Instant Runoff Normalized Ratings Proportional

Use ratings ballots on any scale, or Borda-convert from rankings.

1. Maintain a 'weight' for each choice, staring at 1.0.
2. Sum up the normalized de-weighted preferences from the voters
   For each vote:
   • multiply each voted preference by the current weight for that choice (deweight)
   • divide these by the square root of their summed squares (normalize)
   • add those results to the per-choice sums
3. The total vote is the sum of the vote summed up across choices. The quota is (total vote)/(seats + 1)
4. For each choice with a sum greater than the quota, that choice's weight becomes ((old weight) * (quota / sum)). This will distribute surplus vote to voters' other choices on the next round.
   If negative ratings are allowed changes may cause a choice's sum to fall, in which case if it was above the quota it may fall below the quota. It's weight should be adjusted upwards to be (weight * (quota/sum)), but it's weight shall be limited to 1.0.)
5. If no choices are greater than quota* then the choice with the lowest sum has its weight set to zero. This disqualifies that choice and voters will have their vote distributed to their other choices on the next round.
6. Repeat steps 2-5 until the right number of candidates have a sum greater than or equal to quota.

I think it's pretty simple, I can fully describe it in a few lines as above. It implicitly achieves many of the things STV does. If a vote was going to a disqualified choice but gets redistributed to a winning choice, everyone's vote for the winning choice equally gets the benefit of redistributed to their other choices.

Alternate name "Continuous Transferrable Vote"?

* In practice, to make up for a modern computer's floating point arithmetic roundoff error, this will be (sum > quota + epsilon) where epsilon will be about (total vote/1000000).