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Political Philosophy and the Theory of Martingales

My political philosophy is the theory of martingales.

A martingale is a dynamic stochastic process which— don’t fucking freak out. “Dynamic” simply means changing over time and “stochastic” means having a random component. In other words, dynamic stochastic processes are Life, the Universe, and Everything.

Anyway, a martingale is a generalization of the concept of a random walk, a dynamic stochastic process which has an expected change of zero. That’s all, no biggie. If you can’t handle this go look at some funny cat videos on YouTube and I’ll see you for my next post. Besides, I’m shuffling some ignorable technical asides off to the footnotes.(1) Maybe that will get this published in USA Today; they fucking love the theory of dynamic stochastic processes.

It’s trivially easy to prove that the evolution of a rational person’s beliefs over time is a martingale.(2) Basic idea: If you’re rational you’ll have anticipated all future events that are anticipatable, so the only thing left over to change your beliefs over time is events that weren’t anticipatable. That is, you cannot predict the future evolution of your own beliefs.

The more precise statement of this explicitly mentions events’ probabilities, but it’s the same idea.

Sample path: Rational agent’s belief over time in 2-space.

I briefly discussed some implications that this fact has for politics in one of my first posts, The Mind Cannot Foresee Its Own Advance, and I want to return to this theme. Despite the opening sentence of this post, my entire political philosophy is not really the theory of martingales; I just wanted to open with a strong statement. Like Beethoven’s famous duh duh duh DUH.

Now the human race (SPOILER ALERT) is not rational, but we are learning over time in way that involves paying attention to data. (Some of us are, anyway.) This is true at least for subjects that aren’t too politicized, e.g. astronomy, and for pretty much all subjects in investigations and discussions outside of our formal institutions (which are hotbeds of reality-hating dogmatism).

But note that crucial caveat: for subjects that aren’t too politicized. We need to keep the “politicize everything” crowd disempowered and at the margins of society so they can’t step on the human race’s ability to advance. Things must be kept as loose as possible so we can continually follow the unpredictable martingale of our evolving beliefs toward the truth.

I mentioned astronomy as a subject that’s not too politicized, but of course no subject is safe from the left. Apparently the USSR had a Marxist dogma about whether the universe is finite. I forget which way Marxist dogma landed on that, but the point is, the dogma didn’t come from data; it came from some notion about whether an infinite universe was consistent with dialectical materialism. (LOL, WTF?) And of course there was the Lysenkoist period, which— according to a Soviet biologist in the Gorbachev era— set Soviet biology back by at least a decade.

Obviously neither astronomy nor anything else is safe from the increasingly insane left, a mob that has decided that acronyms are racist and the statement that 2+2 = 4 is western cultural imperialism.

Not that further examples are needed these days, but an example of how this insanity affects hard science: Bill Nye the Science Guy used to have a video explaining how XY and XX determine a person to be male or female. Netflix censored that video. Nye himself, apparently quite the screaming pussy, disavowed reality and embraced “gender fluidity” theory around that time.

These are examples of the human race moving backwards, but it’s not enough to not regress; we need to advance. And no dogma can ever say “We’ve figured it out; no further intellectual innovations are valid,” because the future evolution of our beliefs is unpredictable.

This doesn’t mean you can’t hold the opinion that certain matters are for practical purposes settled. Often the probability of further significant revisions is small enough (based on current information) that that’s a reasonable belief. But it does mean that no person or group should ever be allowed the power to stop other people from investigating the allegedly settled subject.

Einstein sure as shit wasn’t predictable based on Newton. If future discoveries were predictable they wouldn’t be discoveries.

I’ll return again (probably ad nauseam) to a theme of this blog: The things that many of us used to believe about women were largely the exact opposite of the truth. God forbid that we not be allowed to revise our beliefs over time! I won’t get into specifics much— I rehash them enough— but let me mention that some of this body of knowledge about female psychology is relevant for a single man on the dating market and some of it is relevant from a point of view of “social policy.” (A lot of it is relevant for both.) An example: That a lot of women want to play a game of “Let’s you and him fight” between men, including groups of men at a societal level, has existential implications for the survival of our society. That’s something I never could have foreseen when I was 15, or probably when I was 25.

As Eliezer Yudkowsky said in a lucid moment: “Let the winds of evidence blow you about as though you are a leaf.” This is nothing but a poetic formulation of the martingale proposition.

Does all this imply that free speech absolutism should be non-negotiable? Actually, yes, in principle that’s exactly what it implies. But. We have seen in the last 75 years or so that that may not be a long-run stable situation. Total freedom of speech, as well as providing enormous benefits, also provides malign power-seekers unrestricted opportunity to coordinate and plan with each other. This is a problem because (along with 99 other reasons) when they acquire power one of their first moves is to crush all ideas they don’t like. So it’s possible that level-1 censorship might be necessary to prevent level-10,000 censorship. E.g. we might have to exclude communists from universities because if we let them in, they’ll soon take over and exclude everyone but communists.

Or maybe it’s not that simple. There are enormous practical problems with ceding anything to the idea of censorship because that abandons the clearest Schelling point on the issue. Maybe the best formulation of the problem is not “Choose zero censorship,” because that might not be a long-run tenable situation, but “Choose the minimum sustainable level of censorship.” Not to cop out, but: It’s complicated.

In any case…

The human race faces fearsome challenges, as it always has and always will. We must be free to have our beliefs changed unpredictably by new evidence if we are to learn, adapt, and overcome the tests.

Or to put it more tersely: Rational learners’ belief revisions are mean-zero, so kill all the censors!


(1) A martingale is a generalization of the concept of random walk because the only requirement for a variable to be a martingale is that it have an expected (mean) change of zero. A random walk, at least the versions that I’m familiar with, also typically assumes that the probabilities are symmetric about that mean and indeed, frequently assumes that the probabilities are Normal. It also assumes that the probability distribution governing the dynamics is constant over time. A martingale allows the probability distribution to mutate all it wants, provided that one feature, the mean-zero change, always holds. For example, a martingale needn’t have a constant variance.

(2) It’s an immediate consequence of the Law of Iterated Expectations. Here’s another way of seeing it: If you’ve ever studied Statistics, you’ll remember the obvious fact that a rational forecast algorithm has zero-mean forecast errors. So if you’re rational, then the mean revision to your beliefs as you correct your forecast errors will be… See? Not that hard.
By the way, note that if Joe has data that Jill doesn’t, then Joe can predict how Jill’s beliefs will change when she gets the data, but Jill can’t predict that. She has to wait until she gets the data.

(3) Invisible bonus footnote only for those who read the other two! If all this sounds vaguely familiar but you can’t quite place it, it might be because you once read about the Efficient Markets Hypothesis in Finance. Note the EMH assumes rational market participants. Its random walk implication is an example of the point I’m making in this post. I exposited this idea here.

2 replies on “Political Philosophy and the Theory of Martingales”

Nah, rational actors act on what is known. When the Spanish knew that anabaptist ideals lead to peasants revolts they launched the inquisition and saved themselves from the consequences of peasant revolts.

Banning the speech of Commies, radicals, suicide cults, or other overtly destructive talkers is rational. To say ‘we need free speech because maybe those wackjobs could lead us on the next random step towards enlightenment’ is not any more sensible than saying you ought to burn your paycheck on the lotto because someone has to win.

Of course it’s possible the wackjobs ideas are the next random and unforeseeable step in understanding. And it’s possible you would get a good ROI on the lotto. But building policy on that chance is ludicrous.

Because if you’re talking about the unforeseeable you can’t act rationally. A policy of mass censorship itself could be the thing that sparks a new innovation in thought. It’s not likely, but it’s rather more likely than tried and failed ideologies being a net positive to keep around.

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“rational actors act on what is known.”
No kidding. I didn’t argue that no one should do anything ever.

“Banning the speech of Commies, radicals, suicide cults, or other overtly destructive talkers is rational.”
I allowed for this possibility.

I like it when I get people interested enough to comment. But please read all the words.

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