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ThrustVectoring comments on A Difficulty in the Concept of CEV - Less Wrong
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On first inspection, it looks like "linear combination of utility functions" still has issues with strategic voting. If you prefer A to B and B to C, but A isn't the winner regardless of how you vote, it can be arranged such that you make yourself worse off by expressing a preference for A over B. Any system where you reward people for not voting their preferences can get strange in a hurry.
Let me at least formalize the "linear combination of utility functions" bit. Scale each person's utility function so that their favorite option is 1, and their least favorite is -1. Add them together, then remove the lowest-scoring option, then re-scale the utility functions to the same range over the new choice set.
Arrow's Theorem doesn't say anything about strategic voting. The only reasonable non-strategic voting system I know of is random ballot (pick a random voter; they decide who wins). I'm currently trying to figure out a voting system that is based on finding the Nash equilibrium (which may be mixed) of approval voting, and this system might also be strategy-free.
When I said linear combination of utility functions, I meant that you fix the scaling factors initially and don't change them. You could make all of them 1, for example. Your voting system (described in the last paragraph) is a combination of range voting and IRV. If everyone range votes so that their favorite gets 1 and everyone else gets -1, then it's identical to IRV, and shares the same problems such as non-monotonicity. I suspect that you will also get non-monotonicity when votes aren't "favorite gets 1 and everyone else gets -1".
EDIT: I should clarify: it's not 1 for your favorite and -1 for everyone else. It's 1 for your favorite and close to -1 for everyone else, such that when your favorite is eliminated, it's 1 for your next favorite and close to -1 for everyone else after rescaling.