Write-In Lottery Voting (WILV) would allow voters to vote for any candidate with the final election winner(s) statistically approaching actual proportional representation as the number of winners increases.
Write-In Only Voting (not Mail-In Voting) and Write-In Asset Voting are discussed in the posts:
Information about Lottery Voting is at:
Overview of WILV:
Voters would fill-in ballots by writing-in a list of candidate(s) up to the number of winners.
Ballot(s) are randomly selected in a lottery equal to the number of winners.
The top-listed, non-winner candidate on each selected ballot would become a winner.
More Detail:
Every citizen is assigned a unique (random ten-digit) identification (ID) number (similar to a Social Security Number).
Each candidate would publish their ID number as part of their campaign.
Voters would be allowed to bring a list of ID numbers with them to the voting booth.
Voters would fill-out their ballots using the ID number (with filled-in bubbles) for each candidate up to the number of winners.
Ballots would be placed in voting machines that would briefly and privately display the names matching the ID number(s) of the candidate(s) that the voter selected.
If the displayed candidates' names are incorrect, then the voter can correct errors to avoid spoiled ballots.
After the conclusion of voting, random precinct(s) are selected from all the respective precincts (weighted by number of votes cast in each) equal to the number of winners.
In each selected precinct, a ballot is randomly selected in a lottery.
The top-listed candidate on each selected ballot is a winner.
If a top-listed candidate is already a winner or refuses the office, then a top-most non-winner candidate on each selected ballot would become a winner.
If a top-listed candidate is already a winner or refuses the office and no non-winner candidate is listed, then a new random ballot from a new random precinct is selected.
This process continues until all of the winners are selected.
WILV may not work well for single-member or small multi-member elections, but could work very well in large multi-member elections.