PROP1 doesn't imply M1S for unit marginals and n=2

Dependencies:

1. Fair division
2. PROP1
3. EF1
4. Minimum fair share

$\newcommand{\defeq}{:=}$ Consider a fair division instance with 2 agents having identical additive valuations. Let $t \in \{-1, 1\}$. Let there be 2 items, each of value $t$. Let the entitlement vector be $(2/3, 1/3)$. Let $A$ be an allocation where the first agent gets both items. Then $A$ is PROP1 but not M1S.

Dependency for: None

Info:

• Depth: 6
• Number of transitive dependencies: 8

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. EF1