Abstract: We study few-shot reranking for multi-hop QA (MQA) with open-domain questions. To alleviate the need for a large number of labeled question-document pairs for retriever training, we propose PromptRank, which relies on language model prompting for multi-hop path reranking. PromptRank first constructs an instruction-based prompt that includes a candidate document path and then computes the relevance score between a given question and the path based on the conditional likelihood of the question given the path prompt according to a language model. PromptRank yields strong retrieval performance on HotpotQA with only 128 training examples compared to state-of-the-art methods trained on thousands of examples --- 73.6 recall@10 by PromptRank vs. 77.8 by PathRetriever and 77.5 by multi-hop dense retrieval.