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There are versions of PR that mitigate this issue. Mixed-member PR sacrifices a little bit of precision in the proportionality, but limits the seats assigned to party lists to only some additional ones used to balance out the un-proportionality of the results. Most of the elected body is not from party lists.
You can also carry out a vote where you choose the party for the proportional vote, and then rank the members of that party. And the party assigns the seats they win to the candidates with the widest support.
That doesn’t solve the issue of people liking candidates from multiple parties though.
I've not heard of that one before, but I can see the reasoning behind it. Is there a name for the system that I can look up?
I’d love to help more, but it’s been years since I studied electoral systems. I’m not even sure if there is anyone currently using that system, or if it was just a theoretical election model.