Proportional allocation

Dependencies:

1. Fair division

In fair division, an allocation $A$ is PROP-fair to agent $i$ iff $v_i(A_i) ≥ w_iv_i(M)$ (here $w_i$ is agent $i$'s entitlement). A PROP-fair allocation is also called a proportional allocation. $w_iv_i(M)$ is called agent $i$'s proportional share or PROP share.

Dependency for:

1. MEFS implies PROP for subadditive valuations
2. Cake cutting: PROP implies EEF for additive valuations
3. PROP implies WMMS and pessShare
4. PROP implies EF for n=2
5. PROP implies APS
6. APS can be > MMS
7. PROPx
8. PROPm
9. PROP cake division doesn't exist for supermodular valuations
10. PROP but not MEFS
11. PROP doesn't imply M1S for unit-demand valuations
12. MEFS+PROP doesn't imply EEF1 for chores

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