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So where do people place the bar for being a fan of a genre? The content quality for every genre typically follows a power law distribution. If I only like the top 5% of anime, am I really an anime fan?
There is a list of anime shows, numbered n from 0 to nshows − 1.
The list is organized in descending order of quality q, from 1 to 0.
You like all shows from 0 to nyou − 1. (nDradisPing ≈ nshows × 5 %.)
If ∑0nyou − 1(q) ÷ ∑0nshows − 1(q) > 0.5—that is, if you like more than half of all anime shows on a quality-weighted basis (or if you estimate that you would like them if you were to watch all anime shows and could judge all their quality)—then you are a fan of anime.
(epistemic status: probably only 25 percent a joke)
I definitely like the mathematical approach here, but wonder if it survives contact with subcategories and niches in broader genres. For instance, I would definitely consider myself a fan of videogames but... there's a LOT of different types of videogames and I only like some of them.
Let's suppose as a simplified example that there are 20 categories of video game, Puzzle games, RPGs, Roguelites, MOBAs etc..........
And suppose in our imaginary example that all of them have an equal number of games, and all of the same distribution of games by objective quality. But I only like 9 of the categories. Suppose I like every single game in my 9 favorite categories, but no games in the other 11 categories. Then my score would sum to 0.45 < 0.5.
Is it fair to say that I am not a fan of videogames in general and should only describe myself as a fan of those 9 categories? If it was only one category: suppose I only liked Puzzle Games, then I would agree that I should be called a fan of "puzzle games" and not a fan of video games in general. But if it's 9 different categories across the spectrum that differ wildly from each other then it seems hard to describe my preferences as anything other than a "fan of videogames".
IMO, yes.
I can think of another standard that addresses your complaint, but it's even less workable than the first one.
There is a list of all non-video-game creative works, numbered n from 0 to nworks − 1.
The list is organized in ascending order of quality q, from 0 to 1.
There is also a list of what those non-video-game works would look like if they were video games, numbered n from 0 to nworks − 1.
For each work, the imagined video-game quality q′ presumably will not be the same as the actual non-video-game quality q.
If ∑0nworks − 1(q′) > ∑0nworks − 1(q)—that is, if you think that, on average, the overall quality of a non-video-game creative work would be improved if it were turned into a video game—then you are a fan of video games.
This only measures the difference in video-game fan-ness in comparison to creative works fan-ness. So would give a false positive for someone who hates all creative works but hates video games slightly less. I suppose you could further modify it by hacking the two measures together, perhaps take this and add a minimum amount of video games liked from the previous rating. But that ends up a lot less elegant.
Maybe the issue here is just the strict cutoff threshold. Ie maybe you take the first score and instead of saying someone > 0.5 is a fan and someone less than 0.5 is not a fan, you say that someone's fan-ness is a sliding scale from 0 to 1. Ie, someone who likes all video games ever is more of a fan than someone who only likes half, who is more of a fan than someone who only likes 0.1 (while still keeping the quality weighting so someone with horrible taste who likes the worst games is less of a real fan than someone who likes good ones).
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