How Beast Games helped me understand non-causal decision theory

[Estimated time: 5 mins]

SPOILER WARNING for Beast Games, Episode 3 ahead

I confess that my taste in TV isn’t exactly, uh, “high-brow”. While I read books to learn, I watch TV to switch off and decompress. Which is why I was surprised to find myself learning about non-causal decision theory in a recent episode of Beast Games.

What happened during Beast Games?

Beast Games is a reality show in which 1,000 contestants compete for a prize of $5 million plus some smaller prizes along the way.

In Episode 2, the remaining 242 contestants are split into 4 teams. Each team has to select a captain. As a big screen shows a rapidly increasing amount of money, each captain can press a button at any time to claim that money for themselves. But if they do so, they’ll eliminate their entire team.

The reward for betraying your team eventually reaches $1 million and stops there. We find out at the start of Episode 3 that none of the four captains presses the button. This is pretty remarkable.

Many viewers soon commented on how irrational the captains’ decisions were, that the captains haven’t known their teammates that long, that this is a competition in which every contestant but one will eventually get eliminated anyway and that if they were in the captains’ position they would have totally taken the money.

And, like—sure, those are all valid points. But this kind of completely misses the point, which is that the kind of person who would take the $1 million is exactly the kind of person who would not be in a position to make that decision in the first place.

The kind of person that gets to be a captain

There are at least four reasons why the kind of person who makes rational, expected-value (EV) maximising decisions was highly unlikely to ever be in a position to take the $1 million.

First, and most obviously, the teams pick the captain. The teams have every incentive to pick someone who they think is unlikely to betray them. These people have been living together for some time—possibly weeks by now. What this $1 million challenge showed is that people are somewhat competent at assessing what kind of person is likely to betray them. If you would betray your team for $1 million, you’d need to be very good at convincing others that you are not to even have a chance at being a captain.

Second, the earlier rounds had already weeded out many rational EV-maximisers. Beast Games already had several challenges aimed at weeding out any rational EV-maximisers. The very first challenge allowed contestants to instantly win around $20,000 by choosing to eliminate themselves. Another challenge allowed people to win $100,000 by betraying fewer people who they’d spent far less time with.

Third, a rational EV-maximiser would have probably pressed the button before it reached $1 million. The kind of person who would betray their team for $1 million would have probably pressed the button at $500,000. Or even $200,000. Bear in mind that there were four captains. You don’t know when one of the other three captains might press the button at any time. So once the counter hit your “reserve” (the lowest amount for which you’d be willing to betray your team), it’s risky to keep holding out for a larger reward. Pressing the button a second too late would mean you’d get no money, but you’d still get the reputation of being someone who was willing to betray their team members for the rest of the show (and thereafter).

Lastly, rational EV-maximisers may be less likely to apply for the show to begin with. The show started with 1,000 contestants and a chance to win $5 million. After tax, that’s probably around $3 million (and could be less depending on which US state you live in). I’m not sure how much time contestants had to take off work, but one month is a reasonable guess. That gives us an expected value of $3,000, which many rational people wouldn’t consider worth it.

What do we learn from this?

The Beast Games challenge shares many similarities with Newcomb’s paradox, a classic example in non-causal decision theory. Newcomb’s paradox is basically a thought experiment where the rational EV-maximising decision will leave you with less money than if you’re the kind of person who makes non-EV maximising decisions. I’d heard of the paradox before on Rationally Speaking and 80,000 Hours but, ironically, I found Beast Games to be a much clearer and more visceral demonstration of it.

Some people call this Newcomb’s problem, because it’s not really a paradox at all. It merely points out that there is a sense in which our past choices, as well as characteristics like the kind of person we inherently are, end up determining what choices we get to make. Thought experiments often assume we make decisions in a vacuum, but we don’t. The world is full of selection effects, in which our choice set is limited by the past decisions we’ve made and the kind of person we are.

So you might say:

• “If I were a captain, I’d press the button for a $1 million”, or
• “If I were a billionaire, I’d give away 99% of my money to charity” or
• “If I were president, I’d prioritise the good of the country over my electoral chances”.

That’s all well and good, and may even be true. But if it is true, you’re unlikely to find yourself as a captain, billionaire or president in the first place. Ultimately, the kind of person you are and the ways in which you usually make decisions will determine what choices will ever be available to you.

We have less agency than we often think.

Let me know your thoughts in the comments below!

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• Book Summary: Thinking in Systems by Donella Meadows points out how systems often stay the same even when you switch out the players. Systems are interconnected and tend to be resistant to change.
• Book Summary: Algorithms to Live By by Brian Christian and Tom Griffiths
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