[EM] Efforts to improve on CR's strategy

[Brian Olson]

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/