[iainmerrick]

I’ve had a similar idea: assign a weight to each party, and multiply each vote by the appropriate weight.

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).

[dane-pgp]

I like this idea as well, and first encountered it at this site:

http://www.dprvoting.org/

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).