New algorithm beats 1/2 barrier in fair resource allocation with subjective divisibility
Researchers improve MMS fairness guarantee from 1/2 to 5/9 for heterogeneous agents...
Deep Dive
Xiaohui Bei, Ke Ding, Bo Li, and Fangxiao Wang published new results on approximate maximin share (MMS) fairness under subjective divisibility. They prove the optimal approximation ratio is 2/3 for unary valuations, improve the general-case guarantee from 1/2 to 5/9, and achieve tight 2/3 bounds for up to four agents. This deepens the understanding of MMS fairness under heterogeneous valuations and subjective divisibility.
Key Points
- Proves optimal MMS ratio is exactly 2/3 for unary valuations with subjective divisibility
- Improves general-case guarantee from 1/2 to 5/9 using novel algorithmic techniques
- Achieves tight 2/3-approximation for up to 4 agents with polynomial-time algorithms
Why It Matters
Advances fair division theory for AI systems allocating resources when agents have conflicting views on divisibility.