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’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: