If the answer is only when p=0, then your value of sparrows should never affect your choices, because it will always be dominated by the greater probability of your own welfare.
Not sure that holds. Surely there could be situations where you can't meaningfully calculate whether acting to preserve the life of a sparrow increases or decreases the probability of your death, therefore you act to preserve its life because though you consider it a fundamentally lesser terminal value, it's still a terminal value.
Surely there could be situations where you can't meaningfully calculate whether acting to preserve the life of a sparrow increases or decreases the probability of your death
In this case you try harder to figure out a way to calculate the impact on your chance of death. The value of information of such an effort is worth infinite sparrow lives. Lower tier utility functions just don't matter.
Happy New Year! Here's the latest and greatest installment of rationality quotes. Remember: