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?
You might be interested in mixed member proportional voting. It’s not exactly what you described, but similar in philosophy. It has FPTP elections and then a second round of regional electors which compensate for the disproportionality of of the first round. It doesn’t achieve perfect proportionality and is potentially open to abuse by some methods involving puppet parties, but it mitigates a lot of the issues with FPTP
Seeing as you referenced the UK Labour Party you might already know this as the system used in the Scottish and Welsh assemblies