  Diversification of recommendation results is a promising approach for coping
with the uncertainty associated with users' information needs. Of particular
importance in diversified recommendation is to define and optimize an
appropriate diversity objective. In this study, we revisit the most popular
diversity objective called intra-list distance (ILD), defined as the average
pairwise distance between selected items, and a similar but lesser known
objective called dispersion, which is the minimum pairwise distance. Owing to
their simplicity and flexibility, ILD and dispersion have been used in a
plethora of diversified recommendation research. Nevertheless, we do not
actually know what kind of items are preferred by them.
  We present a critical reexamination of ILD and dispersion from theoretical
and experimental perspectives. Our theoretical results reveal that these
objectives have potential drawbacks: ILD may select duplicate items that are
very close to each other, whereas dispersion may overlook distant item pairs.
As a competitor to ILD and dispersion, we design a diversity objective called
Gaussian ILD, which can interpolate between ILD and dispersion by tuning the
bandwidth parameter. We verify our theoretical results by experimental results
using real-world data and confirm the extreme behavior of ILD and dispersion in
practice.
