  It has long been recognized that it is not enough for a Recommender System
(RS) to provide recommendations based only on their relevance to users. Among
many other criteria, the set of recommendations may need to be diverse.
Diversity is one way of handling recommendation uncertainty and ensuring that
recommendations offer users a meaningful choice. The literature reports many
ways of measuring diversity and improving the diversity of a set of
recommendations, most notably by re-ranking and selecting from a larger set of
candidate recommendations. Driven by promising insights from the literature on
how to incorporate versatile Large Language Models (LLMs) into the RS pipeline,
in this paper we show how LLMs can be used for diversity re-ranking.
  We begin with an informal study that verifies that LLMs can be used for
re-ranking tasks and do have some understanding of the concept of item
diversity. Then, we design a more rigorous methodology where LLMs are prompted
to generate a diverse ranking from a candidate ranking using various prompt
templates with different re-ranking instructions in a zero-shot fashion. We
conduct comprehensive experiments testing state-of-the-art LLMs from the GPT
and Llama families. We compare their re-ranking capabilities with random
re-ranking and various traditional re-ranking methods from the literature. We
open-source the code of our experiments for reproducibility. Our findings
suggest that the trade-offs (in terms of performance and costs, among others)
of LLM-based re-rankers are superior to those of random re-rankers but, as yet,
inferior to the ones of traditional re-rankers. However, the LLM approach is
promising. LLMs exhibit improved performance on many natural language
processing and recommendation tasks and lower inference costs. Given these
trends, we can expect LLM-based re-ranking to become more competitive soon.
