  Rankings are a type of preference elicitation that arise in experiments where
assessors arrange items, for example, in decreasing order of utility. Orderings
of n items labelled {1,...,n} denoted are permutations that reflect strict
preferences. For a number of reasons, strict preferences can be unrealistic
assumptions for real data. For example, when items share common traits it may
be reasonable to attribute them equal ranks. Also, there can be different
importance attributions to decisions that form the ranking. In a situation
with, for example, a large number of items, an assessor may wish to rank at top
a certain number items; to rank other items at the bottom and to express
indifference to all others. In addition, when aggregating opinions, a judging
body might be decisive about some parts of the rank but ambiguous for others.
In this paper we extend the well-known Mallows (Mallows, 1957) model (MM) to
accommodate item indifference, a phenomenon that can be in place for a variety
of reasons, such as those above mentioned.The underlying grouping of similar
items motivates the proposed Clustered Mallows Model (CMM). The CMM can be
interpreted as a Mallows distribution for tied ranks where ties are learned
from the data. The CMM provides the flexibility to combine strict and
indifferent relations, achieving a simpler and robust representation of rank
collections in the form of ordered clusters. Bayesian inference for the CMM is
in the class of doubly-intractable problems since the model's normalisation
constant is not available in closed form. We overcome this challenge by
sampling from the posterior with a version of the exchange algorithm
\citep{murray2006}. Real data analysis of food preferences and results of
Formula 1 races are presented, illustrating the CMM in practical situations.
