This indeed puts me in a conundrum: If I answer anything but p=0, I'm giving a kind of weighting factor that destroys the supposedly strict separation between tiers.
Well, you could always play with some fun math...
Even that would be equivalent to an expected utility maximizer using just real numbers, except that there's a well-defined tie-breaker to be used when two different possible decisions would have the exact same expected utility.
Happy New Year! Here's the latest and greatest installment of rationality quotes. Remember: