  The Kemeny method is one of the popular tools for rank aggregation. However,
computing an optimal Kemeny ranking is NP-hard. Consequently, the computational
task of finding a Kemeny ranking has been studied under the lens of
parameterized complexity with respect to many parameters. We first present a
comprehensive relationship, both theoretical and empirical, among these
parameters. Further, we study the problem of computing all distinct Kemeny
rankings under the lens of parameterized complexity. We consider the target
Kemeny score, number of candidates, average distance of input rankings, maximum
range of any candidate, and unanimity width as our parameters. For all these
parameters, we already have FPT algorithms. We find that any desirable number
of Kemeny rankings can also be found without substantial increase in running
time. We also present FPT approximation algorithms for Kemeny rank aggregation
with respect to these parameters.
