.
Yeah I agree, the only purpose is to arrive to an outcome based on predetermined rules IMO
This is what happens when you invent an axiom that you like, and then derive an explanation which works backwards to support your unfounded axiom.
Because an election is intended to decide how things are run, and if common ground is not found, then things are not running probably, if you vote on a restaurant choice with a group of friends, and three people go hungry due to dietary constraints, then that election has been a failure. Why should the same not apply to regular elections?
@@mynameisben123 What purpose should those rules serve?
@@teebob21 Expressing the will of the people is like the whole point of democracy
I found your remark about not being able to tell alone from a simple ranking of movies which the author actually likes and dislikes very insightful. Is there a voting system where you provide your list of preferences and also indicate whether you actually like each candidate (possibly even on a scale)? I feel like these inputs both provide different and useful information and I don’t really see why you couldn’t theoretically account for both.
All voting is strategic, that's the point.
What if you make only 1 round and ask everyone to sort candidates from best to worst. They won't know what strategy to use and you'd just chose from that
Leaves too much room for conspiracies alleging that a system is only chosen post-hoc to benefit certain groups/candidates.
@@terencetsang9518 No it doesn't.
This is called ranked choice voting, and is the best available option.
What happens when theory meets actual people? I would think that Condorcet cycles become rarer as population increases. And I suspect that, for many voting systems, the efficacy of strategic voting likewise decreases as population increases. Of course, these are questions with empirical and historical answers. Does anyone know which electoral systems are probabilistically more reasonable and more stable in the limit?
You can check out the lesswrong post linked in our blog post (link in video description). If I recall correctly, in practice you have condorcet cycles in something like 5% cases or so.
@@PolylogCS Also, the voting system in use could actually incentivize Condorcet cycles in the ballots, even if there weren't any in the voters true preferences.
I see two problems with votings, none of which are mentioned in this video: 1. Sometimes all presented choices are awful, it does not matter what you choose. 2. Most of the voters does not understand topic enough, which makes voting result useless.
What specific criteria define a 'reasonable voting system' as mentioned in this video?
You might enjoy the blog post!
Thank you! I read it just now and I'm a bit closer to an answer. It seems that what composes a "reasonable" voting system will vary depending on the specific context and values of a given society. For proper discourse, here are my four definitions for a "Reasonable" voting system: 1. Fair Representation: Ensuring that the elected officials reflect the diversity of opinions & interests within the electorate. 2. Accountability: Allowing voters to hold elected officials responsible for their actions and decisions. 3. Transparency: Making the voting process clear and understandable to all participants. 4 Efficiency: Conducting elections in a manner that is timely and cost-effective.
I'm going to challenge that definition of "reasonable voting system" Consider a case where Candidate A is the top choice of 51% of the population and the bottom choice of 49%, while candidate B is the second choice of the 51% and the top choice of the 49%. I argue that candidate B is the more correct result.
Not if there are only two candidates. With three candidates, imagine the candidate C is a youger brother of candidate B, generally less popular and more extreme than B. The 51% group will rank A>B>C. The 49% group will rank B>C>A. You argue B should win, reasonable voting system picks A.
@@ariaden I think the separate phrasings of "second choice" and "bottom choice" adequately imply that they are not the same, and that there are thus 3 or more people and either way, it only takes one counterexample to show that the formal definition of "reasonable" given here is not an adequate definition of reasonable. If my example is a counterexample for 3+ candidates, then it is a counterexample period. I'm showing that the formal definition in the video is overly restrictive. I don't get what the point of your second paragraph is. Nothing about C's relationship to B or C's politics changes the fact that the voting base as a whole comparatively tolerates B more than A, while A is a comparatively polarizing candidate who only caters to the slim majority. If there are 3 candidates (which is what I had in mind when writing the original post), then the placement of C you provide is the *only* placement of C compatible with the presupposed placements of A and B, so I don't see what point you could be trying to make about the candidate orders. And your final statement feels very circular -- effectively "You argue that B is a better outcome than the A that the provided definition of reasonable gives, but the provided definition of reasonable dictates A, therefore you're wrong"
i'd actually argue at 6:21 it's entirely reasonable for coconut to be the winner. If banana wins, then half the monkeys love it, and the other half(roughly) hate it. If coconut wins everyone but two monkeys are okay with it.
Yup! You can check out our blog post, where we are discussing this issue.
Consider a deterministic voting system that treats all votes equally and declares B the winner in the case described by klikkolee for N>2 candidates. The same voting system must declare A the winner for N=2 candidates to be reasonable. Thus, the outcome of this voting system depends on the number of candidates in the race. In general, there can be arbitrarily many candidates with (nearly) identical properties (think different politicians with the same agenda). Therefore, I argue that the outcome of a reasonable voting system may not depend on the number of candidates. Then, there is no reasonable voting system that declares B the winner in the case described by klikkolee, and all reasonable voting systems must fulfill the definition given in the video.
I'd love to see a video on "rating system voting" where each voter instead gives each candidate a rating (say, one to five) on how much they want them to win. I don't think it's possible for strategic voting to work on that system, but I'd love to see if it did.
well you’d just vote 5 for candidates you like and 1 for ones you dislike, inbetweens don’t really help you. now it’s multiple choice voting.
That's called Score Voting.
@@goatsfluffy8254 If every voter chooses only the highest and lowest scores, it is mathematically equivalent to Approval voting. In between votes can help if someone would have voted to not approve vs giving a candidate at least some score higher than the lowest.
@@pace1195 thanks grammer man, have a cookie, 🍪
@@goatsfluffy8254 Grammer / Grammar man? I don't get it.
This systems talk only about the situation when only one post is to fill. In parliament are usually multiple persons to elect so. So you can make election districts that have more the one seat. In this case use some proposal systems like they use in Germany and Switzerland. The disadvantage is that result is multi party parliament means coalition are necessary.
Thank you, I learned a lot
Glad to hear it!
Isn't the biggest problem here, the winner take all scenario?
@@Feroce I would propose the following question though. Are people inherently unable to compromise? Or are people's ability to compromise reduced due to the winner take all approach? What you are saying, seems a lot like, "People are unable to compromise so to force action, we have to select one option only." And that seems like a rather extreme stance, for the default method of voting. I feel the default method of voting should be one that includes as many opinions as possible and gives desirable results to as many people as possible. If you have that system in place, then you can come up with another system for like resolving deadlock on some important issue. I don't think we should base the main voting system on the idea that we shouldn't compromise at all though.
@@Lilitha11 Basically yes, look up Duverger's law. The system causes the binary choice. Most people want to vote for a winner and not waste their vote. Also, at some point there must be a winner because there are only a limited number of seats available for candidates to be elected to.
"Democracy is two wolves and a lamb voting on what to have for lunch. Liberty is a well-armed lamb contesting the vote." Benjamin Franklin
So liberty is when the loser rules.
Liberty can contest the vote, but they all still have to live with the final outcome.
"Democracy is the dictatorship of the majority."
I was curious to check out the worst voting systems on the list 16:49, but I was unable to find Fishburn's method of voting, just some drug related stuff. Could you provide some sources?
Not sure, wikipedia links to this stub. en.wikipedia.org/wiki/Landau_set
@@PolylogCSYeah, that's the thing… And »untrapped set« is just plain-text. Thank you for the reply anyway! Really cool video!
note how the avocado is the only fruit in this video that is depicted as sliced-open. This is because it was drawn this way.
Through most of this the flaw in the voting systems seemed obvious to me - once you hit the second round you ignored the second choice of all those who voted for the 'top two'... which means those voting for the eliminated candidates (a minority) are given the deciding vote (over the majority). I immediately thought the second choice of _all_ voters should be included with no candidates being eliminated. (Avocado's win btw: 7a, 6b, 5c). When approval voting was mentioned and discarded as usable with rankings I wondered why? Going through layers considering 1st choices only - if no majority, include 2nd choices as approvals and so on. Allow voters to rank as many candidates as they wish, and allow them to exclude ones they disapprove of and you get quite close to a ranked approval system that reflects voters true opinions. I'm sure a ranked approval system would be susceptible to some tactical voting but at least it would avoid the flip-flop two party scenarios which dominate a lot of single winner voting systems... which is a different problem than the one here... i.e. I better vote for 'a' because I don't want 'b' to win, despite wanting 'c' => nobody votes for 'c' even if it became what a majority wants - what we see in the UK. Of course the USA are even worse as voters only ever have two choices there! "Anyone who is capable of getting themselves made President should on no account be allowed to do the job." (HHGTTG)
Great video! I'm sad you didn't include any Condorcet systems though (especially single methods) . That being said, the monkeys might just get mad for having to learn math to have to understand who won the vote (which is a good reason to be off the island anyways).
But also, the preferences of the monkeys form a condorcet cycle, which means that Condorcet systems are not really that helpful in this concrete scenario, right? (they are guaranteed to work if there is a candidate that beats everybody in head to head election).
@@PolylogCS People act all dramatic about Condorcet cycles like they somehow fundamentally invalidate Condorcet methods, but they're just a special type of tie. Every voting system can have ties. Condorcet cycles occur in like ~1% of real-world elections.
Another great video!
Thanks :)
Can you analyze negative ranked duel voting. I can't figure out if there is incentivized voting. Rank candidates, and we look at the 2 least preffered, and out of those 2, we analyze ALL of the votes again, and then discard the least liked party. Then, we repeat. I'm pretty sure it outcomes as A in this scenario, but I can't analyze larger samples right now. Might check it out on excel later. I think this conforms to Arrow's Theorem, since it involves duel voting until there is only one outcome, but can't tell absolutely sure.
If I'm understanding this correctly, it could be gamed by the banana voters if they voted for coconut as their #1. You'd get a duel between avocado and banana, which avocado wins. Then in the final round, coconut defeats avocado, thus giving the banana voters their 2nd preference instead of their 3rd.
@@brandonm949 Sorry. I think I explained really badly. Using the data at 6:40 The least preferred candidate is Coconut, and next least preferred (when we temporarily ignore coconut votes), is Banana. Then we compare coconut to banana, 6 banana vs 3 coconut. Then we compare the last 2, Avocado to banana, and we have 7 Avocado to 2 Banana. If coconut and banana were reversed, it would still be Coconut vs Banana in the first round. 4 dislike coconut the most, and then ignoring all coconut votes, Banana is in the exact same situation as previously.
@@lightknightgames I was thinking you take the two with the fewest first place votes, but you meant you'd take the two with the most last place votes. Got it. Still, I think my suggestion is the strategic play, because even though it would still be a banana/coconut matchup, coconut would win 5-4 thanks to the banana fans switching their order. Then coconut wins against avocado, 5-4.
Please consider STAR Voting method (strategic voting has a 50% chance to backfire) and is very accurate. Question: does Gibbard-Satterthwaite theorem apply to "Scoring" (as opposed to Rankings) methods as well (like Approval and STAR Voting?)
What would you say is the difference between scoring and ranking?
Ranking is just putting candidates in order - favorite, 2nd favorite, 3rd favorite, etc. Scoring is like a test 0 to 100, or an Amazon rating 1 to 5 stars.
Yes it does. G-S applies to all voting method ever conceived and all voting methods yet to be conceived.
It applies to all systems that satisfies the criteria of the theorem.
I think STAR voting is the best. It takes into account whether you approve of a candidate and by how much. Approval voting on the other hand is too binary.
We are also fans of star voting here :)
Star voting gives _more_ room for strategic voting. Everyone is going to vote a minimum and a maximum score for at least one candidate. Approval voting gives less room, which is probably why it's so good from this video's perspective.
@@danielyuan9862 Score voting (the S of STAR voting) also gives more flexibility for honest voting. As you stated, "Approval voting gives less room..." Score gives more room. The Automatic Runoff (AR of STAR voting) is where the bulk of strategy comes in. To get a vote in the runoff, you must give a more preferred candidate a higher score even if you see both as equally good. That would negate only using maximum scores. For Score voting, if every voter gave every candidate the lowest or the highest score, it is mathematically equivalent to Approval Voting.
Just wanted to address one important clarification: Arrow's impossibility theorem only applies towards voting systems with *strict* preferences. You can, in fact, have a voting system that obeys universal domain, Pareto efficiency, and IIA if you allow for *non-strict* preferences (i.e., A > B = C > D, where a voter is indifferent between B and C), i.e. "avoid" Arrow's impossibility theorem. Suppose you have some ordered ranking of individuals, where this ranking determines the true outcome of a vote. If voter #1 to vote for their preference, then the overall result is that preference. However, if voter #1 decides to be indifferent with all preferences, then voter #2 decides. As you can see, UD, PE, and IIA are all obeyed, while not being a true dictatorship (i.e. there are outcomes where voter #1 does not decide the outcome).
Hey, amazing video! Really interesting stuff. By the way, all the credits at the end seem slavic, I'm guessing Czech? I'm Slovak myeslf so I recognized them pretty quickly
Jo, Češi :)
@@PolylogCS paráda, ešte raz super video
@@PolylogCS Taky mě napadlo, že asi budete Češi, hlavně podle přízvuku
This Social Choice problem is much larger than simply elections, where it is avoided by proportional voting. It concerns ANY situation where a group have to choose an UNIQUE option among more than two: which local city project to implement, where to go eat, who shall pronounce a speech, what type of association should we set up,...? Most people unconsciously trust the decision of a " dictator".
Random is the best mathematically. But imagine neo nazis winning with a 0.5% or something
Maybe make a candidate only eligible if it gathers a minimum % of votes? Like, 5% or 10%? If 5-10% of a population votes for neo nazis, then an election would by far not be my biggest concern 😅
@@besknighter good idea. However, randomness cannot be assured
Awesome job!
This is a crazy good video🤯
great video. my feedback is please put a dark background to the animations. it is really harsh to see white for 15 mins continuously. there's a good reason channels like 3blue1brown are full dark mode
Disagree. Dark mode has its own issues and causes eye strain in a different way (pupil dilation). It’s easier to dim your screen when in light mode to make it more comfortable.
The problem isn't voting, the problem is the need for a singular outcome which is unnecessary. The solution is to elect all people running and give them voting power equivalent to percentage of votes they receive. This fixes all of the errors inherent in current or theoretical voting mechanisms as all voters' preferences will be accurately reflected in the election outcome.
I agree with the sentiment, but even in parliamentary systems you need a prime minister. Also, our setup covers more than politics, it covers things like lists of top100 movies, too.
In Germany, we had an election in a small town to vote for a mayor. Nobody got over 50 percent but the right candidate got most and the center candidate got second most. So it got into the next round. Then all the parties (that were 3th, 4th and so on place) said to their voters to vote for the center candidate because they dont wont the right candidate. Even the really left parties supported the center party even tho they hate each other. Speaking of strategically voting, this was probably the most obvious one I have ever seen. Funny enough, the right candidate still won because most people were really appelled by this strategy and did not like how their party would collaborate in that kind of way.
For anyone interested: It was in Sonneberg and got really much media attention even tho it was a village with like 20k people.
Just like France 2002 election. Chirac rounded 80% of votes against JM Le Pen.
The weird thing about this example is the fact that it exists in a cycle (as you said), while in modern politics we mostly think of politics as a line from one edge to the other (whether or not that's a good thing is a different question) that means you will not have this problem. If we say banana is on one side, coconut is on the other side, and avocado is in the middle. So the monkeys who like banana, like avocado second, and hate coconut, the monkeys who like coconut like avocado second and hate banana. The monkeys who like avocado find themselves in the middle and so they might need to vote strategically, but if you use a parliamentary system, they will have representatives in parliament and thus they'll be fine.
The flaw in any voting system? Voters.
Why?
@@emptywindexbottle97cause voters are irrational
@@ahusainim i don't think they are
I don’t really see strategic voting as a flaw. If your interest is anything but coconuts it makes sense to vote banana over avocado if you know that avocado will not win.
You might enjoy the blog post that discusses this a bit at the end.
Amazing video. I love the fact that I only have to watch for 5 minute.
A very clearly-explained video. I do have one question that I've never seen discussed before. The Gibbard-Satterthwaite and Arrow's theorems only apply to voting systems with finitely many possible outcomes. Are there generalizations of these theorems which apply to voting systems with infinitely many (even continuum-many) outcomes under appropriate conditions? It's not really relevant to most real-world cases (e.g. even though prices could in principle have any real value, in practice they are always multiples of some small increment, say $10⁻⁸). But it's still mathematically interesting. Some people have mentioned cardinal voting, but I assume similar results to Gibbard-Satterthwaite and Arrow holds as long as the number of different valid votes remains finite. But if there are infinitely many possible ways to vote, it's not clear that they do.
Interesting question. How does an infinite outcome election apply when a finite number of officials will be seated after the election? Originally, Arrow's theorem was for ranked voting methods only. Cardinal voting methods can pass Arrow's original requirements for a voting system. However, G-S still applies and ALL voting systems (including the cardinal voting systems) do have some way to vote strategically. Professor Warren Smith showed most cardinal systems are less likely to be affected by strategic voting over most ordinal systems.
@@pace1195 For seating a finite number of people, it's always possible that some finite set of candidates are much preferred over all others, which reduces to the finite case. But for instance, imagine you are trying to set the thermostat for an office. If the thermostat has infinitesimal increments, then that allows for infinitely many possible outcomes. The same is true for a market with infinitely-divisible currency, or similar things.
@@EebstertheGreat Oh, I see. Score voting could be near infinite if you allowed any score from say 0 - 1,000,000. Professor Warren Smith along with colleagues in the consumer retail space showed people prefer somewhere around 9-11 options. Any less and we start adding fractions. Any more and we start using fractions. Say you had a ballot to score candidates from 0 - 100. Most people will use scores of 50 (1/2), 25, 50, 75 (1/4), 20, 40, 60, 80 (1/5), numbers ending in 0 (1/10), or numbers ending in 5 (1/20). Rarely will people score an option at 87, 23, or 41. Your infinite outcomes is limited by the finiteness of human psychology.
@@pace1195 But the interesting question here is a mathematical one. Clearly in practice, if we think of this as a literal voting system, there is no meaningful distinction between the finite and infinite cases, because people can only contemplate finitely many options. But mathematically, using the formal definitions in play, there could well be a difference. I feel like a similar theorem should still apply to sufficiently well-behaved voting systems and preferences, but it would be interesting to work out what those are.
@@EebstertheGreat So, if you could score any candidate mathematically from 0 to infinity theoretically, yet you cannot rank every candidate because there are not infinite candidates; does that mean Score voting is mathematically superior in some way to the ranking methods?
The flaw with voting is that whomever you vote for, they end up making the same garbage. It doesn't matter who you vote for.
That’s only because capitalism has fully corrupted our government that wasn’t defending against it. All the candidates are the same because they are all sponsored by corporations through lobbying (bribes )
There are some very rich people that are very happy people actually believe this.
Voting is the major flaw in democracy, and we should try another system.
Those have been tried.
I agree. We should just do what *I* say.
Listen to me, I know the best
I am currently at the end of definitions. The single transferable vote is good for large groups and many options, because the likeliness of this scenario is too low, is good enough and the best option of the implemented systems for presidency (AKA only one can win), but in small groups that wouldn't be the case, then having a single vote is an error, everyone should vote as many times as they want, no rounds, in this case it would be avocados: 7 votes, bananas: 6 votes, coconuts 5 votes, in this scenario you have the best possible scenario with the least people unhappy, there is no way to make everyone happy, this is also a scenario with only one choice, when the options are many then there are ways to make everyone not unhappy (meaning everyone would prefer that their option has full control, but that wouldn't be reasonable in a multiple option scenario) one such scenario, where to go to dinner, people that want meat and people that want vegetables, best option, not to go to a slaughterhouse or to a full vegan/vegetarian restaurant, go to somewhere you have both options.
Something I've wondered for ages: are point-based voting systems a thing? A ranked-choice voting system, but not with several rounds, because it always bothers me that voting systems do not take negative preference into account. I mean ranked as in: Here are three candidates, someone's top choice receives 3 points, the second choice 2, and the third 1. I quickly calculated it for this example, and avocado would win with 20 points, and the other two would be tied with 17 points each. One obvious drawback is that people would be forced to rank (not that difficult with three candidates, but potentially quite difficult with five, or eight, or seventeen - US-primaries, I'm looking at you!) because every candidate you didn't put in would receive 0 points from your ballot. I haven't calculated this, but possibly it could be counteracted by distributing the remaining points between the remaining candidates as an average. Say there are seven candidates, someone fills in the top two and the bottom two and leaves the rest blank - then twelve points would be left to be distributed, so each of the remaining three candidates would receive four points from that ballot. Apart from this (I would have said "and the personell this requires, but in the digital age, this is the sort of thing a computer could definitely do), is there any good reason why this couldn't work?
Look up the Borda count, that's basically the idea behind it.
Surely it can be simplified down to "Since every vote counts, and every candidate has an equal chance, you can always imagine a tie, and thus one person changing their vote will break the tie"
Add "In a 2 candidate system, they either dont care to change the tie, or wouldnt want to change to the losing side to make it win. In any size bigger, imagine their favourite is not gonna win, and their least favourite is tied with the 2nd favourite. By that one person changing their vote to put the second favourite above the first, they win the tie"