I don't have a SO account. Do you mean when someone downvotes you, or when you downvote someone else? Or both?

To downvote on SO you need a certain number of points, which you get by doing other activities [like posting or answering questions]. After reaching that threshold, you can choose to downvote a question or response, which costs you one point and costs the other person 2 points. I.e. If you wanted to downvote this post, i would lose 2 karma and you would lose 1.