- [Narrator] Thanks to Brilliant
for sponsoring this video. Here in the United States, and in many other places around the world, there are two dominant political parties, and it's not so good. The question is if everyone
hates two-party systems, why are they so common? Well, one big reason is the
voting system most of us use. So in this video, we're
gonna simulate elections to see why plurality is so bad, and we'll also look at
two better voting systems. (slow soft music) Okay, so here are the three voting systems we're gonna look at. First, there's plurality voting, where every voter votes
for exactly one candidate. This is also called first past the post. I'm honestly not quite
sure why it's called that, but apparently it's a
reference to horseracing. Second, we have instant runoff voting, sometimes called ranked choice voting where each voter ranks the candidates from best to worst, and
then those rankings are used to eliminate one candidate at a time. And finally, there's approval voting where each voter can vote for as many candidates as they want. Each of these systems will have a flaw and a voting strategy
related to that flaw, and we'll fill those in as we go. These are all voting systems
that choose one winner. There are also systems that
select multiple winners and those frankly, are way better, really just because they don't try to collapse a bunch of
different preferences into one single outcome. We might talk about multi-winner
systems in a future video, but for now we're going to focus on these single-winner methods since multi winner elections
aren't always an option without restructuring the government, which I guess is hard. But okay, before we
dive into the specifics of these methods, let's
talk about how we're going to model the voters preferences. One way to do it which is pretty common is to put everything on a one-dimensional left to right spectrum. In this model, each
candidate and each voter would sit at some position on this line that represents their views. Now, obviously this is much, much simpler than the real world,
since all possible issues are just collapsed into one line. We can do a little bit better by using a two-dimensional issue space. This is still a lot
simpler than real life, but it at least allows a voter to agree with a candidate on one issue, but disagree on another. And it gives political parties more ways to vary from each other. And just for fun, we can be specific about what these two issues are in this nation of blobs. One issue is whether the
government should focus on promoting the production
of apples or mangoes, and the other is whether blob homes should be these cute, modern-looking homes or these wacky spooky, curvy ones. A candidate positioned right here would be pretty strongly
in favor of mangoes and modern-looking homes, and a candidate down here
would be somewhat in favor of spooky, curvy homes and
slightly in favor of apples. Each time we set up an election scenario, we'll place a few
colorful candidate blobs, and we'll also place 100 gray blobs throughout this issue space as voters. Okay, so now we can look
at the plurality system. This is the one where each voter votes for exactly one candidate
and the candidate with the most votes or the plurality wins. All right, let's run our first election. (slow soft piano music) In this case, orange beats green. Great. This system works just fine when there are only two
candidates or parties, and sure, there'll be some disagreement, but it's hard to think of
anything that could be more fair than just seeing who most voters prefer. But now let's add a
third purple candidate. What do you think will
happen in this case? Well, let's see. With purple in the mix, green ends up winning instead of orange. If you live in a place
with a two party system, you probably saw that coming. This result is a bit weird. Purple joined the race
just to get last place, but they still changed the winner. Orange voters are going
to be mad about that and even most purple voters would have preferred orange over green. This is called the spoiler effect. So these purple voters are presented with a difficult choice. Do they vote for their honest favorite, leaving the choice to others? Or do they strategically
vote for the second choice, hoping to get an outcome they prefer? The argument for voting honestly, is that you need to do this if your favorite party
is going to have a chance at building more support
over time to eventually win. But that'll mean throwing
a lot of elections to your least favorite party over time. It's really hard to ignore the tangible, immediate stakes in any given election. So, it turns out that most people don't even consider third parties, and the two major parties mostly just need to worry about each
other in a zero sum game. Just look how complacent they are. Any-who, now let's see how
these other ones behave. Next we have instant run-off voting, where each voter ranks the candidates from most to least favorite. A runoff system is a series of elections, each one narrowing the list of candidates until a winner is found. And with instant run-off voting, we use the voters rankings
to do the runoff instantly. So, that's where the name comes from. As an example, let's
step through the process using the same set of voters
and candidates we used before. Step one is to see how many
times each candidate was ranked as the first choice. (slow soft music) Notice how these are the same totals as in the honest plurality election. And if this were a plurality
election, we'd be done. But in instant runoff, we eliminate the candidate in last place and then run the election again, this time counting the second
choices of the purple voters. And this process can be
repeated as many times as needed depending how many candidates there are. And now these are the
same final totals we saw in the plurality elections
when the voters were strategic. So, one way to think about it is that instant runoff
voting allows voters to vote honestly, but if
their favorite candidate ends up getting last anyway, they can fall back on being strategic with their second favorite. Pretty nice, honestly. Now you might be thinking
we fixed the spoiler effect, there's no longer a conflict
between honesty and strategy, instant runoff forever. And in some cases that's true, but there are still some situations where something weird happens, once again, forcing some voters to make that difficult choice
between honesty and strategy. Before we go through an
example of that together, try pausing the video to see if you can find
the situation yourself. Okay, so if we arrange
the candidates like this, we're gonna get a weird result. So let's see how that works. First, let's run without purple just to see the baseline results. Okay, Orange beats
green, just like before. But now let's add purple
back in and see what happens. Purple ends up doing well
enough to pass the first round, but by doing so, it knocks
orange out of the race, and in the end, green wins. If the purple voters had
instead put orange first, orange would have made it
through the first round and then beaten green in the final round. And the purple voters like orange better. It boils down to the same situation as the spoiler effect from before. Instant runoff elections are in danger of running into this kind of situation when the three parties
are roughly on a line with one party between two other
reasonably popular parties. So it's called the center
squeeze phenomenon, and here, orange is in
danger of being squeezed out. And with how much we like
to discuss political issues on that one-dimensional
left to right spectrum, this situation honestly doesn't
seem too unlikely to me. Now, you might be wondering
how this would work in real life. Great empirical thinking. Well, we unfortunately don't
have too many examples, but Australia has been
using instant runoff for over a century now. On the question of party choice, it does seem to be a bit
better than the United States, with several parties that managed to have some national representation, but they do still have
two dominant parties, as you might expect, from this
center squeeze phenomenon. So we shouldn't see instant runoff voting as a silver bullet for our democracy, but all this said it is way
better than plurality voting, where you're almost always
incentivized to ignore everyone, but the two most popular parties. All right, the final system
we're gonna talk about is approval voting. Compared to instant runoff voting, approval is pretty simple. Instead of just voting for one candidate, you can vote for as many as you like. For this method, we need to
define an approval range. It'll be this big. If a candidate is within
this distance of a voter, the voter will approve of that candidate, otherwise it won't approve, and it'll be easier to visualize if we draw the circles
around the candidates. So let's do that. Now all the voters within
these candidates circles will vote for that candidate. Okay, with that in place, once again, we'll try it first with
just orange and green. Okay. Again, it turns out that orange wins a head-to-head with green, and now let's add purple
and see how it goes. (lighthearted music) Hey, look, orange still wins. No spoiler effect this time. And not only that, but
vote totals for orange and green didn't change at all. Voters could approve
or disapprove of purple without needing to change
whether they approve of orange or green. And this would be the case no matter how the
candidates were arranged. With approval voting, it turns out that as long as everyone
is voting honestly, a new candidate can only change
the outcome of the election by winning it, which is
a pretty nice feature. But you may have noticed that I said, "As long as everyone is voting honestly." Even though approval voting doesn't have the same
kind of spoiler effect as plurality voting had and
instant runoff sometimes had, there are still some reasons for voters to be strategic about their votes. Again, before we go through it together, pause and try to figure
out what you might do if you're in the position
of some of these voters. (lighthearted music) Okay, there are actually
a few layers of strategy. First, approving all three
candidates has the same effect as not voting at all. So voters that honestly
approve of all three should strategically disapprove of their least favorite candidate, making it more likely that one of their two favorites can win. When we redo the election with the voters following this rule, these are the voters who
approve of all three, so they'll strategically cut
out their least favorite, and purple actually comes out ahead now. This isn't the best since fewer voters genuinely
approve of the outcome, but it's also not the worst since purple and orange
are so near each other and everyone's still got to be honest about their first choice,
but still not the best. And now there's a second layer of strategy that involves noticing
that purple and orange have very similar totals and both are significantly ahead of green. Out of the voters that approve
of both orange and purple, every voter has a favorite of the two. If two of those voters
who like orange more decide to strategically betray purple, they can make orange win. But then, if two other
voters who like purple best, strategically betray orange,
then purple wins again. So now purple and orange
both have lower totals, but green's total is the same. But the orange voters still want to win, so they betray some more, and then team purple betrays, and so on. And green keeps getting
closer and closer to winning. Of course, the purple and orange voters wouldn't purposely hand
the election to green, but since the election
happens all at once, they have to decide ahead of time how much to betray each other. Each side can win by
out-betraying the other side. But if they both go
too far, green will win and they'll both be sad. I mean, green will be happy, but purple and orange will be sad. This is called the chicken dilemma because they're kind of
seeing which one chickens out. And it has a similar structure
to the hawk-dove game from Game Theory, which I
have another video about if you wanna check it out. So if we take this chicken dilemma to its extreme conclusion, everyone just votes for their
favorite and nobody else, which is basically just
the plurality system. But I think it's still worth noting that even in the case with
rampant, strategic voting, no voter ever had a reason not to approve of it's actual favorite. All the strategizing was around the second or third favorites, so
that's still a nice feature. Before we go back to look at
all of the systems together, there are a few more things
to say about approval voting. First, approval voting is a special case of a category of voting
systems called score voting, or range voting systems. Approval voting basically
lets you score each candidate on a range of zero or one, but some systems let you assign a score from a different range,
like from one to 10 or from A to F if you like letter grades. And finally, we should also
talk about real-world examples. Unfortunately, I couldn't
find any examples that were long-lasting
and well-documented, at least for governments. So I'm not sure we can really
say anything too definitive about approval voting without giving it a
little bit more of a try. Okay, so now that we've
looked at all three, what can we say? Well, none of the systems are perfect, but we can say that it's pretty clear that plurality voting is the worst. It's just bad. But as far as the other two go, it's hard to say which is better without more real-world examples. One nice thing about instant runoff is that it's the second most common single winner voting method. So it might have the best chance of actually replacing plurality. On the other hand, I do
tend to like approval because voters can always be honest about their first choice. Whether you're a very aggressive
and greedy with your vote or you're very willing to compromise and vote for your second favorite, you can always, always, always
vote for your first choice, which I find really convincing,
if you can't tell. (laughs) But in the end, I'd happily
take either one of these over plurality voting, because again, plurality voting is bad. But having said that, even
though that system sucks, it's still much better than nothing. So vote every time you get the chance. Thanks to Brilliant for
sponsoring this video. Brilliant has over 60 courses in math, science, and engineering, all
with interactive components to help you learn deeply, and their courses are
now available offline using their Android and iOS apps. So you can learn anywhere, anytime, even when you're in line to vote. I use Brilliant myself and
it's seriously, really good. The first 200 people to sign
up at brilliant.org/primer will get 20% off the annual
premium subscription, and it'll help support Primer. And if you'd like to learn
more about voting theory, Brilliant also has a great introduction to the mathematics of voting. As always, thanks for watching. And again, vote every
time you get the chance. (slow soft music)
This guys videos are fucking rad
This is a great explanation no doubt.
The problem, to be blunt, is that US voters are stupid and/or lazy. While I think this is probably more informative overall, I think the better explained video is this: https://www.youtube.com/watch?v=3Y3jE3B8HsE
It dumbs it down and it makes it even easier to understand. So for individual understanding I think the linked video is better, but for spreading awareness to others, I prefer the one I linked because it's a little easier to understand.
Great video
I still prefer ranked choice now, but only because I’m stumped on what an Approval Vote ballot design might look like: is it really just vote for all the candidates you want and whoever gets the most votes wins?
I would see STAR Voting as the next step after Approval Voting even though Approval Voting might be easier to sell to the masses based on its simplicity and ease of implementation.
Oops. I didn’t see this before posting the same link.
😅