We introduce LAMPO, a novel paradigm that leverages Large Language Models (LLMs) for solving few-shot multi-class ordinal classification tasks. Unlike conventional methods, which concatenate all demonstration examples with the test instance and prompt LLMs to produce the pointwise prediction, our framework uses the LLM as a preference machine that makes a relative comparative decision between the test instance and each demonstration. A self-supervised method is then introduced to aggregate these binary comparisons into the final ordinal decision. LAMPO addresses several limitations inherent in previous methods, including context length constraints, ordering biases, and challenges associated with absolute point-wise estimation. Extensive experiments on seven public datasets demonstrate LAMPO's remarkably competitive performance across a diverse spectrum of applications (e.g., movie review analysis and hate speech detection). Notably, in certain applications, the improvement can be substantial, exceeding 20% in an absolute term. Moreover, we believe LAMPO represents an interesting addition to the non-parametric application layered on top of LLMs, as it supports black-box LLMs without necessitating the outputting of LLM's internal states (e.g., embeddings), as seen in previous approaches.