[EM] Fixing Range Voting

[Raph Frank]

On Tue, Oct 14, 2008 at 2:04 PM, Brian Olson <bql at bolson.org> wrote:
> Once upon a time, I designed an election method to fix the strategy problem
> with Range Voting.
> The method I call "Instant Runoff Normalized Ratings" (IRNR):
> 1. Collect ratings ballots
> 2. Normalize each ballot so that each has an equal magnitude

Magnitude = max rating - min rating
or
Magnitude = sum of ratings (negative ratings allowed)
?

> 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 )

It id heard to determine which plot refers to which method.

> and encourages people to vote
> honestly and uses those honest votes to the best possible effect.

Maybe, I can't see any obvious strategy and it seems to protect people
from casting weak votes.

> 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.

I am not so sure candidates need to actually be eliminated.
Candidates who are out of the running would still be rated by each
voter.   However, they would not be used to determine the truncation
window used.  Ofc, that could mean that the method doesn't converge.

This is especially true if there is a condorcet cycle.

For example, if a voter votes

A: 10
B: 3
C: 0

initially, the vote will just be rescaled to give maximum

window = (0,10)
A: 1.0
B: 0.3
C: 0.0

Each candidate would be assigned a score based on the result of the
first round, then the new window needs to be worked out
1.0 = in the running
0.0 = eliminated

For each ballot.

1) work out weighted mean using the scores.
- This will be the centre of the window

2) for each candidate work out
d(candidate) = (score)*(distance from mean)

3) determine the highest distance

4) Set window to
window( mean - dmax, mean + dman )

In the above example

score(A) = 1
score(B) = 1
score(C) = 0.5

mean = (1*10 + 1*3 + 0.5*0)/2.5 = 5.2

distance(A) = 1*4.8 = 4.8
distance(B) = 1*2.2 = 2.2
distance(C) = 0.5*5.2 = 2.6

dmax = 4.8

window = (5.2-4.8 , 5.2+4.8) = (0.4, 10)

The ballot would be rescaled as

A: 1.0
B: 0.27
C: 0

If only 2 candidates remain, then it will set the window as max and
min of those candidates.