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A principal aim of the branch of ethics called ‘population theory’ or ‘population ethics’ is to find a plausible welfarist axiology, capable of comparing total outcomes with respect to value. This has proved an exceedingly difficult task. In this paper I shall state and discuss two ‘trilemmas’, or choices between three unappealing alternatives, which the population ethicist must face. The first trilemma is not new. It originates with Derek Parfit's well-known ‘Mere Addition Paradox’, and was first explicitly stated by Yew-Kwang Ng. I shall argue that one horn of this trilemma is less unattractive than Parfit and others have claimed. The second trilemma, which is a kind of mirror image of the first, appears hitherto to have gone unnoticed. Apart from attempting to resolve the two trilemmas, I shall suggest certain features which I believe a plausible welfarist axiology should possess. The details of this projected axiology will, however, be left open.

John Broome has argued that alleged cases of value incomparability are really examples of vagueness in the betterness relation. The main premiss of his argument is ‘the collapsing principle’. I argue that this principle is dubious, and that Broome's argument is therefore unconvincing.

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