Let’s say you have multi-member constituencies. You hold an election with an outcome that looks roughly like this:
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Candidate #1 received 12,000 votes
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Candidate #2 received 8,000 votes
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Candidate #3 recieved 4,000 votes
All three get elected to the legislature, but Candidate #1’s vote on legislation is worth three times Candidate #3’s vote, and #3’s vote is worth half Candidate #2’s vote.
I know that the British Labour Party used to have bloc voting at conference, where trade union reps’ votes were counted as every member of their union voting, so, e.g., if the train drivers’ union had 100,000 members, their one rep wielded 100,000 votes. That’s not quite what I’m describing above, but it’s close.
Bonus question: what do you think would be the pros and cons of such a system?
It’s similar but it retains the constituency link, which many people feel is important.
You might like single transferrable vote (STV), then. You have districts with several seats in them (preferably ~5), and then do a ranked-choice ballot to select the candidates who will fill those seats. Key advantages over proportional representation are that it maintains the idea of a constituency and that it maintains voting for individual candidates, not just parties.
Downside, of course, is that it’s not as proportional as proportional representation, but it still achieves pretty proportional results. That’s the tradeoff for maintaining constituencies and individual candidates.