  Large language models (LLMs) excel on new tasks without additional training,
simply by providing natural language prompts that demonstrate how the task
should be performed. Prompt ensemble methods comprehensively harness the
knowledge of LLMs while mitigating individual biases and errors and further
enhancing performance. However, more prompts do not necessarily lead to better
results, and not all prompts are beneficial. A small number of high-quality
prompts often outperform many low-quality prompts. Currently, there is a lack
of a suitable method for evaluating the impact of prompts on the results. In
this paper, we utilize the Shapley value to fairly quantify the contributions
of prompts, helping to identify beneficial or detrimental prompts, and
potentially guiding prompt valuation in data markets. Through extensive
experiments employing various ensemble methods and utility functions on diverse
tasks, we validate the effectiveness of using the Shapley value method for
prompts as it effectively distinguishes and quantifies the contributions of
each prompt.
