  Decision making is challenging when there is more than one criterion to
consider. In such cases, it is common to assign a goodness score to each item
as a weighted sum of its attribute values and rank them accordingly. Clearly,
the ranking obtained depends on the weights used for this summation. Ideally,
one would want the ranked order not to change if the weights are changed
slightly. We call this property {\em stability} of the ranking. A consumer of a
ranked list may trust the ranking more if it has high stability. A producer of
a ranked list prefers to choose weights that result in a stable ranking, both
to earn the trust of potential consumers and because a stable ranking is
intrinsically likely to be more meaningful. In this paper, we develop a
framework that can be used to assess the stability of a provided ranking and to
obtain a stable ranking within an "acceptable" range of weight values (called
"the region of interest"). We address the case where the user cares about the
rank order of the entire set of items, and also the case where the user cares
only about the top-$k$ items. Using a geometric interpretation, we propose
algorithms that produce stable rankings. In addition to theoretical analyses,
we conduct extensive experiments on real datasets that validate our proposal.
