Population ethics with thresholds

We propose a new class of social quasi-orderings in a variable-population setting. In order to declare one utility distribution at least as good as another, the critical-level utilitarian value of the former must reach or surpass the value of the latter. For each possible absolute value of the difference between the population sizes of two distributions to be compared, we specify a non-negative threshold level and a threshold inequality. This inequality indicates whether the corresponding threshold level must be reached or surpassed in the requisite comparison. All of these threshold critical-level utilitarian quasi-orderings perform same-number comparisons by means of the utilitarian criterion. In addition to this entire class of quasi-orderings, we axiomatize two important subclasses. The members of the first subclass are associated with proportional threshold functions, and the well-known critical-band utilitarian quasi-orderings are included in this subclass. The quasi-orderings in the second subclass employ constant threshold functions; the members of this second class have, to the best of our knowledge, not been examined so far. Furthermore, we characterize the members of our class that (i) avoid the repugnant conclusion; (ii) avoid the sadistic conclusions; and (iii) respect the mere-addition principle.