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Degrees of Fairness and Proportional Chances

Suppose the following: two groups of people require our aid but we can help only one group; there are more people in the first group than in the second group; every person in both groups has an equal claim on our aid; and we have a duty to help and no other special obligations or duties. I argue that there exists at least one fairness function, which is a function that measures the goodness of degrees of fairness, that implies that we should follow a procedure of proportional chances to determine which group to aid.