It's a network-wide setting; note that it used to be the case that downvoting questions cost reputation too. For answers, this feature is kept to prevent the so-called Slowest Cheater In The East effect; users would downvote answers just because they competed with theirs. By making downvotes not free, this problem has (mostly) disappeared.
Note that when the answer is deleted (usually via the Low Quality Posts review queue) because it's a really bad answer, you'll get your reputation back. Also, when the answer is edited in a shape not being worthy of a downvote anymore, you can undo your vote and you gain your reputation back.