Yeah, they can, but it's a sure fire way to end up in some crappy tribunal, or as a bail court magistrate.
Many judges got away with horrible decisions in the Civil Rights cases. I'm sure I could dig up many more examples, too.

But there's a differece of probabities between judges and jurors, refering to the "popular belief, personal motives, and downright ignorance". But empirical proof demosntrate that the jury tend more to make wrong decitions. Judges take wrong decitions too, but at a minor rate. But most importantly, they know the law, the science, the doctrine, the custom of the sentences; on the other hand juries don't know but the half of it in the most optimistic of the cases. So again if we want to apply one of the both i go for science.
Then, I believe the jury would not be a representative sample of the populace.