Multi-winner elections, including nonpartisan blanket primaries, must represent the voters proportionally rather than giving all seats to the most-organized subgroup or simply picking who has the most first-choice votes. For that, we can used ranked choice voting and, particularly, the Single Transferable Vote (STV).
CGP Grey published an excellent explanation of Single Transferable Vote, as well as a walkthrough of an STV election. Briefly put, voters rank candidates and essentially expend their voting power to elect candidates as they reach a mutual quota.
The Meek-STV method involves highly-complex math to achieve a simple outcome, yet appears somewhat strategy-resistant and highly-fair. Meek-STV in particular can ensure that, given a three-seat election with a 75% majority supporting one set of candidates and a 25% minority supporting another set, one of the minority voters’s candidates will get elected.
With the ballots above—the 75% majority supporting Adam, Bill, and Frank, with the 25% minority preferring Chloe, Debra, and Edna—Meek-STV elects Adam, Bill, and Chloe. No combination of ballots submitted by the 75% majority can get all of Adam, Bill, and Frank elected if any other candidate appears ranked above those candidates on all of the 25% minority ballots.
A Simplified Explanation
While all Single Transferable Vote methods involve complex recursive algebra, Meek-STV uses a more-complex approach—an unfortunate necessity for voting methods which elect fairly and resist manipulation. As with all ranked elections, the election board must publish the full set of ballots and the counting method to ensure the published results are universally verifiable.
We can illustrate Single Transferable Vote with a simpler approach. Assume an election selecting two winners from three candidates who we’ll call Bernie, Warren, and Clinton. The first round may appear below:
Warren receives a full half of the votes, and is elected. The second-ranked choices on Warren’s ballots went 40% to Bernie and 60% to Clinton. Because Warren only needs one-third of all votes cast to win a seat, one-third of her votes are excess.
In this simplified method, we simply count all of Warren’s ballots as one-third of a vote and distribute them to the next candidates. That mean Bernie gets 40% times one-third voting power times the one-half of all votes cast that Warren received, and Clinton gets 60% times one-third times one-half.
Even this simplified method starts chaining algebra, which makes universal verifiability so important and gives us little reason to avoid better implementations like Meek-STV.
After this transfer, no candidate reaches the winning quota. Bernie has the fewest votes, and is eliminated. The full of his original votes—because he didn’t win—plus the one-third voting power of the ballots he received from Warren go to Clinton, who then wins.
As shown above, some Bernie voters didn’t rank Clinton at all. These ballots don’t go to Clinton; they are instead eliminated from the election—they are exhausted ballots.
In practice, multi-winner contests typically involve three or more winners and several candidates. The more winners, the more segments of the population gain their own representative.
In a population with 25% Green Party, 45% Democrat, and 30% Republican voters, a three-winner race with several candidates would very likely elect a Green, a Democrat, and a Republican. Likewise, the variation of values within a single party in a party-dominated district would stand out, electing diverse candidates even when they’re all of the same party. In this way, STV provides greater representation than non-proportional systems.