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

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