Leximin implies GMMS for idval

Dependencies:

1. Fair division
2. Maximin share allocations
3. Restricted agents, pairwise fairness, and groupwise fairness
4. Leximin partition of a set function

$\newcommand{\defeq}{:=}$ $\newcommand{\Ical}{\mathcal{I}}$ $\newcommand{\Icalhat}{\widehat{\mathcal{I}}}$ $\newcommand{\Ahat}{\widehat{A}}$ In a fair division instance with equal entitlements and identical valuations, a leximin allocation is groupwise MMS.

Proof

Let $A$ be a leximin $n$-partition for the common valuation function $v$. Then for any subset $S$ of agents, the allocation $\Ahat$ restricted to $S$ is also leximin. Any leximin allocation is MMS, so $A$ is groupwise MMS.

Dependency for:

1. GMMS doesn't imply APS

Info:

• Depth: 5
• Number of transitive dependencies: 9

Transitive dependencies:

1. /sets-and-relations/countable-set
2. /analysis/sup-inf
3. σ-algebra
4. Set function
5. Fair division
6. Restricted agents, pairwise fairness, and groupwise fairness
7. Maximin share of a set function
8. Maximin share allocations
9. Leximin partition of a set function