You can see downvotes on Steemit! At least you can see the most impactful ones. At the bottom of your post, click where it says 65 votes (or however many you have when you get to this). You'll see a + by most of the names, but if you ever see a -, that means it's a downvote. This list is sorted in order of vote influence, so if @berniesanders downvotes you he'll show up at or near the top.

To see this in more detail, go to the steemd.com page for your post and search the page for "vote details". Click that link, and the column that says "pct" will show a -100% for anybody who downvotes you.