Large Language Models (LLMs) are playing an increasingly influential role in human decision-making. While previous research has primarily considered LLMs as tools that assist human decision-making, less attention has been given to their role in shaping a co-creative decision-making process, in which humans and LLMs iteratively update their distributions through interactions. This study presents a theory and model of LLM-human interaction in co-creative decision-making, formulated within the framework of distributed Bayesian inference, where the iterative process can be interpreted as a sampling-importance-resampling (SIR) algorithm. To examine the validity of the model, we conduct two experiments: (1) a cooperative card-guessing task, analyzing how variations in agent interaction dynamics affect decision convergence, and (2) an iterative brainstorming task, exploring its applicability to broader decision-making contexts. This study aims to establish a theoretical foundation for adaptive and democratic LLM-human decision-making.