The ratio of (jargon+equations):complexity in this shortform seems very high. Wouldn’t it be substantially easier to write and read to just use terms and examples like “a project might have a stair-step or high-threshold function: unless the project gets enough money, it provides no return on investment”?
Or am I missing something in all the equations (which I must admit I don’t understand)?
I’m basically saying that the logarithmic utility function, which is where we get the idea that doubling one’s income from any starting point raises their happiness by the same amount, is a special case of a broader class of utility functions, in which marginal utility can decline faster or slower than in the logarithmic utility function.
a project might have a stair-step or high-threshold function: unless the project gets enough money, it provides no return on investment
All of the maths here assumes smooth utility returns to money; there are no step functions or threshold effects. Rather, it discusses different possible curvatures.
I wasn’t trying to imply that was the only possibility, I was just highlighting step/threshold functions as an example of how the utility of money is not always logarithmic. In short, I just think that if the goal of the post is to dispute that simplification, it doesn’t need to be so jargon/equation heavy, and if one of the goals of the post is to also discuss different possible curvatures, it would probably help to draw rough a diagram that can be more-easily understood.
My fan fiction about what is going on in this thread:
A good guess is that “log utility” is being used by EAs for historical reasons (e.g. GiveWell’s work) and is influenced by economics, where log is used a lot because it is extremely convenient. Economists don’t literally believe people have log utility in income, it just makes equations work to show certain ideas.
It’s possible that log utility actually is a really good approximation of welfare and income.
But sometimes ideas or notions get codified/canonized inappropriately and accidentally, and math can cause this.
With the context above, my read is that evelynciara is trying to show that income might be even more important to poor people than believed.
She’s doing this in a sophisticated and agreeable way, by slightly extending the math.
So her equations aren’t a distraction or unnecessary mathematical, it’s exactly the opposite, she’s protecting against math’s undue influence.
I was hoping for a more dramatic and artistic interpretation of this thread, but I’ll accept what’s been given. In the end, I think there are three main audiences to this short form:
People like me who read the first sentence, think “I agree,” and then are baffled by the rest of the post.
People who read the first sentence, are confused (or think they disagree), then are baffled by the rest of the post.
People who read the first sentence, think “I agree,” are not baffled by the rest of the post and say “Yep, that’s a valid way of framing it.”
In contrast, I don’t think there is a large group of people in category 4. Read the first sentence, think “I disagree,” then understand the rest of the post.
But do correct me if I’m wrong!
Well, I don’t agree with this perspective and its premise. I guess my view is that it doesn’t seem compatible for what I perceive as the informal, personal character of shortform (like, “live and let live”) which is specifically designed to have different norms than posts.
I won’t continue this thread because it feels like I’m supplanting or speaking for the OP.
The ratio of (jargon+equations):complexity in this shortform seems very high. Wouldn’t it be substantially easier to write and read to just use terms and examples like “a project might have a stair-step or high-threshold function: unless the project gets enough money, it provides no return on investment”?
Or am I missing something in all the equations (which I must admit I don’t understand)?
I’m basically saying that the logarithmic utility function, which is where we get the idea that doubling one’s income from any starting point raises their happiness by the same amount, is a special case of a broader class of utility functions, in which marginal utility can decline faster or slower than in the logarithmic utility function.
All of the maths here assumes smooth utility returns to money; there are no step functions or threshold effects. Rather, it discusses different possible curvatures.
I wasn’t trying to imply that was the only possibility, I was just highlighting step/threshold functions as an example of how the utility of money is not always logarithmic. In short, I just think that if the goal of the post is to dispute that simplification, it doesn’t need to be so jargon/equation heavy, and if one of the goals of the post is to also discuss different possible curvatures, it would probably help to draw rough a diagram that can be more-easily understood.
My fan fiction about what is going on in this thread:
A good guess is that “log utility” is being used by EAs for historical reasons (e.g. GiveWell’s work) and is influenced by economics, where log is used a lot because it is extremely convenient. Economists don’t literally believe people have log utility in income, it just makes equations work to show certain ideas.
It’s possible that log utility actually is a really good approximation of welfare and income.
But sometimes ideas or notions get codified/canonized inappropriately and accidentally, and math can cause this.
With the context above, my read is that evelynciara is trying to show that income might be even more important to poor people than believed.
She’s doing this in a sophisticated and agreeable way, by slightly extending the math.
So her equations aren’t a distraction or unnecessary mathematical, it’s exactly the opposite, she’s protecting against math’s undue influence.
I was hoping for a more dramatic and artistic interpretation of this thread, but I’ll accept what’s been given. In the end, I think there are three main audiences to this short form:
People like me who read the first sentence, think “I agree,” and then are baffled by the rest of the post.
People who read the first sentence, are confused (or think they disagree), then are baffled by the rest of the post.
People who read the first sentence, think “I agree,” are not baffled by the rest of the post and say “Yep, that’s a valid way of framing it.”
In contrast, I don’t think there is a large group of people in category 4. Read the first sentence, think “I disagree,” then understand the rest of the post. But do correct me if I’m wrong!
Well, I don’t agree with this perspective and its premise. I guess my view is that it doesn’t seem compatible for what I perceive as the informal, personal character of shortform (like, “live and let live”) which is specifically designed to have different norms than posts.
I won’t continue this thread because it feels like I’m supplanting or speaking for the OP.