In this method, elect the winner set with the least “Total Average Load”. If the Phragmen load for each ballot is the sum of 1/total candidate approval for each approved candidate, the TAL is the weighted average of the Phragmen load with each ballot having weight proportional to its load. In other words, minimize the sum of the squared loads.
Unlike Phragmen, this method behaves as Sainte-Laguë in the party list case. This is because the TAL in the party list case is the sum of (party seats^2)/party votes for each party, divided by total votes. Therefore giving a party an additional seat when they had s seats already increases the TAL by (2s+1)/party votes.
This method measures equality well, but not quality. I don’t consider it a good method but it could be useful for developing a better one.