All of JonasMoss's Comments + Replies

The number of elements in $0N$ won't change when removing every other element from it. The cardinality of  $0N$ is countable. And when you remove every other element, it is still countable, and indistinguishable from $0N$.  If you're unconvinced, ask yourself how many elements $0N$ with every other element removed contains. The set is certainly not larger than $N$, so it's at most countable. But it's certainly not finite either. Thus you're dealing with a set of countably many 0s. As there is only one such multiset, ... (read more)

I don't understand what you mean. The upgraded individuals are better off than the non-upgraded individuals, with everything else staying the same, so it is an application of Pareto.

Now, I can understand the intuition that (a) and (b) aren't directly comparable due to identity of individuals. That's what I mean with the caveat "(Unless we add an arbitrary ordering relation on the utilities or some other kind of structure.)"

Pareto: If two worlds (w1 and w2) contain the same people, and w1 is better for an infinite number of them, and at least as good for all of them, then w1 is better than w2.

As far as I can see, the Pareto principle is not just incompatible with the agent-neutrality principle, it's incompatible with set theory itself. (Unless we add an arbitrary ordering relation on the utilities or some other kind of structure.)

Let's take a look at, for instance, $N\cup 0N$ vs $2N\cup 0N$, where $nN$ is the multiset containing $n,2n,3n,\dots$ and $\cup$ ... (read more)

Okay, thanks for the clarification! Let's see if I understand your setup correctly. Suppose we have the probability measures $p_E$ and $p_1$, where $p_E$ is the probability measure of the expert. Moreover, we have an outcome $x\in \{A,B,C\}.$

In your post, you use $p_1(x\mid z)\propto p_E(z\mid x)p_1\left(x\right)$, where $z$ is an unknown outcome known only to the expert. To use Bayes' rule, we must make the assumption that $p_1(z\mid x)=p_E(z\mid x)$. This assumption doesn't sound right to be, but I suppose some strange assumption is necessary for this simple framework. In this model, I agree with your calculation... (read more)

Do you have a link to the research about the effect of a bachelor of education?

I find the beginning of this post somewhat strange, and I'm not sure your post proves what you claim it does. You start out discussing what appears to be a combination of two forecasts, but present it as Bayesian updating. Recall that Bayes theorem says $p(\theta \mid x)=\frac{p(x\mid \theta )p\left(\theta \right)}{p\left(x\right)}$. To use this theorem, you need both an $x$ (your data / evidence), and a $\theta$ (your parameter). Using “posterior$\propto$ prior $\times$ likelihood” (with priors $p_1,p_2,p_3$ and likelihoods $e_1,e_2,e_3$), you're talking as if your expert's likelihood equals&... (read more)

Children became grown-ups 200 years ago too. I don't think we need to teach them anything at all, much less anything in particular.

According to this SSC post, kids can easily catch up in math even if they aren't taught any math at all in the 5 first years of school.

In the Benezet experiment, a school district taught no math at all before 6th grade (around age 10-11). Then in sixth grade, they started teaching math, and by the end of the year, the students were just as good at math as traditionally-educated children with five years of preceding math educati

I found this post interesting, especially the first part, but extremely difficult to understand (yeah, that hard). I believe some of the analogies might be valuable, but it's simply too hard for me to confirm / disconfirm most of them. Here are some (but far from all!) examples:

1. About local optimizers. I didn't understand this section at all! Are you claiming that gradient descent isn't a local optimizer? Or are you claiming that neural networks can implement mesa-optimizers? Or something else?

2. The analogy to Bayesian reasoning feels forced and unrela... (read more)

I disagree. Sometimes your entire payoffs also change when you change your action space (in the informal description of the problem). That is the point of the last example, where precommitment changes the possible payoffs, not only restricts the action space.

Paradoxical decision problems are paradoxical in the colloquial sense (such as Hilbert's hotel or Bertrand's paradox), not the literal sense (such as "this sentence is false"). Paradoxicality is in the eye of the beholder. Some people think Newcomb's problem is paradoxical, some don't. I agree with you and don't find it paradoxical.

Ah! Edited version: "there's no *obvious* distribution $p(a,x)$" (which could have been "natural distribution" or "canonical distribution"). The point is that you need more information than what should be sufficient (the effect of the action) to do evidential decision theory.

Evidential decision theory boggles my mind.

I have some sympathy for causal decision theory, especially when the causal description matches reality. But evidential decision theory is 100% bonkers.

The most common argument against evidential decision theory is that it does not care about the consequence of your action. It cares about correlation (broadly speaking), not causality, and acts as if both were same. This argument is sufficient to thoroughly discredit evidential decision theory, but philosophers keep giving it screen time.

Even if we lived in a ... (read more)

Just like this classic!  https://slatestarcodex.com/2014/03/24/should-you-reverse-any-advice-you-hear/

About that paper.

The p-values relevant for testosterone are on the lower side, with one them 0.049 (which screams p-hacking) and another at 0.02 (also really shitty). A reasonable back-of-the-envelope method to correct for p-hacking and publication bias involves multiplying the p-values with 20 (the reasoning is not super-involved. think about what happens to the truncated normal distribution in the case of complete publication bias); in that case, none of the testosterone-related p-values in said paper are significant. I feel comfortable ignoring it.

It's a game, just a trivial one. Snakes and Ladders is also a game, and its payoff matrix is similar to this one, just with a little bit of randomness involved.

My intuition says that this game not only has maximal alignment, but is the only game (up to equivalence) game with maximal alignment for any set of strategies $s,r$. No matter what player 1 and player 2 does, the world is as good as it could be.

The case can be compared to the $R^2$ when the variance of the dependent variable is 0. How much of the variance in the dependent variable does th... (read more)

This reminds me of the propensity of social scientists to drop inference when studying the entire population, claiming that confidence intervals do not make any sense when we have every single existing data point. But confidence intervals do make sense even then, as the entire observed population isn't equal to the theoretical population. The observed population does not give us exact knowledge about any properties of the data generating mechanism, except in edge cases. 

(Not that confidence intervals are very useful when looking at linear regressions with millions of data points anyway, but make sure to have your justification right.)

I believe the upper right-hand corner of $a$ shouldn't be 1; even if both players are acting in each other's best interest, they are not acting in their own best interest. And alignment is about having both at the same time. The configuration of Prisoner's dilemma makes it impossible to make both players maximally satisfied at the same time, so I believe it cannot have maximal alignment for any strategy. 

Anyhow, your concept of alignment might involve altruism only, which is fair enough. In that case, Vanessa Kosoy has a similar proposal to mi... (read more)