  We consider the fair allocation problem of indivisible items. Most previous
work focuses on fairness and/or efficiency among agents given agents'
preferences. However, besides the agents, the allocator as the resource owner
may also be involved in many real-world scenarios, e.g., heritage division. The
allocator has the inclination to obtain a fair or efficient allocation based on
her own preference over the items and to whom each item is allocated. In this
paper, we propose a new model and focus on the following two problems: 1) Is it
possible to find an allocation that is fair for both the agents and the
allocator? 2) What is the complexity of maximizing the allocator's social
welfare while satisfying the agents' fairness?
  We consider the two fundamental fairness criteria: envy-freeness and
proportionality. For the first problem, we study the existence of an allocation
that is envy-free up to $c$ goods (EF-$c$) or proportional up to $c$ goods
(PROP-$c$) from both the agents' and the allocator's perspectives, in which
such an allocation is called doubly EF-$c$ or doubly PROP-$c$ respectively.
When the allocator's utility depends exclusively on the items (but not to whom
an item is allocated), we prove that a doubly EF-$1$ allocation always exists.
For the general setting where the allocator has a preference over the items and
to whom each item is allocated, we prove that a doubly EF-$1$ allocation always
exists for two agents, a doubly PROP-$2$ allocation always exists for binary
valuations, and a doubly PROP-$O(\log n)$ allocation always exists in general.
  For the second problem, we provide various (in)approximability results in
which the gaps between approximation and inapproximation ratios are
asymptotically closed under most settings.
  Most results are based on novel technical tools including the chromatic
numbers of the Kneser graphs and linear programming-based analysis.
