What If AI Could Split Things Fairly For Everyone?
Imagine AI that divides chores or prizes without anyone feeling cheated...
Recent work in fair division has focused on either simultaneously satisfying closely related fairness notions or achieving a single notion across the ex-ante and ex-post worlds. We study the compatibility of two fundamentally different fairness notions: envy-freeness and equitability.
For indivisible goods-only and chores-only settings, we study the existence and complexity of simultaneously satisfying their relaxations, revealing sharp contrasts between the two settings. For normalized binary goods, we give a polynomial-time algorithm for computing an EF1+EQ1 allocation with at most seven agents, but also construct a normalized instance with a larger number of agents for which no such allocation exists.
In sharp contrast, binary chores admit the stronger EFX+EQX guarantee for any number of agents, even without normalization. We further initiate the study of cross-notion ex-ante and ex-post guarantees, asking whether randomized allocations can provide ex-ante guarantees for one notion while preserving ex-post guarantees for another.
- AI can now split tasks or rewards fairly among groups, ensuring no one feels left out or jealous.
- It works best in simple scenarios (like identical items) but struggles with complex situations (like irregularly shaped rooms).
- The goal is to reduce real-life conflicts over fairness, like chores or bonuses, but it’s still early days.
Why It Matters
Could one day make sharing easier and fairer for families, offices, or communities.