It would work, but it would make the results less useful to you. Just as useful to me, though, so I wouldn't mind. I just couldn't feed back the results, that's all.
Since you say it would "just as useful to me", then I would assume that means it doesn't have to do with the actual person who submitted it (and correlate to age, or something) because you couldn't do that (easily) without a name attached.
Couldn't you then, in that case, give each anonymous user a number, and say "Anonymous User 1"? On the other hand, given that it might be possible to reverse it to the user who made those upvotes.
Absolutely. I can just call each of you XX_01 up to XX_(however many) and then do my analysis. If it shows something interesting about you and your voting patterns (and I don't know what it might show - this is (informal) research so I don't (yet) know what I'm doing) then I could only tell those who weren't anonymous.
I'll probably try to arrange something so that people can semi-reverse engineer their results. Once I've worked out what I'm doing, and get any results, I'll let people know, and they can decide whether to release their data, or become known, or whatever.
I have thought about this, I haven't got any firm conclusions, my principle is that people's data is theirs to release.
Couldn't you then, in that case, give each anonymous user a number, and say "Anonymous User 1"? On the other hand, given that it might be possible to reverse it to the user who made those upvotes.