What if congressmen only got fractions of votes: the fraction of the voters who voted for them in the general election? So if they only got 51% of the vote, they only get 0.51 votes in the house.
So gerrymandering which largely works by dividing up the opposing voters and grouping theirs to have just enough to win or grouping most of the opposing voters into a few districts so they get to keep the rest of the seats, fails. The districts where they grouped the opposition now gets a stronger vote correlating perfectly to the ratio of voters, and the seats where they put just enough voters to win their district have weaker votes, correlating perfectly to the ratio.
It all ends up being balanced based on the true vote counts rather than just needing 51% to get an entire vote in the House. It seems to at the very least weaken gerrymandering.
Does this solve or lessen the problem of gerrymandering?
Alternatively, what about this twist to the concept?
A more dramatic twist: Double the size of the House - every district now elects two seats: The final two opponents with the most votes, and each one gets a vote value based on their percentage of the voters, so they loser with 49% of the vote gets 0.49 votes in the house and the winner with 51% of the vote gets 0.512 votes in the house - this way the losing side gets represented too. I feel this way, while more severe of a change, really truly destroys gerrymandering and doesn't damage the system in any way.