[EM] Fixing Range Voting

[Brian Olson]

With all the talk about Range Voting and its plusses and minuses, I  
wanted to inject this back into the mix.

Once upon a time, I designed an election method to fix the strategy  
problem with Range Voting.

The strategy problem:
You shouldn't cast a ballot with your honest ratings, you should  
maximize them along Approval strategy lines.

It also fixes the counting problem of how if someone does cast votes  
throughout the range, they might have done better in the end by  
different values.

The method I call "Instant Runoff Normalized Ratings" (IRNR):
1. Collect ratings ballots
2. Normalize each ballot so that each has an equal magnitude
3. Sum up normalized ballots
4. If there are more than two choices, drop the one with the smallest  
sum. If there are two choices remaining, one is the winner.
5. Re-normalize from original ballot values but as if dropped choices  
weren't there
6. Go to 3


I think it gets very near to a utilitarian ideal solution ( http://bolson.org/voting/twographs.html 
  ) and encourages people to vote honestly and uses those honest votes  
to the best possible effect.

Its Instant Runoff nature does have some drawbacks. It is not summable  
by parts and requires all the data to be collected in one place.

It also has some small discontinuities in the Ka-Ping Yee diagrams:
http://bolson.org/voting/sim_one_seat/www/4c_IRNR.png

But at least it's not as bad as IRV:
http://bolson.org/voting/sim_one_seat/www/4c_IRV.png

I have some ideas about smoothing out the discontinuity, but haven't  
gotten around to trying it yet. I think the key is to make the process  
more continuous and take smaller steps. Don't disqualify a choice all  
at once, but over several steps. Blend out the losing choices, blend  
out the nasty jumps in the decision process. Needs to be  
experimentally (in simulator) checked, though.


Brian Olson
http://bolson.org/