Learning Inconsistent Preferences with Gaussian Processes

On the Linear Ordering Problem and the Rankability of Data

“…Digraph III Digraph IV In ranking applications, the data is often assumed to be totally rankable, i.e., observations are some noisy evaluations of an objective function that reflects the true unique ranking. Recently, however, some in the ranking community have challenged this assumption; specifically, in [1,4] quantitative metrics are proposed for measuring the rankability of data, and in [8] general preference modeling methods are developed without assuming total rankability. Since the linear ordering problem results in a ranking that is optimal with respect to the objective function in (1a), it is natural to consider what properties of the LOP can be used to analyze the rankability of the underlying data.…”

“…In many ranking applications, the data is often assumed to be totally rankable, i.e., observations are some noisy evaluations of an objective function that reflects the true unique ranking [8]. In [1], the authors questioned this assumption by proposing the concept of rankability, which refers to a dataset's inherent ability to be meaningfully ranked.…”

“…(10,7,8,5,1,6,9,2,4,3), σ 2 = (10, 7, 5, 8, 1, 6, 9, 2, 4, 3), σ 3 = (10, 7, 5, 1, 8, 6, 9, 2, 4, 3), σ 4 = (10, 7, 8, 5, 1, 6, 9, 2, 3, 4), σ 5 = (10, 7, 5, 8, 1, 6, 9, 2, 3, 4), σ 6 = (10, 7, 5, 1, 8, 6, 9, 2, 3, 4).…”