New paper proves chores fairness impossible beyond 1.26x approximation
Even submodular cost functions can't guarantee fair chore assignments within a 26% margin.
Deep Dive
Vasilis Christoforidis shows that for 3 agents and 6 indivisible chores with monotone subadditive costs, no α-EFX allocation exists for any α < 2^(1/3) ≈ 1.26, narrowing the gap with the known upper bound of 2. A separate weighted-coverage instance yields no α-EFX allocation for any α < 20/19 under submodular costs, proving constant-factor inapproximability for fair chore division even within complement-free preferences.
Key Points
- 3-agent, 6-chore instance with monotone subadditive costs proves no α-EFX allocation exists for α < 1.26 (2^(1/3)).
- Submodular costs yield even tighter bound: α < 20/19 ≈ 1.053.
- Closes the gap with previous best known upper bound of 2 for EFX chore division.
Why It Matters
Proves fundamental limits on fairness in task allocation, with direct implications for scheduling algorithms and AI systems.