  Human decision-makers often receive assistance from data-driven algorithmic
systems that provide a score for evaluating objects, including individuals. The
scores are generated by a function (mechanism) that takes a set of features as
input and generates a score.The scoring functions are either machine-learned or
human-designed and can be used for different decision purposes such as ranking
or classification.
  Given the potential impact of these scoring mechanisms on individuals' lives
and on society, it is important to make sure these scores are computed
responsibly. Hence we need tools for responsible scoring mechanism design. In
this paper, focusing on linear scoring functions, we highlight the importance
of unbiased function sampling and perturbation in the function space for
devising such tools. We provide unbiased samplers for the entire function
space, as well as a $\theta$-vicinity around a given function.
  We then illustrate the value of these samplers for designing effective
algorithms in three diverse problem scenarios in the context of ranking.
Finally, as a fundamental method for designing responsible scoring mechanisms,
we propose a novel approach for approximating the construction of the
arrangement of hyperplanes. Despite the exponential complexity of an
arrangement in the number of dimensions, using function sampling, our algorithm
is linear in the number of samples and hyperplanes, and independent of the
number of dimensions.
