> It assumes that every book has an equally likely chance of being good.
No it doesn't, it just has to assume that
P(good|obscure) > - P(popular)/(P(popular)-1)
Or, more practically, when P(good|obscure) is just a hair more than P(popular)
Let's say all popular books are good, so
P(good|popular) = 1.
Then we'll say 1/1000 books are popular.
This means P(popular|good) == P(obscure|good) (i.e this is when the number of good books that are popular equals the number of obscure books that are popular.) when P(good|obscure) = 1/999. This true if we assume that P(good|popular) = 1, which is the highest value it can take. If this number is lower than this constraint is reduced, so we can take this as an upper bound of the relationship.
So knowing nothing about the rate of goodness among popular books, we can assume as that there is a huge number of obscure books, and a book is just reasonably more like to be obscure and good, than it is to be popular, the we can confirm that there are more good obscure books.
This constraint is much less demanding than assuming all books are equally likely of being good.
No it doesn't, it just has to assume that
P(good|obscure) > - P(popular)/(P(popular)-1)
Or, more practically, when P(good|obscure) is just a hair more than P(popular)
Let's say all popular books are good, so
P(good|popular) = 1.
Then we'll say 1/1000 books are popular.
This means P(popular|good) == P(obscure|good) (i.e this is when the number of good books that are popular equals the number of obscure books that are popular.) when P(good|obscure) = 1/999. This true if we assume that P(good|popular) = 1, which is the highest value it can take. If this number is lower than this constraint is reduced, so we can take this as an upper bound of the relationship.
So knowing nothing about the rate of goodness among popular books, we can assume as that there is a huge number of obscure books, and a book is just reasonably more like to be obscure and good, than it is to be popular, the we can confirm that there are more good obscure books.
This constraint is much less demanding than assuming all books are equally likely of being good.