Fairness and social risk .2. Aggregated analyses

This paper is the second of a two-paper study of fairness issues for decisions that affect the benefits received and the risks encountered by a population. The study examines fairness for individuals and for homogeneous groups within the population. It considers fairness both for population benefit-risk profiles and for probability distributions over profiles. Our study bases fairness on notions of envy among individuals and groups. The first paper focused on fairness in profiles and profile distributions when benefits and risks are not aggregated. The present paper uses individual preferences to assess fairness when benefits and risks are aggregated within groups or over the population. It concentrates on intergroup envy measures and fairness indices that account for ways that aggregated benefits and risks might be allocated to members of groups or to groups within the population.