The "badging" I refer to in the title is the little enclosed number that shows how much rep you gained since you last opened the drop-down. Nothing to do with bronze/silver/gold "badges".
In the badging on the Achievements drop-down, SE does not show how much rep you lost to downvotes, deleted or undone upvotes, suggested edits to deleted posts, and so on, because those are all essentially indicators that you're dumb and should feel dumb, and it's felt that shoving that in your face is impolite and not worth the possible advantage. I can understand that for the most part, although I'm not entirely sure I fully agree; it is at any rate fairly consistent and has a decent rationale.
There are two exceptions to that consistency, though. The major one is in the cause for rep loss: downvoting someone's answer is in no possible sense an indication of how dumb the voter is or should feel; if anything, more the reverse. And in a sense, being willing to sacrifice a bit of rep to make the 'net a better place is an Achievement and should be signaled accordingly. Let's take a bit more pride in a well-placed downvote!
(The other inconsistency is that if you have received enough upvotes since the last time you opened the dropdown, the badging will show a number that reflects your rep increase minus rep decrease for any cause. So for some reason it's apparently felt that it's OK to let someone know that they've been downvoted if they've also been upvoted recently.)
Therefore, I'd like to request that the -1s from downvoting answers be displayed in little badgings in the top bar, perhaps yellow instead of green or red, or whatever seems appropriate. These should be added together, so that downvoting thrice will get you a little -3 up there, but should not in any way include other sources of negative rep the way the current positive badging does: if you downvote once and get downvoted once, it should show -1, not -3. (There's no need to indirectly show negative rep in two ways instead of one.)
A natural corollary of this is to show rep sacrificed to bounties similarly. This is rare enough for most folks that it's not a big deal, but it would also be nice to have for the same reasons.