Voting Paradoxes | Exploratorium
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- เผยแพร่เมื่อ 10 พ.ย. 2016
- Voting is a tool that groups use when they need to make a collective decision. But how effective is this tool? In this video we explore some of the ways in which the democratic process can go wrong.
Simply a brilliant presentation
It should be mentioned that cardinal voting does not suffer from Arrow's impossibility theoreom.
Isn't that just majority voting?
@@ADerpyReality No Cardinal voting is, when you use numbers to rate how much you want or don't want a candidate.
@@someone2973 - How about approval voting? its strength is its simplicity.
In cardinal voting, couldn't voters help their favorite candidate by intentionally downgrading their scores for that candidate's most powerful rivals -- i.e., by lying about their feelings? And couldn't this lying encourage lying by other voters, possibly causing the election of a relatively unpopular candidate?
@@AB-ct3kj Yes, and no. There is never tactical reason in this voting system for a voter to dishonestly give a less preferred candidate more points than a more preferred candidate (called "burying"). For example, if you like the Democrat, would accept the Republican (but know they're the competition) and absolutely can't stomach the Libertarian, there is no tactical advantage to giving the Libertarian more points than the Republican. All that does is increase the Libertarian's chances.
The criticism of Range (or Score) voting is that a voter can maximizes their impact on the election by assigning every candidate either the maximum or minimum score, and nothing in between. So although you wouldn't reverse the Republican and the Libertarian you might want to give both a 0, which maximizes how much of a boost your ballot gives to the Democrat vs both. If everyone does that, the method reduces to Approval Voting. So in that sense, yes, there is an incentive to downgrade scores for rivals, but whether they are powerful rivals or not is not really at issue.
Some would argue this basically neuters the point of the system. It's advantage is supposed to be it's additional expressiveness. You can indicate not just the order in which your prefer candidates but how strongly you prefer candidates. However, if the "smart" voters are just going ignore this feature (and perhaps gain an advantage over honest voters by doing so), some argue it would be better just to implement Approval voting, which is simpler for everyone to understand.
It would be great if you could do a version 2 of this video with an evaluation of STAR voting.
What is STAR voting?
@@AB-ct3kj think "Grade Point Average for Candidates" with the added step "if more people prefer the Salutatorian to the Valedictorian, they become Valedictorian instead." If you don't like that extra step (as I don't), the simple "GPA, Valedictorian Wins" is called "Score Voting" or "Range Voting"
Nifty video. Instan Runoff Voting (called "elimination voting" in the video) mitigates spoilers, but does not* eliminate it. Arrow's theorem holds for ranked voting methods, not for cardinal / score-based voting methods. It is* always nice to seem people point out IRV's non-monotonicity.
Really well presented. Haven't seen it as clearly as here
Excellently explained. Though Arrow's Impossibility Theorem only applies to ranked voting (this includes first-past-the-post/plurality voting, as in these one candidate is ranked over the others). Cardinal voting systems such as score voting can avoid all of these problems.
In cardinal voting, couldn't voters help their favorite candidate by intentionally downgrading their scores for that candidate's most powerful rivals -- i.e., by lying about their feelings? And couldn't this lying encourage lying by other voters, possibly causing the election of a relatively unpopular candidate?
@@AB-ct3kj Technically, yes, that's possible. I would point out that Gibbard's Theorem is not limited to ranked methods, and holds that all voting methods suffer from Some form of strategy.
Additionally, you're pointing out the feature of Score: by _lying_ about their preferences, that voter _might_ end up with a worse result (the greater evil defeating both their favorite _and_ the lesser evil that they downgraded), which creates pressure against such downgrades.
So, which would you prefer: a voting system that gets a bad result from honest voting (such as "Elimination Voting" aka IRV, commonly called RCV), or one that gets bad results from dishonest voting (your hypothetical scenario)?
@@Londubh Thank you for your reply. It seems that cardinal voting can produce bad results from both honest voting and dishonest voting.
My original comment, which was about voters' doing better by dishonesty, was based on the fact that honest voting might produce an undesirable result for some voters, thereby encouraging dishonest voting.
Your reply was that sometimes dishonesty can produce a bad result. Both of us seem to be correct.
Based on what you wrote about Gibbard's Theorem, all voting systems are flawed. Right now I cannot say which system is the least flawed. RCV appeals to me intuitively. Cardinal voting does not, because assigning cardinal grades to different candidates seems to me to be far more complex than simply ranking those candidates in order of my preference.
@@AB-ct3kj consider How Gibbard's theorem applies.
Under cardinal voting, honest ballots can result in the Lesser Evil winning.
Under RCV, honest ballots can result in the Greater Evil winning.
Given that the "failure" of cardinal voting is the strategic Objective under RCV, I cannot understand how anyone can think that an indictment of cardinal voting, when the results of RCV are obviously worse...
Arrow's Impossibility Theorum refers to RANKING paradoxes. Approval Voting is immune to all of Arrow's paradoxes.
I finally understand this thank you so much
For the record, Arrow's Theorem only applies to Ranked voting methods. It does not apply to "Cardinal" voting methods, like Score.
What an awesome video !! Good job
You now need to talk about the Majority Judgement created by French searchers mathematicians! It's an excellent video and I hope you'll find further information about what I've talked about! The main scientists who solved this question are Michel Balinsky and Rida Laraki !
Looking forward !
Great Video. I hope you do more on this subject.
Good video as mentioned by others it doesn't apply to some non ranked voting systems.
We can also do like this
if some flavour gets 1st priority it gets 2 points
if it gets 2nd priority it only gets 1 point
and if last priority it gets 0 points
Then add the points
This we can account for all of them rationally
Fortunately, there are voting methods that don't suffer from any of those problems. Arrow's Impossibility Theorem only applies to voting methods using a ranked list.
There are two examples of such voting methods: approval voting and range voting. In fact, these two are used often in many everyday situations, and are two of the best ways to making voting better in general.
This was great, thank you!
What Exploratorium calls Ranked Choice here is not Ranked Choice. Ranked Choice / Instant Runoff Voting is what he describes as “elimination voting.” Second if you watched the monotonicity bit and you were like “well, if chocolate suddenly got better, why didn’t everyone else move it up their rank as well?” Then you might appreciate this writeup on the topic from fairvote.org.
archive.fairvote.org/monotonicity/
Thank you!
Honest understanding as a way of group decision?
It seems like the easy solution to that is a modified version where you eliminate each flavor in turn and see how many 1st place votes each item gets. Doing so would lead to strawberry winning the last example before the coins (12 votes with chocolate eliminated as a choice), and chocolate winning after the coins (after vanilla is eliminated as a choice). The "paradox" in the example given isn't really a paradox --- the result only comes about because the method of elimination was not well thought out.
wonderful!
helped alot thanks :)
Please do a video on STAR voting! It is by far the best system around.
Meh, strategic voting kinda strips it off its biggest advertised benefits, and the optimal strategy for a voter is confusing
@@iwersonsch5131 What strategy? You have to rank choices for the runoff.
@@TheDilla Range voting leads to strategic voting because if you like candidates A, B, and C in that order and don't like D and E, but think candidates B and C are the most likely to win, you will likely make the gap between B and C as large as you can in order to have as much voting power as possible. There was another video outlining what happens if voters do not vote strategically, making it obvious that they would want to.
@@iwersonsch5131 its not range voting???
@@TheDilla You'll have to explain it to me then. Someone cheered for both very similarly under another video
what software do you use for 3d animations??
dear adarsh, I will ask the content maker of this piece and let you know.
thanks for watching!
Does anyone know how weighting votes according to initial ranking would change the frequency of the paradox's being an issue?
Note something about one of these "paradoxes". The one where the money is added to the chocolate choice. Adding that money works as an investigative experiment. Notice the results. Only some people decided that it was now worth changing their choice. Why didn't the others? Because their preference was somehow stronger than even the allure of the added money. So if you're measuring some kind of preference satisfaction magnitude to determine whether the voting system is good or not, perhaps the result (vanilla wins) actually is truly best. Resolving the apparent "paradox". (of course, to make sure this is correct, you'd have to quantify the preference of everyone else too, not just the vanilla voters...and a problem remains any time the math shows that actually vanilla creates a lower average satisfaction magnitude or whatever. But then that's solved by a new method which just maximizes the magnitude of that variable directly.)
The next problem that you run into, and I consider this to be a more significant issue than a voting paradox, is measuring the magnitude of preferences. Well, the issue isn't with measurement so much as trying to compare these cardinal (on a scale) rather than ordinal (in an order) preferences.
Specifically, if I ask two people to rate the pain of a knife stab out of ten, then they will each give me a number. Say, 3 and 5. So, wouldn't it be fair to say that stabbing the second person causes more pain in the world? I don't think it is fair to say that. The first person may simply have a more painful concept of what '10' is on the pain scale, and so rate my stabbing lower than the second person.
Ultimately, this is the core issue with utilitarianism (see 'utility monsters') and political scientists are trying to stay clear of this issue by sticking with ordinal preferences.
Ya, in fact, the utility monster thought experiment brings into question how we should use the cardinal preference measurements even if we did have them! That's pretty foundational to whether or not such a utilitarianism is sensible. For the best thinking I've seen on the subject of scientific morality/decision making, I recommend Richard Carrier:
www.richardcarrier.info/archives/11776
As for the difficulty of measuring magnitude, we'll always have to do the best we can currently. Just because it isn't perfect doesn't mean we're better off without trying. And I think we can currently do fairly well.
Of course, forcing one flavor on everyone is kind of setting yourself up for failure anyways. Wherever possible, more than one subgroup should be able to get their own different preferred flavor.
Obviously it doesn't apply to this scenario but I believe that STV doesn't suffer from this problem. In the final scenario, let's say you had 2 representatives. Chocolate will be one of those representatives regardless of the change later on.
Very goood
Too bad this video doesn’t call the methods by name. For anyone watching, the first method is Plurality (aka First Past The Post.) The next method, looking at pairs of candidates, is Condorcet voting. The third elimination method is Instant Runoff, the method most people not call generically… Ranked Choice Voting.
I think this does a great job of showing why ranked voting in general is not as transparent as it seems. What it needs to do is follow up with a simpler option. STAR Voting!
With STAR Voting you only vote once, scoring the candidates from 0 up to 5 stars. Ballots are counted in two steps.
1st. Add up the scores (just like Score voting) and determine the two highest scoring candidates. Those are your finalists.
2nd. Count the number of voters who preferred each finalist. The finalist preferred by a majority wins.
The 1st round counts the *level of support* for each candidate, and the 2nd round counts the *number of voters* who support each finalist, so it's like the best of both worlds between rating methods and ranking methods.
Would it be possible to make the ranked votes like a percentage of preference? Let's say someone's top choice is chocolate, then vanilla, then strawberry. For the first elimination vote, the 1st choice is worth 1 vote, the 2nd and 3rd choices each get 1/2 and 1/3 of a vote. After this round, the least favorite gets eliminated. If there are more than 3, this process gets repeated until there are only two choices and a majority vote.
Hi Vaness!
That's a great variation on the idea of elimination voting (better known as "instant-runoff voting")! Your system doesn't seem to solve the failure-of-monotonicity problem, but it does bring up an interesting new idea: Instead of indicating the direction of their preferences, what if voters could indicate the degree of their preference between choices?
People have considered many approaches to this idea, but one that we think is super interesting is known as quadratic voting ( en.wikipedia.org/wiki/Quadratic_voting ). In this system, voters get a certain number of voting tokens. You can vote for something more than once, but each additional vote costs more tokens than the last. The first vote costs one token. The second vote costs two tokens. The third vote costs four tokens, and so on, doubling the number of tokens each time you cast a vote. In this system, voters can more efficiently indicate their preferences by concentrating their votes on the issues they care about the most. This system turns out to produce good outcomes and is resistant to many paradoxes. Best of all, the "Arrow Impossibility Theorem" mentioned at the end of the video doesn't apply to quadratic voting. So it's fundamentally more efficient than the options considered above.
Quadratic voting is a new idea, first studied seriously in 2013. We believe that it's important to keep coming up with new ideas about group decision making, and are thrilled to hear about your own thoughts along these lines!
@@exploratorium Wow! Thank you for sharing this. I will look into it and share the info!
@@exploratorium P.S.: Also just wanted to mention your link includes the end parenthesis so it doesn't go to the page on Wikipedia. I mean, I got to the page by removing it myself, but I thought you might like to edit your message so it is easier for others to find the info. I'm very grateful for this!
@@parenthesisss Thanks for flagging this! We updated our message. 👍
The last example perfectly described the 2016 election
How? Please explain.
I used to think that RCV might be a good idea, but after seeing this, I realized that it isn’t. Thanks for making this!
the example he made is very unlikelly. it has only happened a few times
Solution: Map out every possible voting scheme, then tally up the winners of those various schemes, then settle on the one that won the most schemes.
That's what we will face in the Lake Cowichan Mayoral election.
wow
The example used at 4:53 is wrong. If you add everything up, assigning 3 points to the first choice, 2 points to the second choice and 1 point to the third choice, then you have chocolate with 23 points, strawberry with 23 points and vanilla with 26 points. So there clearly is a social preference.
But that's not the voting system he was talking about at that moment. If you do it that way, yes, the cyclic preference doesn't appear. But that's not what he did.
Is this CGP Grey?! It sounds so much like him...
No, it is Exploratorium staff member Paul Dancstep
This guy's voice is deeper and more resonant, but has a lot of vocal fry. CGP Grey is a bit higher and is very nasal, and talks faster too. I find this guy a lot nicer to listen to.
First example: 5 folks have a slight preference for chocolate and 4 detest it and strongly prefer vanilla. Chocolate wins.
i don't agree with the video on the fact that ranking method can lead to cyclical result, because when he looked into what's the majority's favorite flavor pair to pair he neglected the minority's votes, and one crucial principle that should always be respected in every voting system is "Every vote count", when he said that the majority favors chocolate over strawberry, he should have noted that the minority favors strawberry a lot more than chocolate (because vanilla is between them), so while 8 people favor chocolate over trawberry by 1 degree, 4 people favor srawberry over chocolate by 2 degees, in other words chocolate gets 8 points, but strawberry gets 4x2=8, which makes them equal. In the same manner we will find that Vanilla is the winner in this voting system
shit, I thought voting was easy. man I was wrong.
Who came here for CS50 Tideman?
So Bernie Sanders fans like strawberry ice cream, huh?
Damn hipster channel.