As a teacher, I think that I have a slightly different perspective on the idea of scoring voice in student writing. On one hand, I think it is vastly important. It shows an awareness of audience, an awareness of self, and a mastery of the craft. (If you can write with voice, you can do anything.)
But making an argument for grading voice scares me. Yes, I enjoy reading voiced papers more than the average, dull, wash, rinse and repeat essay. Yes, I think that voice illuminates any given topic. But there are a few issues that I see. For one thing, voice is a sum of its parts: attitude, tone, diction, syntax, punctuation. Wouldn't it be easier to score those things? Why do we have to call it "voice"? As a field, composition is already considered a soft science--we don't operate on standard definitions, and it seems that we are always squabbling among one another. Scoring voice might be one more nail in the coffin that is the field of composition studies. If we are ever to be taken seriously, we should probably stick to things that can be measured.
How can you say that, my expressivist colleagues might ask. Well, here's the thing. I'm all about voice--I think it's vital to good writing. But can you really teach voice? I can teach diction. I can teach syntax variation. I can teach tone. But I can't teach anyone how to be themselves on the page. If I can't teach it, I don't know that I should be scoring it. If we expected students in a biology or an algebra class to learn something as ethereal as voice, and then be scored on that thing that we couldn't honestly teach, we'd be laughed out of the department.
We can encourage voice, but we cannot truly teach it. So why score it?