Either no thumbs, or both red and green thumbs.
Put a limit on the number of red thumbs a person can give to a single person. Other forums work on your ratio of green to red thumbs over time.
Thumbs need to be on the post because it is a popularity poll on the topic, not the person.
Thumbs need to be anonymous to avoid vengeful attacks from bad tempered recipients (as can be seen in this thread and every other time a red thumb appears).
Thumbs are pretty good because you can applaud a good post or blow a raspberry at a crappy post without wasting your life writing well considered arguments dealing with the pros and cons of the subject and the sensitivity of the recipient ... only to cop a blast because the poster was pissed at the time and typing drivel.
A red thumb has to be less offensive than a detailed diatribe on the shortcomings of the poster.
You need red and green because when we had only green somebody would post something incredibly bad (racist, sexist, homophobic, SUPophobic) and it would get a bunch of green thumbs. You can't red thumb it to balance it out and we end up looking like red-necks.