It is terribly confusing, but it should not. Each year we review the posts that are at least one year old, as such, at the end of 2023, we review all posts from 2022, hence “2022 Review”.
For the voting system’s point cost, that was the function that outputs the point costs (1,10,45) from the vote count (1,4,9), which is basically the same as (1,2,3)?
The first option costs 1, the second costs sum(1..4), and the third costs sum(1..9). So the idea is that every vote costs 1 more vote point, and the cost for n votes is simply cost(n)=∑nk=1k. I don’t know where the formula comes from, however.
My thought process on writing that comment was roughly: “This is quadratic voting, right? Let me check the Wikipedia page. Huh, that page suggests a formula where vote cost scales quadratically with vote number. Maybe I misremembered what quadratic voting is? Let me just comment with what I do remember.”
So the problem was that I’d only glanced at the Wikipedia article, and didn’t realize that the simplified formula there, cost(n)=n2, is either an oversimplification or an outright editing error where they drop a factor of 12. The actual approximation of the quadratic voting formula (as explained in the linked Vitalik essay, which I’d apparently also read years ago but had mostly forgotten since), is n22, as per this:
cost(n)=∑nk=1k=n×(n+1)2≈n22
And @trevor, here’s a quote from that essay on the motivation for this formula:
But what do we actually want? Ultimately, we want a scheme where how much influence you “buy” is proportional to how much you care...
So how do we match these two up? The answer is clever: your n’th unit of influence costs you $n .
It is terribly confusing, but it should not. Each year we review the posts that are at least one year old, as such, at the end of 2023, we review all posts from 2022, hence “2022 Review”.
For the voting system’s point cost, that was the function that outputs the point costs (1,10,45) from the vote count (1,4,9), which is basically the same as (1,2,3)?
The first option costs 1, the second costs sum(1..4), and the third costs sum(1..9). So the idea is that every vote costs 1 more vote point, and the cost for n votes is simply cost(n)=∑nk=1k. I don’t know where the formula comes from, however.
It’s quadratic voting: https://vitalik.eth.limo/general/2019/12/07/quadratic.html
My thought process on writing that comment was roughly: “This is quadratic voting, right? Let me check the Wikipedia page. Huh, that page suggests a formula where vote cost scales quadratically with vote number. Maybe I misremembered what quadratic voting is? Let me just comment with what I do remember.”
So the problem was that I’d only glanced at the Wikipedia article, and didn’t realize that the simplified formula there, cost(n)=n2, is either an oversimplification or an outright editing error where they drop a factor of 12. The actual approximation of the quadratic voting formula (as explained in the linked Vitalik essay, which I’d apparently also read years ago but had mostly forgotten since), is n22, as per this:
cost(n)=∑nk=1k=n×(n+1)2≈n22
And @trevor, here’s a quote from that essay on the motivation for this formula:
That is a surprisingly satisfying answer, thank you.
Ah, sorry for the confusion. Thanks!