| Sumario: | Aggregative theories of moral value have difficulty in ranking worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds: without cardinal values, we cannot apply expected value theory. How, then, can we compare such lotteries? To date, we have just one method for doing so (proposed separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and then to represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one that delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and that can be applied alongside almost any ranking of infinite worlds.
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