Saying something has infinite value is not the same as simply saying it outranks all other outcomes in your preference ordering. It is saying that a course of action that has a finite probability of producing it is superior to any course of action that does not have a finite probability of producing a comparable outcome, no matter how low that probability. (Provided, of course, that it does not come with a finite probability of an infinitely-bad outcome.)
In other words: utilities really do need to be treated as scalars, not just orderings, when reasoning under uncertainty.
If two courses of action differ in their probability of producing infinite utility, you might be able to make a coherent argument for maximizing the probability of infinite utility. But when you have multiple distinct infinite-utility outcomes, that gets harder. Really, anything nontrivially complex involving infinite utilities is hard.
Saying something has infinite value is not the same as simply saying it outranks all other outcomes in your preference ordering. It is saying that a course of action that has a finite probability of producing it is superior to any course of action that does not have a finite probability of producing a comparable outcome, no matter how low that probability. (Provided, of course, that it does not come with a finite probability of an infinitely-bad outcome.)
In other words: utilities really do need to be treated as scalars, not just orderings, when reasoning under uncertainty.
If two courses of action differ in their probability of producing infinite utility, you might be able to make a coherent argument for maximizing the probability of infinite utility. But when you have multiple distinct infinite-utility outcomes, that gets harder. Really, anything nontrivially complex involving infinite utilities is hard.