MrBeast's $1,000,000 Dilemma

Vsalsa! Kevin here. With a video gift idea for YouTube's most prolific philanthropist, MrBeast. It gives everyone who sees it, including you, a chance to win a million dollars. Here are the rules of my hypothetical contest. MrBeast makes a video and if that video gets just one like, just one thumbs up in the first 24 hours – the person who liked the video wins a million dollars. However, if more than one person presses the Like button, or no one clicks it, no one wins anything. Oh, and another thing: only MrBeast can see if someone liked the video. Everyone plays blind to the results.

You will have no way of knowing if you are the first and only person to like the video or the 10 millionth. Then 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 control the contest in the hopes that it will ruin someone else's chances? Do you just do nothing and give up the chance to win feeling safe knowing you didn't blow it for anyone else? Here is the most important question: Is it possible to win this game? Welcome to Platonia's

dilemma

. A mathematical game devised by cognitive scientist Douglas Hofstadter.

His version was as follows: the fictional oil baron S. N. Platonia sent telegrams to 20 people. If just one person responded to the telegram, he would make a billion dollars. If no one or more than one person responded, no one wins anything. Collusion, or working together in secret, was strictly prohibited, and the participants didn't even know who the other 19 potential respondents were, so they couldn't all get together and agree that only number 15 would respond and the rest would split the money. billion dollars, you know, in 20 different ways. In an attempt to rationally resolve this

dilemma

in your favor, you are faced with 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 would do? And the answers to these questions are... I don't know. I'm not sure. No idea. And who knows?! Because the thing is... The more rational we all are, the more the correct answer keeps changing. Cheating in the game is a good example of this and we'll get to that in a moment, but... To make the most of Platonia's Dilemma, your rationality alone is not enough. No no! We need superrationality.

Hofstadter described superrationality as a state of knowing what to do perfectly rationally, but also knowing that everyone else knows and will behave in exactly the same way. So, you know, they know, you know that they know and you know that they know that you know. That process goes on forever and everyone comes to the exact same conclusion. It's like a rational singularity. Hofstadter decided that the best way forward, the super-rational, was to roll an icosahedral or 20-sided die and commit to only responding to the telegram if the preset number appeared. Like number one. This is why.

The best odds of someone winning this game come when you transcend the hyperloop of rationality. You have to go beyond just 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 super-rationally, they will each roll a 20-sided die once and commit to answering the telegram only if they roll a 1. That leaves about a 37% chance that someone will win. It's possible that no one rolls a 1 and it's also possible that more than one person rolls a 1, which means that your personal odds of winning are not 1 in 20, which would be 5%, no, your personal odds of winning are around Of 2%.

But at least this super-rational system leaves the game up to the math instead of everyone just guessing. But why not cheat? Oh really! Hey. Why don't you lie and answer anyway if there is only a 37% chance of someone winning? 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 it and would cheat too, which would instantly eliminate the higher chances of winning by lying. The rational thing for you is to cheat. But if everyone thinks that, they will also cheat and everyone will lose.

That is why the suprarational thing is not to cheat. Hofstadter even suggested eliminating the temptation to cheat entirely by using a dice-throwing machine that would instantly respond to Platonia if, and only if, she rolled a 1. But this is all just theoretical, right? It's very difficult to do that with this sticky stuff. We don't actually know how people would behave in a Platonia-like situation, right? Mistaken. It actually happened. Hofstadter convinced Scientific American to organize what he called an “Attractive Lottery” in a 1983 Metamagical Themas column. The basic rules were a little different, but the essence was the same: the prize for a lucky lottery winner was $1 million dollars, which would be divided by N, where N was equal to the number of entries mailed. crucial turn.

Instead of each response counting as one entry, you could write any number on the postcard and it would count toward that same number of entries. So a postcard with a 1 counts as one entry, and a postcard with a 1,000,000 counts as a million entries. A greater number of entries gave the player a greater chance of winning, but also reduced the potential prize money. Some people submitted googolplex entries, which is 10 to the power of a googol. Others wrote mathematical expressions that filled the postcard, resulting in incalculably high numbers. Which meant that total entries reached such an unfathomable number that Scientific American couldn't pick a winner... it became impossible.

And even if they could, the winner would have received $1 million divided by an N so high that the prize would have been an infinitesimal fraction of a cent. The bottom line here is that combining unlimited entries with people pursuing their own interest, while recognizing that everyone else would also do the same, quickly put that $1 million dollar prize to dust. Anyone's won. The intrigue of Platonia's dilemma has less to do with how to win the game and more to do with how to think about how to win the game. It's about merging mathematics... and you. How you behave, how other people behave, and how we can use our minds and mathematics to eclipse our imperfect rationality.

So, if MrBeast releases his version of Platonia's Dilemma and you have to like the video... What do you do? What will everyone else do? Are you rational? Are they rational? Are they all super rational? The most likely scenario for you or anyone to win would require all 10 million viewers to act super-rationally, without cheating or trolling, and for each person to roll a die with 10 million sides. I think MrBeast's million is safe in this case. This pocket is not open. So I can't put that in there. And as always, thanks for watching. "I want a Vsauce hat!" It's a thought that popped into my head one day, so I designed this hat for myself.

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