A weakness in the discussion of population policy for the last decade has been the almost total failure to seriously consider by what criterion alternative futures containing different numbers of people ought to be judged. In other words, what is meant by the term "optimum population." The objective of this article is to repair this omission in the literature by showing the inadequacy of the criterion of per capita welfare and discussing some alternatives. The discussion begins by assuming, with Meade, that there exists individual utility functions that are interpersonally comparable and to examine the 2 alternatives considered: maximizing per capita utility (in his terms, "welfare") and maximizing total utility. Following this, focus is on the possibility of some Pareto-like criterion for population decisions. Lastly considered are what general conditions one might impose on possible social welfare functions designed to allow comparisons of alternative futures with different populations. The criterion of maximizing per capita utility leads to the counterintuitive conclusion that the desirability of a particular life existing is dependent on the accident of whether the other people who happen to exist at the same time are better or worse off than the person who lives the life, so that the existence of 1 particular life will be judged desirable in 1 future and undesirable in another even if it has not interacted at all with those to whom it is being compared. The alternative criterion of maximizing total utility is likely to result in the conclusion that a world of 24 billion people living at the edge of subsistence is superior to a world of 4 billion living in prosperity. New criterion should be selected to avoid the problems generated by both the per capita utility and total utility criteria. It should avoid the fallacy of composition by which below average lives are treated as if, by bringing down the average, they inflicted a positive injury on the rest of the population. It should also reflect at least a decent agnosticism concerning the superiority of a future with large numbers of less happy people to one with fewer numbers of happier people. Of the criteria considered, both per capita and total utility are transitive. In order for the expanded Pareto criterion to be transitive, it must be assumed that in order to guarantee transitivity the comparison among lives must be done independent of the person that is doing it.