They need to weight individual MPs votes by their local approval rating.
Interesting, although the devil is in the details of how approval ratings would be measured.
You might want to consider what other improvements are politically and technically practical. Australia already has a relatively sophisticated vote counting system (instant runoff voting, which is not my favorite, but still pretty good in my opinion). So, perhaps the most universally understandable improvement in responsiveness would come from having more frequent elections. Lowering the stakes in elections and reducing the time that a losing politician needs to wait to run for reelection would encourage them to be slightly more honest in stating their opinions and would give them more accurate feedback about what the public really thinks.
"All the people are so happy now, their heads are caving in. I'm glad they are a snowman with protective rubber skin" -- They Might Be Giants