How should we evaluate worlds containing infinite populations? This is a crucial question for ethical consequentialists - their judgements of acts are determined by the value of the resulting worlds, and some of our best physical theories now predict that our world will inevitably contain an infinite population (see Knobe et al., 2006; Gott, 2008; Carroll, 2017). Various answers have been proposed, notably by Vallentyne & Kagan (1997), Bostrom (2011), and Jonsson & Voorneveld (2018).

Here's a further question: how should we evaluate options involving infinite worlds, when we are not certain of which world will be produced? We live in a risky and uncertain world, so proposals which give no answer won't be of much use to us. But almost none of the current proposals can answer this question – none of them can assign cardinal values to worlds, and so none of them allow us to produce expected values in the usual manner.

Only one solution has so far been proposed – Arntzenius (2014) describes an expansionist principle which takes expected utilities at a local level. This sidesteps the requirement of each world having a cardinal value to input into an expected utility calculation. In this paper, I demonstrate a substantive problem for Arntzenius’ approach. In worlds with infinite populations, there is a decision scenario in which Arntzenius’ method diverges sharply from the intuitively correct judgement. In this scenario, we compare two lotteries, one of which contains only worlds which are strictly worse than every world in the other. Nonetheless, Arntzenius’ method evaluates the lottery containing strictly worse worlds as preferable.

I propose an alternative view which doesn't say such silly things. The weak form of my view neatly preserves our intuitions in finite cases and shouldn't be controversial. The strong form of my view covers far more cases but, controversially, gives consideration to the physical location of instances of value.