Algorithm of recommendations

[R1BLH]

In terms of book discovery, my ideal is for people to get recommendations "manually" from friends, rather than algorithmically based on past reading activity.

At one time RuNet had a server Imhonet.ru, which had a very correct, in my opinion, algorithm of recommendations.
Each user has a profile of the scores he gave to the books he read. If the size of the intersection of the set of books read by two (or more) users exceeds a certain value (a constant in the algorithm settings), then the correlation of users' score profiles on this intersection of sets of books read is calculated. If this correlation exceeds a certain value (also a constant in the algorithm settings), then we can assume that the users are close enough, and recommend something that was not included in the intersection of sets of books read, but received a high score.

The simplest option is to consider the intersection of sets of books read among those that the user follows.

The reasons and criteria by which users gave this or that score are not important. The algorithm does not claim to know everything.

For example: let's say that you give scores to books (no matter what the reason):
1 - 5
3 - 4
4 - 5
5 - 3
8 - 5
10 - 5

Let's assume that I gave scores of
1 - 4
2 - 1
3 - 5
5 - 3
6 - 5
7 - 4
8 - 5
9 - 5

Intersection:
1: 5, 4
3: 4, 5
5: 3, 3
8: 5, 5

We can see that the correlation of the profiles is quite good (the scores differ by a maximum of 1 point). So of the many books you've read, the algorithm can offer me (assuming the rating limit is at least 5): a book number 10, which you gave 5 points, but which I haven't read. And for you the books with numbers 6 and 9 on my reading list.
Understandably, bad choices will happen, but as you fill out the profiles, accuracy increases. This was the case on Inhonet, of the recommendations, not once did I come across anything that wasn't interesting to read.