Thanks for the post—I’ve been having thoughts in this general direction and found this post helpful. I’m somewhat drawn to geometric rationality because it gives more intuitive answers in thoughts experiments involving low probabilities of extreme outcomes, such as Pascal’s mugging. I also agree with your claim that “humans are evolved to be naturally inclined towards geometric rationality over arithmetic rationality.”
On the other hand, it seems like geometric rationality only makes sense in the context of natural features that cannot take on negative values. Most of the things I might want to maximize (e.g. utility) can be negative. Do you have thoughts on the extent to which we can salvage geometric rationality from this problem?
But if your utility function is bounded, as it apparently should be then you’re one affine transform away from being able to use geometric rationality, no?
Thanks for the post—I’ve been having thoughts in this general direction and found this post helpful. I’m somewhat drawn to geometric rationality because it gives more intuitive answers in thoughts experiments involving low probabilities of extreme outcomes, such as Pascal’s mugging. I also agree with your claim that “humans are evolved to be naturally inclined towards geometric rationality over arithmetic rationality.”
On the other hand, it seems like geometric rationality only makes sense in the context of natural features that cannot take on negative values. Most of the things I might want to maximize (e.g. utility) can be negative. Do you have thoughts on the extent to which we can salvage geometric rationality from this problem?
But if your utility function is bounded, as it apparently should be then you’re one affine transform away from being able to use geometric rationality, no?
How much should you shift things by? The geometric argmax will depend on the additive constant.
I don’t think so, primarily since geometric rationality isn’t VNM rational, so we can include infinite utility functions.