An MXS allocation is also PROP1

Dependencies:

1. Fair division
2. PROP1
3. EFX
4. Minimum fair share
5. PROP-unsat implies someone is superPROP

$\newcommand{\defeq}{:=}$ Consider a fair division instance $([n], [m], V, w)$, where agents have equal entitlements. If all items are goods to agent $i$, $v_i$ is additive, and $i$ is MXS-satisfied by allocation $X$, then $i$ is also PROP1-satisfied by $X$.

Proof

Theorem 3 in https://doi.org/10.24963/ijcai.2023/284.

Dependency for: None

Info:

• Depth: 6
• Number of transitive dependencies: 11

Transitive dependencies:

1. /sets-and-relations/countable-set
2. σ-algebra
3. Set function
4. Fair division
5. Envy-freeness
6. PROP1
7. Minimum fair share
8. Subadditive and superadditive set functions
9. PROP-unsat implies someone is superPROP
10. Submodular function
11. EFX