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- [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.
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.
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.
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And if you'd like to learn more about voting theory,
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As always, thanks for watching.
And again, vote every time you get the chance.
(slow soft music)