Interesting read. Vector Victor sounds like a linear correlation algorithm. I wonder what coefficient they're using under the hood...
Once we've collapsed all pairs down to a Vector Victor, we treat matching Vector Victors as a thumbs up and non-matching as a thumbs down, take the square root of both then take the lower bound of the Wilson interval as our ranking function.
More questions? Shoot!
So say.. "Same in both dimensions" = 0 "Same quality but more rewatchable." = +1 "Same quality but less rewatchable." = -1 "Higher quality but less rewatchable." = +2 "Higher quality but same rewatchability." = +3 "Better in both respects." = +4 etc..
Then you could pass those to a coefficient like Pearson's R.
x = [0, 1, 2, -1, -3, 4, -4] y = [0, 1, 1, 2, -1, -2, 0]
It'd be an interesting experiment to see what results that gives vs. your current algorithm.
The really significant change would be that agreeing in one dimension (yes A is better quality than B, but we disagree on which is more rewatchable) still contributes to your correlation with someone. We're not doing that at the moment, because it felt like pairwise partial agreement would weaken the signal - I wanted _real_ agreement (in both dimensions) to stand out.
While there might be a way to capture that with a linear function, I've favoured solutions that reflect that our ratings are two-dimensional.
Say we start at 0 and user A likes the next move in both directions (+4) and user B only likes it more in one direction and the same in the other (+2) then you're still going to get a positive correlation, just a slightly lower one than if both users liked it in both directions.
R([0, 4, 4], [0, 4, 4]) = 1.0
R([0, 4, 4], [0, 2, 4]) = 0.852
R([0, 4, 4], [0, -4, -4]) = -0.9
If you factor your vector weights by the scale of your quality rating (0 - 10?) then if user A liked the quality film X vs. film Y +6 more points than user B's +1, this would give you a more accurate correlation.
Anyway, food for thought. A very fun problem to be working on!