I just worked out: You shouldn't eliminate candidates from the bottom (unless the following fails). Instead, eliminate every candidate who can't win on a preference distribution against any other remaining candidate. Thank you Brisbane and McNamara electorates (in the Australian 2022 election) for pointing this out.
If a seat elects N people then eliminate everybody who can't get a quota against any other set of remaining N candidates. This could be computationally expensive, particularly when combined with my method for determining the quota (https://grampsgrumps.blogspot.com/2020/06/counting-votes-in-optional-preferential.html) when every set will lead to a different quota.
In case anyone misses the point, this is why we sometimes fall back on eliminating the lowest vote: Suppose 3 candidates are left A, B and C. If A is left out B beats C, if B is left out C beats A, if C is left out A beats B. So my proposal doesn't eliminate anyone.
Another idea I had once was that we send the top two candidates to parliament, but when they vote in parliament their vote is weighted by their electoral vote. The main advantage of this is that it doesn't matter if electorates have different sizes, so they can be more uniform. To do this with the above plan: First do it as an electorate determining 2 winners, with quota 1/3. Then those two get all their first preferences plus votes transferred from eliminated candidates.
https://twitter.com/rks987/status/1599626398758768640?s=20&t=YVxigMmt_OkgAgPRG292iQ
ReplyDeleteA partial solution to this is to eliminate all candidates who will lose against any other, and only eliminate the lowest when that doesn't work. So if Lab will lose to either LNP or Teal then it is eliminated, even if not 3rd.