In standard FPTP, all the weights are one. To make the results proportional, just assign weights such that the seat counts match the overall vote shares (rounding in favor of the parties with the most votes).
Edit to add: I would guess there’s probably a single solution for any given election, or rather a contiguous set of solutions, but I haven’t verified that.
It probably wouldn’t survive a legal challenge, as some would complain that votes are being counted unequally. Though in this situation I’d argue that the ends (PR) justify the means (unequal weights).
Their system is called "Direct Party and Representative Voting" (DPR Voting) and it has some weird edge cases (like dealing with independent candidates, or parties that win a big vote share but no actual seats), but it definitely seems like an improvement over FPTP, and uses a very easy/quick ballot counting process (unlike IRV or Approval voting, for example).
[1] https://en.m.wikipedia.org/wiki/Mixed-member_proportional_re...
As the name "mixed-member" suggests, the winners from this other source (such as a party list) can be seen as "less valid" and lacking a constituency.
Also I think most MMP systems require a change in the ballot papers and counting process, whereas the system I am proposing would look like a normal First Past The Post election in all cases where district boundaries are drawn "fairly".
I would hope that the majority of voters would see that they are getting better (proportional) representation under this system (even if that representation wouldn't always be as local as it would be for the lucky few districts that aren't gerrymandered into irrelevance in the current system).
In any case, by changing the game theory (removing any incentive to gerrymander districts), my expectation is that in practice no results would get flipped, so no one would experience any bad effect attributed to this system.
It reinforces the idea that parties are more important than anything.
I'm a Democrat mostly, but I might vote for particular Republicans if I feel like they are outstanding individuals with good moral character.
If I cross the isle to vote for John McCain would you take away my McCain vote and give me someone from my party that I didn't want?
My proposal, which I call "merrymandering", involves comparing the number of seats won by each party in a state after an election, with the aggregate percentage of votes won by each party in that election. If there is an imbalance, then the over-represented party has one of their seats assigned to the next-most-over-represented party, and so on until any seat change would result in a more disproportionate result.
The choice of which seat gets reassigned could be chosen based on how close the other party came to winning that seat, to make it deterministic, or a random process could be used, to avoid safe seats.
In practice, what I think would happen is that with this system in place, there would be no advantage to partisan redistricting, so the merrymandering ruleset would never actually be applied, and no seats would flip. Nevertheless, I have some confidence that the system would survive a legal challenge, since it only changes election results to make them strictly more compliant with the "one person one vote" principle.