PROP1

Dependencies:

1. Fair division

In fair division of indivisible items, an agent $i$ having entitlement $w_i$ is PROP1 satisfied if at least one of the following hold:

1. $v_i(A_i) ≥ w_iv_i(M)$.
2. $v_i(A_i \cup \{g\}) > w_iv_i(M)$ for some $g \in M \setminus A_i$.
3. $v_i(A_i \setminus \{c\}) > w_iv_i(M)$ for some $c \in A_i$.

Dependency for:

1. PROPm implies PROP1
2. An MXS allocation is also PROP1
3. EF1 implies PROP1
4. Additive chores and binary marginals
5. Additive goods and binary marginals
6. PROP1+M1S allocation doesn't exist
7. MMS+APS doesn't imply PROP1 for chores
8. PROP1 doesn't imply M1S for unit marginals and n=2
9. M1S doesn't imply PROP1
10. MXS doesn't imply PROP1 for chores
11. EF doesn't imply PROP for supermodular valuations

Info:

• Depth: 4
• Number of transitive dependencies: 4

Transitive dependencies:

1. /sets-and-relations/countable-set
2. σ-algebra
3. Set function
4. Fair division