1. I would have thought that VNM utility has invariance with alpha>0 not alpha>=0, is this correct?
2. Is there any alternative to dropping convex-linearity (perhaps other than changing to convexity, as you mention)? Would the space of possible optimisation functions be too large in this case, or is this an exciting direction?
Convexity rather than linearity would make OP an infra-expectation. It’s not something we’ve looked into but perhaps somebody may find something interesting there.
You definitely wouldn’t want to drop invariance, I think. Probably zero for unchanged expected utility and strict monotocity could go, but I think you would need a conceptual argument about what you want OP to measure in order to constrain the search space a bit.
1. I would have thought that VNM utility has invariance with alpha>0 not alpha>=0, is this correct?
2. Is there any alternative to dropping convex-linearity (perhaps other than changing to convexity, as you mention)? Would the space of possible optimisation functions be too large in this case, or is this an exciting direction?
Correct
Convexity rather than linearity would make OP an infra-expectation. It’s not something we’ve looked into but perhaps somebody may find something interesting there.
Changed 1, thanks.
You definitely wouldn’t want to drop invariance, I think. Probably zero for unchanged expected utility and strict monotocity could go, but I think you would need a conceptual argument about what you want OP to measure in order to constrain the search space a bit.