If you are truly risk neutral, ruin games are good. The long term outcome is not worse, because the 99% of times when the world is destroyed are outweighed by the fact that it’s so much better 1% of the time. If you believe in risk neutrality as a normative stance, then you should be okay with that.
Put another way; if someone offers you a 99% bet for 1000x your money with a 1% chance to lose it all, you might want to take it once or twice. You don’t have to choose between “never take it” and “take it forever”. But if you find the idea of sequence dependence to be desirable in this situation, then you shouldn’t be risk neutral.
Deciding to apply risk aversion in some cases and risk neutrality in others is not special to ergodicity either. If you have a risk averse utility function the curvature increases with the level of value. I claim that for “small” values of lives at stake, my utility function is only slightly curved, so it’s approximately linear and risk neutrality describes my optimal choice better. However, for “large” values, the curvature dominates and risk neutrality fails.
If you are truly risk neutral, ruin games are good. The long term outcome is not worse, because the 99% of times when the world is destroyed are outweighed by the fact that it’s so much better 1% of the time. If you believe in risk neutrality as a normative stance, then you should be okay with that.
Put another way; if someone offers you a 99% bet for 1000x your money with a 1% chance to lose it all, you might want to take it once or twice. You don’t have to choose between “never take it” and “take it forever”. But if you find the idea of sequence dependence to be desirable in this situation, then you shouldn’t be risk neutral.
Deciding to apply risk aversion in some cases and risk neutrality in others is not special to ergodicity either. If you have a risk averse utility function the curvature increases with the level of value. I claim that for “small” values of lives at stake, my utility function is only slightly curved, so it’s approximately linear and risk neutrality describes my optimal choice better. However, for “large” values, the curvature dominates and risk neutrality fails.