[!NOTE] Moved here from src/lib/score.jl in GlobalBrain.jl.

weight returns a score for determining the top comment for purposes of calculating the informed probability of the post. It is a measure of how much the critical thread that starts with that comment changes the probability of upvoting the post.

ranking_score returns a score for determining how much attention a post should receive – the value of a user considering that particular post.

These are different values. To understand the difference, suppose we have posts A->B->C, P(A|not B, not C) = 10%, P(A|B, not C)=90%, and P(A|B,C) = 15%. So C mostly erases the effect of B on A. The effect of B is p=15% (fully informed), q=10%(uninformed), and r=90% (partially informed).

So B, without C, makes users less informed! If users only consider B and not C, their upvote probability is r=90%, which is further from the informed probability p=15% then where we started at q=10%. This means considering B and not C only increases cognitive dissonance.

Cognitive dissonance before considering B:

relative_entropy(p, q) = relative_entropy(.15, .10) = .0176

Cognitive dissonance after considering B:

relative_entropy(p, r) = relative_entropy(.15, .9) = 2.2366

So for purposes of ranking, B has negative information value, because considering B without considering C actually makes users more uninformed! The information value of B (without C) is

information_gain(p,r,q) = relative_entropy(p, q) - relative_entropy(p, r) = .0176 - 2.2366 = -2.2189.

On the other hand, for purposes of calculating the informed probability of A, the most informed thread may be: A->B->C. The relative entropy for the thread is:

relative_entropy(p, q) = relative_entropy(.15, .1) = .0176

So unless there are threads with higher scores, B might be the start of the most informative thread, even though B as a post has negative information value.

We multiple weight by p_size as a heuristic to deal with duplicates. Suppose we have the same posts A->B->C. Before C is submitted, the informed probability of A will be close to 90%. However, C will reduce the this significantly to 15%.

At this point, a user could submit a near duplicate of B, B’, and before somebody submitted a duplicate of comment C, C’, B’ would become the top comment and the informed probability of A will bounce back up to 90%.

Multiplying weight by p_size is a heuristic that kinds of deals with this. We give more weight to comments that have had more attention, and therefore have been exposed to more scrutiny and there is therefore a greater chance of users responding with a counter argument. So at first, even though B’ has a high relative_entropy, it has a low score because its p_size is low. As its p_size increases, the probability that somebody responds with C’ increases.

If people keep on submitting duplicates, users should start to notice and start downvoting the duplicates, so that they never receive enough attention to become the top comment and people don’t have to respond to them. Code for generating above calculations: p = .15 q = .1 r = .9 GlobalBrain.relative_entropy(p, q) GlobalBrain.relative_entropy(p, r) GlobalBrain.information_gain(p, q, r) GlobalBrain.relative_entropy(p, q) - GlobalBrain.relative_entropy(p, r)