On May 22, 2004, at 9:15 PM, Ken Johnson wrote:
Which brings me back to the original topic: Can CR be improved? I hope someone will pick up on this topic because I would be very interested in people's opinions about this. The proposed "Normalized CR" method is as follows:
(1) Voters give candidates CR ratings. There no need for any range limit - any finite CR value, positive or negative, can be allowed.
(2) Apply an additive shift to each voter's CR profile so that the sum of the absolute values is minimized.
(3) Apply a multiplicative scale factor to each voter's CR profile so that the sum of the absolute values is 1.
(4) After applying the above transformations, select the candidate with the highest average CR.
The basic idea is that scaling the sum of the absolute values to 1 is a better way of limiting individual voting power than restricting individual CR's to a fixed range (e.g. 0 to 1). With a fixed range, the optimum strategy is to give all candidates polarized ratings - equivalent to Approval. But the above normalization process removes the incentive for voters to polarize their ratings, and they are more likely to vote sincerely. (At least that's my hypothesis, I'm not sure if it's actually true.)
The additive shift is applied because it is strategically advantageous to the voter. (If the scale factor were not applied the additive shift would have no effect on the election. With the scale factor, the additive shift maximizes voting power by making the scale factor as large as possible.)
Does anyone have thoughts on how this form of Normalized CR would perform and how it compares to other methods?
With the exception of step 2, I've simulated this.
On this graph it's labeled "Rated Vote, equal sum": http://bolson.org/voting/graph/v10000/e0_17.png
It doesn't stand out on the graph, but it's in with the cluster of things at the top which are very near to maximizing social utility. But, that's with simulations of voters casting honest ballots.
As Mike O is fond of saying: given honest ballots, straight CR is perfect. So we take steps away from that in order to have a system that is more "fair" or is harder or impossible to cheat. I have a mode in my simulator that runs a few basic strategies against the election methods, but I'm working on adding an AI/ALife system to learn the best strategy against each election method. If the AI learns that honest votes are most likely to get it what it wants, we win.
Brian Olson http://bolson.org/
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