  The widespread use of machine learning and data-driven algorithms for
decision making has been steadily increasing over many years. The areas in
which this is happening are diverse: healthcare, employment, finance,
education, the legal system to name a few; and the associated negative side
effects are being increasingly harmful for society. Negative data \emph{bias}
is one of those, which tends to result in harmful consequences for specific
groups of people. Any mitigation strategy or effective policy that addresses
the negative consequences of bias must start with awareness that bias exists,
together with a way to understand and quantify it. However, there is a lack of
consensus on how to measure data bias and oftentimes the intended meaning is
context dependent and not uniform within the research community. The main
contributions of our work are: (1) a general algorithmic framework for defining
and efficiently quantifying the bias level of a dataset with respect to a
protected group; and (2) the definition of a new bias measure. Our results are
experimentally validated using nine publicly available datasets and
theoretically analyzed, which provide novel insights about the problem. Based
on our approach, we also derive a bias mitigation algorithm that might be
useful to policymakers.
