Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fair assignment of indivisible objects under ordinal preferences   We consider the discrete assignment problem in which agents express ordinal
preferences over objects and these objects are allocated to the agents in a
fair manner. We use the stochastic dominance relation between fractional or
randomized allocations to systematically define varying notions of
proportionality and envy-freeness for discrete assignments. The computational
complexity of checking whether a fair assignment exists is studied for these
fairness notions. We also characterize the conditions under which a fair
assignment is guaranteed to exist. For a number of fairness concepts,
polynomial-time algorithms are presented to check whether a fair assignment
exists. Our algorithmic results also extend to the case of unequal entitlements
of agents. Our NP-hardness result, which holds for several variants of
envy-freeness, answers an open question posed by Bouveret, Endriss, and Lang
(ECAI 2010). We also propose fairness concepts that always suggest a non-empty
set of assignments with meaningful fairness properties. Among these concepts,
optimal proportionality and optimal weak proportionality appear to be desirable
fairness concepts.

19
The categories of this paper are: eess
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th