How can we deal with decision making under ignorance of probabilities when all possible negative or positive outcomes of one alternative are equal to that of the other(s)? I put forth the following example: Let's say that I can choose either to deal with a current personal security matter, which might otherwise bring about death, or to deal with a health issue that, if left untreated, might have the same consequence; and let's suppose that I have no access to the probability of mortality from any problem, nor to the probability of mortality provided that I assess either of them. As I see it, normative accounts for these instances, such as the maximin, minimax, maximax, and Laplace criteria would hold the alternatives to be equally good, as they have the same expected utility. But I am sincerely dissatisfied with the idea of making choices at random, so I want to know what you think. I also see the possibility of the decision making process being tainted by an "anything goes" type of mentality, as coming from the notion that most often than not, we ultimately don't know what the consequences of our actions can be, which, under ignorance, becomes even a bigger concern. I would also like to know this: How would Decision Theory (or even consequentialism) deal with the notion that we often can't ultimately know what the outcomes of any given choice can be, and that thismay make the decision making process be tainted with an "anything goes" mentality?

If I understand your question correctly, it's this: in a case where the available considerations don't favor one alternative over another, how can we choose rationally what to do, where "rational" entails that anyone in the same situation (same preferences, values, information, probabilities or lack thereof...) would choose the same way?

Unless I'm missing something, you can't choose rationally in this case in that sense. The way you've set the situation up leaves no room for singling out one alternative.

One possibility is to add "do nothing" to the list of alternatives. If that's better, or likely better than each of the alternatives, do nothing. But if doing nothing is worse overall, then the obvious question is: what's wrong with picking randomly? After all, picking randomly only in cases where you need to make a choice and there's no principled way to do it isn't the same as thinking that anything goes in any circumstance.

That should be clear in general. But an artificial example may help. Suppose I'm given a blind choice between two boxes. One, I know, has $1000 in it. The other has $10, but I don't know which box is which. By calling this a blind choice, I mean that I have no information at all to guide which box I pick. I would be foolish not to choose. And by choosing randomly I'm not adopting what you call an "anything goes" point of view. I'm making the rational choice to end up with something rather than nothing, but making an arational choice between two ways of getting something. It's arational because I don't appeal to any principles or reasons for picking the box I pick. But it's not irrational; in the circumstances, the choice to pick arationally is the rational choice.