While I appreciate the goal, I have been put in such situations before and must say I hate such questionaires and ratings. Of course they are not anonymous. And if that is so, do I tell the truth or do I lie? I don't want to lie. But I also don't want to cause trouble for my coworkers because of some misunderstanding.
Admittedly, I don't have a better alternative though.
For example, when downvoting: flip a coin, if it comes up heads, downvote that person. If it comes up tails, only downvote that person if you think they deserve to be downvoted.
Doing it this way, each person can be expected to get roughly 50% of people downvoting them. If the number is enough higher than that, then that person probably deserves the downvotes, but you can't tell who they came from.
You'll see patterns in the upvotes and downvotes. The upvotes might signal "This person helped me a lot." The downvotes can catch interpersonal problems that might otherwise be hidden from you. For instance, someone on your team might be guilty of sexual harassment, but they are clever about hiding it from you. Your only clue will be that, say for instance, all the women keep downvoting that person.