Sorry, didn’t notice that. But then, that’s a mighty complicated formula. And most of the complication comes from insisting on the lower bound of that interval, which was not justified in any way (other than “it works better than the two simple methods above”). Why not use the upper bound instead? Or the center?
When using the center instead of the lower bound, the function simplifies dramatically. More exactly, it reduces to (p+z²/(2n))/(1+z²/n), or after multiplying by n, (pn+z²/2)/(n+z²). Given that pn=upvotes, and n=upvotes+downvotes, that further simplifies to (upvotes+z²/2)/(upvotes+downvotes+z²). Which actually is basically my formula with an adjustable parameter added; my formula is recovered by setting z=sqrt(2).