The mixed solution to the number problem

You must either save a group of m people or a group of n people. If there are no morally relevant differences among the people, which group should you save? This problem is known as the number problem. The recent discussion has focussed on three proposals: (i) Save the greatest number of people, (ii) Toss a fair coin, or (iii) Set up a weighted lottery, in which the probability of saving m people is m/m+n, and the probability of saving n people is n/m+n. This contribution examines a fourth alternative, the mixed solution, according to which both fairness and the total number of people saved count. It is shown that the mixed solution can be defended without assuming the possibility of interpersonal comparisons of value.