I don't know the exact rules, but it looks like it's a certain quantity of karma points. If so, it's more than 200, and less than 1200.
I got my downvote arrows at 500 karma
when I had karma above about 800 or 900, downvote arrows appeared. This was recently. the exact number changes to allow for "karma inflation".
Karma inflation, eh? How does that come about?
Is it the result of HN becoming more popular? More readers and same size front page means more readers per post, so more votes per post, so an individual accumulates karma more quickly?