Asking for more than mere "yes versus no" gives one more information, with more nuance.
This is where the future of democracy is, I think. Number-crunching nuanced responses is more difficult than accounting for "yes versus no," but it isn't
that much harder.
If we allow everyone to submit a nuanced vote, we indirectly encourage nuanced thinking. We foster a society of careful thinkers.
I also feel that this style of voting is more in line with how we regularly make choices. Very rarely are choices made out of two, stark, dueling emotions. Think for a second what it was like when you had some input into who would fill a position at your company and both (or more than two) people were well-qualified.
This is (somewhat) flippant, but I've been thinking recently that a reality-TV style presidential election would be better than what we have now. That is, if all the presidential candidates lived together in an apartment for a few weeks and were videotaped ~24/7, were interviewed, issued challenges, etc., the American public might be better informed. Certainly the candidates would be performing for us, but we'd be able to see that, see cracks in their performances, see them under pressure, see them uncertain, see them lose their cool, see them stand up, speak out, be honorable. And then the public could vote by cell phone for each candidate on a confidence scale of 1 to 10.
The idea is ridiculous, but as ridiculous as it would be it'd be so much more transparent than what we have now!