Trying to explain to the people in the dream why this is better than just taking a straight average caused me to wake up.
Some people think about their dreams and gain insights about their life. I think about my dream and think "well, I would weight the average by counting the judge's vote six or twelve times. And of course it should be the exponential of the average of the logarithms of the proposed sentences, not the other way around".
Add in the rule that the proposed sentences have to be within the statutory range for the crime, and I think it's a pretty reasonable system.