[EM] Fixing Range Voting

[Brian Olson]

On Oct 14, 2008, at 12:11 PM, Raph Frank wrote:

> 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)
> ?

I mean the geometric sense. For ratings a,b,c,etc., sqrt(a*a + b*b +  
c*c ...)

>
>> 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.

In a sense, part of the result is that there's a pretty tight pack of  
similar (good) results and a few outliers (IRV, pick-one).

>
>> 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.

I think that's pretty similar to what I'd planned to implement. I'm  
still expecting some tinkering will be needed to get it to do  
solutions with negligible instability.