New AI research reveals flaws in fair division for couples
AI fairness study shows why splitting chores or assets gets messy in real life
New research delivers bad news for couples: when indivisible items are fairly divided between two-person groups, strong fairness guarantees are impossible. The paper shows that for n agents split into n/2 couples, there are binary instances where envy-freeness up to Ω(√n) items cannot be guaranteed. For the broader group-allocation model with n agents in k groups, it constructs binary instances where envy-freeness up to Ω(√(n-k)) items cannot be guaranteed—matching existing upper bounds except when most agents are singletons. This is surprising, since that upper bound was conjectured not to be tight for small groups like couples. The author also proves improved upper bounds for the remaining sparse regime, using a general theorem that simultaneously ensures approximate envy-freeness with respect to subjective valuations and approximate equality with respect to multiple consensus valuations.
- Max Dupré la Tour's paper proves AI systems can't guarantee fair division beyond Ω(√n) items when allocating to couples
- The research contradicts previous assumptions that small groups would have better fairness guarantees
- New upper bounds provided for prime-power k with O(min{√((n-k)log k), n-k}) complexity
Why It Matters
Exposes fundamental limits in algorithmic fairness that affect real-world resource allocation systems from household division to multi-agent AI