Vsauce! Kevin here. With a video giveaway idea for YouTube’s most prolific philanthropist,
MrBeast. It gives everyone who watches it, including you, a chance to win one million
dollars.
Here are the rules of my hypothetical contest.
MrBeast makes a video and if that video gets one single like, only one thumbs up in the
first 24 hours -- the person who liked the video wins a million bucks. However, if more
than one person smashes that like button, or nobody clicks it at all, then no one wins
anything.
Oh, and another thing: only MrBeast can see whether anyone has liked the video. Everyone
is playing the game blind to the results. You’ll have no way of knowing whether you’re
the first and only person to like the video or the 10 millionth.
So, what do you do? Do you click like and magically hope you’re the only person who
did? Do you like the video just to troll the contest hoping it’ll ruin someone else’s
chances? Do you just do nothing, and forego the chance of winning feeling safe in the
knowledge that you didn’t ruin it for anyone else? Here’s the biggest question: Is it
even possible to win this game?
Welcome to the Platonia Dilemma.
A mathematical game devised by cognitive scientist Douglas Hofstadter. His version went like
this: 20 people were sent telegrams by fictitious oil baron S. N. Platonia. If only one person
replied to the telegram, that person would win $1 billion dollars. If nobody or more
than one person replied, no one wins anything. Collusion, or secretly working together, was
strictly forbidden, and participants didn’t even know who the other 19 potential respondents
were anyway, So, like, they couldn’t all get together and agree that only number 15
would reply and the rest of them would split the billion dollars, y'know, 20 different
ways.
In an attempt to rationally solve this dilemma in your favor, you face four important questions:
What should I do? What will other people do? What should I do after knowing what other
people will do? What will other people do after knowing that I know what they’d do?
And the answers to these questions are... I don’t know. Not sure. No idea. And who
knows?! Because the thing is... The more rational we all are, the more the right answer keeps
changing. Cheating the game is a good example of this and we’ll get to that in a bit but...
To make the best of the Platonia Dilemma, your rationality alone isn’t enough. No.
No! We need superrationality.
Hofstadter described superrationality as a state of knowing the perfectly rational thing
to do, but also knowing that everyone else knows and will behave that exact same way.
So, you know, they know, you know they know, and you know they know you know. That process
goes on forever, and everyone arrives at the same exact conclusion. It’s like a rational
singularity.
Hofstadter decided the best way forward, the superrational thing to do, was to to roll
a 20-sided or icosahedral die and commit to only replying to the telegram if his pre-chosen
number came up. Like the number one.
Here’s why.
The best odds for someone to win this game occur when you transcend the rationality hyperloop.
You have to move beyond simply trying to figure out, “What should I do?” “What will
other people do?” etc. and create an artificial probability mechanism.
If all 20 people in the game act superrationally, they’ll each roll a 20-sided die once and
commit to replying to the telegram only if they roll a 1. That leaves about a 37% chance
of somebody winning. It is possible for no one to roll a 1 and it’s also possible for
more than one person to roll a 1, so that means your personal odds of winning are not
1 in 20 which would be 5%, no, your odds of winning personally are about 2%. But at least
this superrational system leaves the game up to math instead of everyone just guessing.
Why not cheat, though? Seriously! Uhh. Why don't you just lie and reply anyway if there’s
only a 37% chance that somebody won? That way, you would be the winner if none of the
other 19 players rolled a 1. Genius! But if you know that -- then that means other people
know that and they’d cheat too, which would instantly wipe out the boosted odds of winning
by lying.
The rational thing for you to do is cheat. But if everyone thinks that, they’ll also
cheat and everyone loses. That’s why the superrational thing to do is not cheat.
Hofstadter even suggested removing the cheat temptation entirely by using a die-rolling
machine that instantly replied to Platonia if, and only if, it rolled a 1.
But this is all just theoretical, right. It's really hard to do that with these sticky things.
We don’t actually know how people would behave in a Platonia-like situation, right?
Wrong.
It actually happened. Hofstadter convinced Scientific American to run what he called
a “Luring Lottery” in a 1983 Metamagical Themas column. The basic rules were a little
different, but the essence was the same: the prize for one lucky lottery winner was $1
million bucks, which would be divided by N, where N equaled the number of entries mailed
in.
There was, however, a crucial twist. Instead of each reply counting as one entry, you could
write any number on the postcard and it would count for that many entries. So, a postcard
with a 1 on it counts as one entry, and a postcard with 1,000,000 on it counts as a
million entries. A higher number of entries gave the player a better chance of winning,
but it also reduced the potential prize money.
Some people submitted googolplex entries, which is 10 raised to a googol. Others wrote
mathematical expressions that filled the postcard, resulting in incalculably high numbers. Which
meant the total entries hit such an unfathomable number that Scientific American was unable
to choose a winner… it became impossible. And even if they could’ve, the winner would’ve
received $1 million dollars divided by such a high N that the prize would’ve worked
out to an infinitesimal fraction of one cent.
The takeaway here is that coupling unlimited entries with people pursuing their own self-interest
-- while recognizing that everyone else would do that too -- quickly bulldozed that $1 million
dollar prize into dust. Nobody won.
The intrigue of the Platonia Dilemma is less about how to win the game and more about how
to think about how to win the game. It's about merging math... and you. How you behave, how
other people behave, and how we can use our minds and math to eclipse our imperfect rationality.
So if MrBeast launches his version of the Platonia Dilemma and it’s your turn to like
the video… What do you do? What will everyone else do? Are you rational? Are they rational?
Is everyone superrational?
The most likely scenario for you or anyone to win would require all 10 million viewers
to act superrationally, with no cheating, no trolling, and each person rolling a die
with 10 million sides.
I think MrBeast’s million is safe on this one.
This pocket's not open. So I can't put that in there.
And as always -- thanks for watching.
"I want a Vsauce hat!" is a thought that popped into my brain one day so I designed this hat
for myself. If you want to get one for yourself go to CuriosityBox.com/Store. If you just
want to keep watching Vsauce2 videos, well, I recommend The Missing Dollar Riddle. That's
a good one. And if you aren't subscribed yet to Vsauce2, do that right now if you ever
want to see the sun rise again. That's a little dramatic. The sun doesn't actually rise or
set contingent upon whether or not you are subscribed to Vsauce2. I think.