Message: 1 From: [EMAIL PROTECTED] Date: Sat, 15 May 2004 23:09:19 -0700 (PDT)
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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.
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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
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