EF1 doesn't imply PROPx or MXS

Dependencies:

1. Fair division
2. PROPx
3. Minimum fair share
4. EFX
5. EF1

$\newcommand{\defeq}{:=}$ Let $t \in \{-1, 1\}$. Consider a fair division instance with 2 agents having equal entitlements and identical additive valuations. There are 2 items of value $4t$ and 3 items of value $t$. Let $A \defeq (\{4t\}, \{4t, t, t, t\})$. Then $A$ is EF1 but $A$ is not PROPx and $A$ is not MXS.

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. Proportional allocation
6. Envy-freeness
7. Minimum fair share
8. EF1
9. Submodular function
10. PROPx
11. EFX