Newcomb’s Paradox occurs in real life

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?

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Rock Paper Scissors and variants

Rock Paper Scissors is a game where two players simultaneously pick one of the three things in the title. Rock beats Scissors, Scissors beats Paper, Paper beats Rock, and if both players pick the same thing they tie.  Rock Paper Scissors is important in game theory, because it is a toy model that helps understand a much broader class of games.

To understand the correct strategy in Rock Paper Scissors, we must understand the difference between pure strategies and mixed strategies. A pure strategy is deterministic, where a mixed strategy is random. There are only three possible pure strategies: pick Rock, pick Paper, and pick Scissors. There are infinitely many mixed strategies available, for example assigning 50% probability to Rock, 25% to Paper, and 25% to Scissors.

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Macroeconomics with Peter Navarro

Back when I started working in finance in 2020, I remarked to a colleague that I felt pretty ignorant about all this finance stuff. So they suggested a basic online course in macroeconomics. That course: “The Power of Macroeconomics: Economic Principles in the Real World” taught by Dr. Peter Navarro.

In case the name doesn’t ring a bell, Dr. Navarro is currently the senior counselor for trade and manufacturing, in the Trump administration. He is seemingly the only economist in the world who thinks universal tariffs are a good idea. That guy. Even at the time I took the course, Navarro had been the director of the White House National Trade Council during the first Trump administration. But I swear, I didn’t realize who he was until 2022, when he was arrested in relation to the conspiracy to overturn the 2020 election.

No deep dive here–I’m not going back through the course to sift for oddities. This is just storytime, recalling what I can about Dr. Peter Navarro from several years ago.

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It’s the economy

When playing the blame game for the 2024 presidential election, a lot of people point towards social issues. Not to dispute the importance of white identity politics, but polling suggests that the largest concern among voters was the economy, so let’s at least give that issue the time of day.

The funny thing about the economy is that it tends to lag behind economic policy, or just do its own thing based on external factors. During elections, people blame current economic conditions on the current president, even though those economic conditions might have little to do with the president’s actions, or could even be blamed on the previous president. The nightmare scenario is people blaming Biden for the consequences Trump’s bad policies, and then later crediting Trump for the consequences of Biden’s good policies.

This is why it might help to understand what good or bad economic policy looks like. In general, this is hard. But Trump makes it easy, with his very obviously bad economic proposals.

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My economic simulation of spacefaring kittens

Kittens Game is a clicker game that you can play in your browser. It makes a strong first impression, as it tempts you into choices that will kill off your kittens within twelve minutes. But I’m not here to review the game, I’m here to talk about spreadsheets!

Clicker games often support passive gameplay (e.g. leave it running overnight), active gameplay, or any combination of the above. On the very active end, you could try to optimize it, setting up spreadsheets to run calculations. So, I spent a thousand years tinkering with spreadsheets, and I liked it. There’s a story there, a mathematical story.

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The Random Number Game

I invented a game, and it goes like this. We’re going to pick a 20 digit number by taking turns choosing each digit. I choose the first digit, then you choose the second digit, I choose the third and so on. Once we’ve chosen all the digits, we use our number as the seed to a random number generator. The random number generator picks a number between 0 and 1, and if the number is greater than 0.5 then I win; if it’s less than 0.5 then you win.

Obviously this isn’t meant to be a “fun” game, it’s more of an open-ended math problem. What’s the strategy? Is there a strategy? Who wins?

The idea behind the random number generator, is that it’s deterministic, and yet opaque. Given any particular seed, the random number generator will consistently pick the same result—either you win, or I do. But there’s no particular pattern to it. It behaves as if the result were randomly chosen. The only way to predict the game’s outcome is to individually plug in each random seed into the random number generator. However, this might be intractable, as there are 10^20 possible seeds.

This game is deterministic, finite, and perfect information—much like Chess. However, it appears that the only real strategy is brute force, by plugging in seeds into the random number generator.

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Capital in board games

In economic strategy board games, it’s very common to have an arc of growth over the course of the game. You start out with few resources, and then you invest those resources to bolster your income, which then gets reinvested to grow even more, following an exponential trajectory. Central to this growth trajectory is the concept of capital.

In economics, capital is understood as durable goods that are used to increase or enable production. The classic example of capital is factory machines, but capital could also be something abstract, such as an education. People commonly understand capital as simply money, which is true insofar as money is commonly invested into capital. And so it is in economic board games, where you invest fictional money into fictional capital in order to increase fictional production.

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