Specifically, on a continuous quality scale from 0 to 1, with a prior of a uniform density in this interval with k upvotes and n downvotes, one receives for the posterior distribution the (unnormalized) measure p(x)=xn⋅(1−x)k.
A Gaussian-like prior might be more suited here, though.
Knowing the actual probability distribution and not just the average can be useful if, for some reason, you’re not interested in the comments with the best average, but in those which are least or most controversial.
The beta distribution is a conjugate prior for Bernoulli trials, so if you start with such a prior the posterior is also beta, which greatly simplifies the calculations. It also converges to normal for large alpha and beta, and in any case can be fit into any mean and variance, so it’s a good choice.
Whatever your target function is, you’ll want the item with the greatest posterior mean for this target. To do this generally you’ll need the posterior distribution of p rather than the mean of p itself. But the distribution just describes what you know about p, it doesn’t itself encode properties such as “controversial”.
Specifically, on a continuous quality scale from 0 to 1, with a prior of a uniform density in this interval with k upvotes and n downvotes, one receives for the posterior distribution the (unnormalized) measure p(x)=xn⋅(1−x)k.
A Gaussian-like prior might be more suited here, though.
Knowing the actual probability distribution and not just the average can be useful if, for some reason, you’re not interested in the comments with the best average, but in those which are least or most controversial.
The beta distribution is a conjugate prior for Bernoulli trials, so if you start with such a prior the posterior is also beta, which greatly simplifies the calculations. It also converges to normal for large alpha and beta, and in any case can be fit into any mean and variance, so it’s a good choice.
Whatever your target function is, you’ll want the item with the greatest posterior mean for this target. To do this generally you’ll need the posterior distribution of p rather than the mean of p itself. But the distribution just describes what you know about p, it doesn’t itself encode properties such as “controversial”.