  We investigate a class of polyhedral convex cones, with $R^k_+$ (the
nonegative orthant in $\mathbb{R}^k$) as a special case. We start with the
observation that for convex cones contained in $\mathbb{R}^k$, the respective
cone efficiency is inconsistent with the Pareto efficiency, the latter being
deeply rooted in economics, the decision theory, and the multiobjective
optimization theory. Despite that, we argue that convex cones contained in
$\mathbb{R}^k$ and the respective cone efficiency are also relevant to these
domains.
  To demonstrate this, we interpret polyhedral convex cones of the investigated
class in terms of assessment functions, i.e., functions that aggregate multiple
numerical attributes into single numbers.
  Further, we observe that all assessment functions in the current use share
the same limitation; that is, they do not take explicitly into account
attribute proportionality. In consequence, the issue of {\em attribute balance}
(meaning {\it the balance of attribute values}) escapes them. In contrast,
assessment functions defined by polyhedral convex cones of the investigated
class, contained in $\mathbb{R}^k$, enforce the attribute balance. However,
enforcing the attribute balance is, in general, inconsistent with the
well-established paradigm of Pareto efficiency. We give a practical example
where such inconsistency is meaningful.
