Individual-Fair and Group-Fair Social Choice Rules under Single-Peaked Preferences

We propose novel fairness notions for social choice under single-peaked preferences, for group-fairness as well as individual-fairness. Agents are assumed to be partitioned into logical groups, which could be based on natural attributes such as gender, race, or location. To capture fairness within each group, we introduce the notion of group-wise anonymity. To capture fairness across the groups, we propose a weak notion as well as a strong notion of fairness. The proposed fairness notions turn out to be natural generalizations of existing individual-fairness notions. We characterize the fair deterministic social choice rules and provide two separate characterizations of the fair random social choice rules: (i) direct characterization (ii) extreme point characterization (as convex combinations of deterministic rules). We also explore individual fairness by looking at the special case with singleton groups.