If you can see this from the data, then the votes are not anonymous. They are just not published to other members of the team.

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.