[jpfed]

I'm curious about whether anyone has studied using the harmonic mean (or at least, the reciprocal of the sum of reciprocals) as a way of aggregating utilities. I haven't had time to research this, but the thought repeatedly occurs to me as I have kids that are gifted in a school district that is especially concerned with the gap in achievement between the highest and lowest performers. I can't shake the feeling that what they really should want is a measure that prioritizes helping the lowest performers but does not consider the performance of the highest performers to have literally negative value, and the harmonic mean fits that bill.