It could do, but a represents the amount of utility remaining.

Maybe the more natural thing would be to have a be the effective tax rate, and have it be (z/x)^a.

x is the initial income, and I forgot to cancel it. Good point.

Turns out, it's far simpler than I had it as.

Pseudo-flat tax formula:

Assume utility is logarithmic in income, and the goal is to set the experienced tax burden to be constant.

Then, we have the formula that the average tax rate, where $a$ is a parameter controlling the experienced tax burden and $z$ is the break-even point, is as follows:

$x$ is the input income, and $f\left(x\right)$ is the average tax rate.

My assumption here would be, not that everyone I knew was evil, but that I was evil and was being told this as a level-2 means of getting me away from potential victims.

Thanks for the review!

I will start by saying that the odds and evens structure isn't especially original. I've seen similar things discussed in previous posts and comments, mostly as a dimension of a 2x2 grid. As such, your review seems like the classic quote, falsely attributed to Samuel Johnson: "this is both original and good, but the original parts aren't good and the good parts aren't original".

Of course, I disagree with that (if I thought the new levels weren't useful, I wouldn't have come up with them), and will try to explain why the original parts are good, or at least have some value.

To start with, level -1. This is pretty useless. I'm not sure it actually even exists, it's just a natural consequence of the structure. Inasmuch as it does exist, it is incompatible with the existence of an agent. Perhaps the view of a camera would be level -1.

However, I see levels 5 and 6 as real, useful, and importantly not the same as levels 3 and 4.

Specifically, I see levels 5 and 6 as ungrounded. Levels 3 and 4 are not grounded in object-level reality, but are at least grounded in something, namely signalling and tribal affiliation. While "there's a lion across the river" no longer means anything about actual lions, it still means something. It could not be replaced with "there's a foobar across the bazquux".

At the recursive tier, the words "lion" and "river" become irrelevant, and the system of references no longer roots itself in reality. Now this could presumably be considered "mask[ing] the absence of a basic reality", but I'm not sure it even masks it. Reality is just absent. This is Baudrillard's true level 4 of "pure simulacrum".

Part of me wants to renumber the entire system, given that this is allegedly Baudrillard's model. In this case, the political tier would all be level 3 and the recursive tier would all be level 4.

What, Dimir Bastard?

I'm not entirely sure my use of that example as level 5 was accurate, it might actually be levels 3 and 6, because the goal of the slogan is to change people's maps to include a recursive statement rather than merely to express a belief in a recursive statement.

I have found a separate post that firms up the dodgy second paragraph. I would have linked to it, but while there's a time loop involved in the theory, there wasn't enough of one to link to a post written in 2024 in my post in 2022.

In Strategic Time, Open-Source Games Are Loopy

This is very closely related to a discussion in my post on simulacra levels, but I think this is importantly false.

Yes, mathematics refers to nothing outside itself, but that is not to say that things within it cannot prove other things within it. It is a highly abstract field (my simulacra level 5, which is a form of Baudrillard's 4), but that is not why it hasn't been solved.

Take the question "what is 2 + 2". This is made up of pure abstraction (calling this abstraction simply "1s" is not actually correct - "1" is a quantity defined in this abstraction), and does not directly apply to reality, except through a translation layer where the symbol "2" is equated to * *. However, the answer is still 4.

It's a shame I wasn't able to use a time loop to have this exist when I wrote my post on Newcomb's problem being an iterated PD.

This concept is exactly what I needed, and it's explained far better than I did.