[EM] New PR method, IRNRP

[Brian Olson]

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.
           * divide these by the square root of their summed squares
           * add those results to the sum
    3. The total vote is the sum of the choice's vote sums. The quota is 
(total vote)/(seats + 1)
    4. For each choice with a sum greater than the quota, that choice's 
weight becomes its old weight * (quota / sum)
    5. If no choices are greater than quota* then the choice with the 
lowest sum has its weight set to zero.
    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).

Brian Olson
http://bolson.org/