> A beta prior is equivalent to assigning “pretend votes” to each new item. Instead of starting out with 0 upvotes and 0 downvotes, we start out with a upvotes and b downvotes. If we expect that most items are bad, we could start with 3 upvotes and 10 downvotes. After getting u real upvotes, and d real downvotes the posterior distribution is Beta(a+u, b+d).

Fascinating. Does this follow as a straightforward consequence of how the beta distribution is defined? Otherwise, is there a proof that someone could point me toward?

> The popularity of an item has a Beta(a,b) prior

Is there an optimal choice of a, b given, say, a specific utility function?