  Envy-freeness is a widely studied notion in resource allocation, capturing
some aspects of fairness. The notion of envy being inherently subjective
though, it might be the case that an agent envies another agent, but that she
objectively has no reason to do so. The difficulty here is to define the notion
of objectivity, since no ground-truth can properly serve as a basis of this
definition. A natural approach is to consider the judgement of the other agents
as a proxy for objectivity. Building on previous work by Parijs (who introduced
"unanimous envy") we propose the notion of approval envy: an agent $a_i$
experiences approval envy towards $a_j$ if she is envious of $a_j$, and
sufficiently many agents agree that this should be the case, from their own
perspectives. Some interesting properties of this notion are put forward.
Computing the minimal threshold guaranteeing approval envy clearly inherits
well-known intractable results from envy-freeness, but (i) we identify some
tractable cases such as house allocation; and (ii) we provide a general method
based on a mixed integer programming encoding of the problem, which proves to
be efficient in practice. This allows us in particular to show experimentally
that existence of such allocations, with a rather small threshold, is very
often observed.
