Newcomb’s paradox is a philosophical thought experiment. There is an entity called Omega, who can predict your choices. Omega presents you with two boxes; you may open one or both boxes, and take whatever you find. The first box contains $1k, guaranteed. The second box contains $1M if and only if Omega predicts that you will leave the first box alone. So the dilemma is between “one-boxing” (taking only the $1M), or “two-boxing” (taking both boxes, finding a total of $1k).

When I put it that way, it seems obvious that $1M is more than $1k, so therefore you should open only one box. The two-boxer argument is that Omega has already decided whether the box contains $1M or not. So whatever’s in the second box is a constant, and it’s only rational to take the free $1k. Omega may have chosen to arbitrarily punish players who behave rationally, but what’s done is done, might as well collect the $1k consolation prize.

Do we care about Newcomb’s paradox?

Newcomb’s paradox has received a great deal of discussion from Rationalists, i.e. the community popularized by Eliezer Yudkowsky. That’s how I know about the paradox. But I’m an outsider, and it appears to me like Rationalists stared at this paradox for so long that they went mad. Yudkowsky is a dedicated one-boxer, and has attempted to construct elaborate theories to justify it. Some of these ideas were crucial in the construction of Roko’s Basilisk.

I believe the reason Yudkowsky and others are so obsessed with Newcomb’s paradox, is because they’re transhumanists. They believe the future will contain a super powerful AI. To most people Omega sounds fantastical—how can any entity make perfect predictions about our actions? But to a transhumanist, a super powerful AI could easily step into the role of Omega.  Additionally, we can think about what happens when AI steps into the role of the player. If the AI is deterministic, then of course we can predict what the AI will choose. So Yudkowsky’s interest is ensuring that an AI will choose correctly in this situation.

But for the rest of us folks who aren’t transhumanists, does Newcomb’s paradox make sense? Is this a problem we even need to think about?

I’d like to argue that Newcomb’s paradox is worth more than it appears. Although Omega may seem unrealistic at first, it describes something that happens in the real world all the time.

I’ll bury the lede no longer—I’m talking about lending. If you take out a loan, you can either pay it back or default (i.e. don’t pay it back). Yes there are punishments for defaulting, such as being sued, getting sent to collections, or destroying your credit score. But sometimes the lender just has to write it off as a loss. The primary protection that the lender has against losses is the power of prediction. When you apply for a loan, they predict whether you will pay it back. If they predict you won’t pay it back, then they won’t lend to you in the first place.

Hopefully at first glance, you can see some similarity. There’s a prediction, there’s a choice, there’s an exchange of money. But there are also significant differences. For example, Omega is supposed to be a perfect predictor, but lenders are not perfect predictors. So I’m going to have to do a bit more work to draw the connection.

Omega the bad predictor

Newcomb’s paradox talks about prizes of $1k and $1M. Have you wondered why those two quantities are so far apart? Doesn’t that kind of skew our intuition? Of course I want to go for the $1M! The $1k prize is just a rounding error. If ignoring the $1k means guaranteeing $1M then it’s totally worth it.

On the other hand, if second box contains $1,001, my intuition pushes in the other direction. If you open both boxes, the second box might be empty, but you still found $1,000 in the first box. So at worst, you lost out on $1, basically nothing. But if the second box is *not* empty, then by opening both boxes you have earned $2001, double what you would have gotten by one-boxing.

This is not how philosophers tend to think about the problem. They either advocate one-boxing, or two-boxing. I’ve never heard anyone say, “I’m a one-boxer if the second box contains $1M, but a two-boxer if the second box contains $1,001.” And yet, that’s the answer I feel in my gut intuition. That’s because I intuitively think in terms of probabilities. I think of it in terms of risk and payoff. The risk of two-boxing is that the second box is empty. The potential payoff is that I could end up with the prizes from both boxes.

Newcomb’s paradox stipulates that Omega is a perfect predictor, but clearly my intuition is unconvinced by the stipulation. That’s because my intuition is tuned towards addressing real world problems, not philosophical thought experiments. In real world problems, predictions are not perfect!

So why does Newcomb’s paradox use such disparate quantities of money? I think the intention is to exaggerate the numbers so much, that they overwhelm probabilitic intuitions.

In order for Newcomb’s paradox to be a paradox, the mathematical requirement is that one-boxers receive a higher expected reward compared to the two-boxers. When the potential rewards are $1k and $1M, the requirement is fulfilled even if Omega is a really shitty predictor. For instance, suppose that Omega is correct only 51% of the time, barely better than flipping a coin. Then the one-boxer on average wins $510,000. The two-boxer on average wins $490,000+$1,000. The one-boxer wins more than the two-boxer, and there’s our paradox.

Omega finance

Aside from idea of perfect prediction, there’s another reason why Newcomb’s Paradox sounds so unrealistic. Why would someone just hand out $1M? Omega is not behaving like an economic actor.

So we have to imagine that you’re not getting these prizes for free, but there’s an actual exchange. For instance, there could be a price to enter.

To really emulate an economic exchange, we have to imagine trading two distinct goods. For instance, when you buy bread, it’s a trade that’s mutually advantageous. You get bread, which is more valuable to you than the money because you can eat bread; you can’t eat money. The bread producer gets money, which is more valuable to them than the bread because they already have enough of bread to eat.

So let’s talk about lending. Lending is an exchange of money for money. But it’s still an exchange of two distinct goods because there are two types of money involved. There’s money today, and there’s money tomorrow. A dollar today is more valuable than a dollar tomorrow, for a variety of reasons. The reason why a loan may be mutually beneficial, is that the lender places more value on the dollar tomorrow, while the borrower places more value on the dollar today.

So we’d like to construct a version of Newcomb’s paradox that emulates the exchange of a loan. We can adjust three quantities in the paradox: the price to entry, the money in the first box, and the money in the second box. Each quantity can be denominated in dollars today, dollars tomorrow, or a mix of both.

For illustration purposes, let’s consider a simple loan. The borrower gets $1,000, and is obligated to pay back $1,200 at the end of the year. The borrower may choose to default, but if the lender predicts this, then the lender will choose not to give them the loan in the first place.

The analogous Newcomb’s paradox is as follows: The first box contains $1,200 of dollars next year. The second box contains $1,000 dollars today. The price to entry is $1,200 dollars next year.

So if you’re a two-boxer (i.e. someone who would default on the loan) and Omega knows it, then your prize is cancelled out by the cost of entry (being declined for the loan). If you’re a two-boxer, but Omega fails to predict it, then you “win” $1000 (taking out a loan and defaulting on it). If you’re a one-boxer, then you lose dollars next year in exchange for dollars today (taking out a loan and paying it back). The reason this exchange works is because Omega is a moderately decent predictor, no perfect prediction required.

Obviously there’s a lot more complexity to real world lending. But this should illustrate how the core of Newcomb’s paradox actually happens in the real world, not just in the thought experiments.

Implications

Once we see loans as a sort of Newcomb’s paradox, one thing stands out to me. Following normal, pro-social behavior, people are supposed to pay back their loans! So in practice, the socially preferred answer to Newcomb’s Paradox is one-boxing. Of course, philosophers are not obligated to follow popular intuition, they’re allowed to argue that people are just wrong. But it poses a philosophical challenge (not insurmountable) to two-boxers, if their stance implies defaulting on loans.

Of course, it’s not universally true that everyone should pay back every loan. Some people might be better off declaring bankruptcy. Does that mean one-boxing is preferred most of the time, but two-boxing is preferred other times? That might pose a bit of a challenge (not insurmountable) to people who argue that one-boxing is always correct.

So, this is a Yudkowsky-negative blog, and I don’t like him enough to even pay much attention to what he says. But to his credit, I really don’t think he’s wrong to be so fascinated by Newcomb’s paradox! Though it sounds like a fantastical scenario, it’s quite relevant to a lot of real world situations.  As philosophical thought experiments go, it’s way more useful than the trolley problem!

Newcomb’s paradox isn’t just about super-intelligent robots and prophets. It’s about a more fundamental question, the question of cooperating and building trust. When you choose whether to cooperate with others, you try to predict whether they will cooperate back. Nobody wants to cooperate with a backstabber. The two-boxer is advocating a Machiavellian strategy of choosing whatever’s best for them, even if that means being the backstabber that nobody trusts. The value of Newcomb’s paradox is explaining why (and when) cooperation is correct.