[EM] Instant Runoff Normalized Ratings

[Ken Johnson]

>Message: 1
>From: bql at bolson.org
>Date: Sat, 15 May 2004 23:09:19 -0700 (PDT)
>
>...
>
>I'm writing today to tell about my new favorite system:
>
>Instant Runoff Normalized Ratings
>(IRNR)
>
>Every voter casts a rating of each choice on a scale of -1.0 to 1.0 or
>some equivalent scale. Each voter's voting power is normalized, each
>rating is divided by the sum of the absolute values of the ratings so that
>each voter has a voting power of 1.0 . All of the normalized ratings are
>summed. The choice with the lowest rating sum is disqualified. On
>successive iterations votes are re-normalized without disqualified
>choices, redistributing a voter's voting power to the still-active choices
>in proportion to the original vote.
>
>...
>
>Brian Olson
>http://bolson.org/
>  
>
Brian:

I suggest the following modification of your procedure: Before 
normalizing each voter's absolute rating sum to 1, apply a constant 
additive shift to the ratings in order to minimize the absolute rating 
sum. (This has the effect of maximizing the normalization scaling 
factor, and is hence strategically advantageous to the voter.)

Rather than using this as an alternative to Instant Runoff, how about 
using it as an alternative to Cardinal Rating? Just do a single-pass 
normalization and pick the winner with the highest aggregate rating. As 
I understand it, the main problem with CR is that it is strategically 
equivalent to Approval. But I don't think this is the case when your 
normalization is applied, so voters may be more inclined to vote sincerely.

Another possible variation: Normalize the sum-square ratings rather than 
the absolute values. Before applying the normalization, apply an 
additive shift so that the average is zero. This method is 
algorithmically simpler, and I think the optimum strategy is also 
simpler: If you don't think a particular candidate is electable, give 
them a rating equal to the average of the other ratings. (Maybe this is 
implicitly what your multi-pass method does.) Whether sum-square 
normalization would make voters more or less inclined to vote sincerely 
on viable candidates, I don't know.

What about write-in candidates or unrated candidates? I think a 
conservative approach would be to exclude unrated candidates from the 
normalization process, and just give them a rating of -1.  (Normalized 
ratings are in the range -1 to 1, so the default is to "assume the worst".)

Ken Johnson