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TobyBartels comments on 5 Axioms of Decision Making - Less Wrong
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You're right that this is an important thing to discuss, and so we'll talk about this more explicitly when I get to micromorts, which are probably one of the more useful concepts that comes up in an introductory survey. (I think it's better to establish this methodology and show that it applies to those situations too than argue it applies everywhere then establish what it actually is.)
A quick answer, though: my sense is that people feel like they have categorical preferences, but actually have tradeoff preferences. If you ask people about chicken vs. p cake or 1-p death, many will scoff at the idea of taking any chance at death to upgrade from chicken to cake. When you look at actual behavior, though, those same people do risk death to upgrade from chicken to cake- and so in some sense that's "worth sacrificing your life for." The difference between the cake > chicken preference and the family alive > family dead preference, for example, seems to be one of degree and not one of kind.
Are you prescribing a rational method of decision making or are you describing actual behavior (possibly not rational)?
Although Vaniver punted this by saying that you shouldn't judge ultimate values on rationality, you're right that this describes behaviour (and not values directly), and inferring values from behaviour assumes rationality.
However … it's intuitively obvious to me that it's perfectly rational to (in some circumstances) to go the store and get some cake when all that you have at home is chicken, even though leaving the house increases your risk of death (car crash etc). I assumed that this is the sort of behaviour that Vaniver was referring to; do you agree that it's rational (and so we can infer values in line with the axiom of equivalence)?