"The majority reads the newspaper."
Translation:Çoğunluk gazeteyi okur.
In your example, "çoğunluğun" is in genitive case because it is the possessor of the children ("çocuğu" = "çocuk" with a possessive suffix). So the literal translation is something like: "The majority's two children exist."
In this sentence however, the majority don't have/possess newspapers, they're just reading them, so we use nominative case: "çoğunluk" :-)