Reads paragraphs of common artists separated by commas
Does this really have to be a class?
You have alot of classmethod's making me wonder if this really has to be a class.
Review

Change the datatype of Artists
You can change it to a set making the lookup a O(0)instead of O(n) operation

You never close the file
It is better to use with open(a) as a: context so python will automatically close the file

We can use collections.Counter to count the elements


Code
from collections import Counter

ARTISTS_FILE = 'list_of_artists.txt'

def read_file():
    with open(ARTISTS_FILE, &quot;r&quot;) as f:
        return [
                    set(artist.strip().split(',')) 
                    for artist in f.readlines()
                ]

def make_ordered_list(artist):
    artists = read_file()
    counts = Counter()
    for similar in artists:
        if artist in similar:
            similar.remove(artist)
            counts.update(similar)
    return sorted(counts, key=lambda x: (-counts[x], x))

def main():
    artist = input(&quot;Type the artist: &quot;)
    print(make_ordered_list(artist))

if __name__ == '__main__':
    main()