Do LLMs Play Dice? Exploring Probability Distribution Sampling in Large
  Language Models for Behavioral Simulation
Jia Gu Liang Pang Huawei Shen Xueqi Cheng
With the rapid advancement of large language models (LLMs) and their
remarkable capabilities in handling complex language tasks, an increasing
number of studies are employing LLMs as agents to emulate the sequential
decision-making processes of humans often represented as Markov decision-making
processes (MDPs). The actions within this decision-making framework adhere to
specific probability distributions and require iterative sampling. This arouses
our curiosity regarding the capacity of LLM agents to comprehend probability
distributions, thereby guiding the agent's behavioral decision-making through
probabilistic sampling and generating behavioral sequences. To answer the above
question, we divide the problem into two main aspects: simulation where the
exact probability distribution is known, and generation of sequences where the
probability distribution is ambiguous. In the first case, the agent is required
to give the type and parameters of the probability distribution through the
problem description, and then give the sampling sequence. However, our analysis
shows that LLM agents perform poorly in this case, but the sampling success
rate can be improved through programming tools. Real-world scenarios often
entail unknown probability distributions. Thus, in the second case, we ask the
agents to change the activity level in online social networks and analyze the
frequency of actions. Ultimately, our analysis shows that LLM agents cannot
sample probability distributions even using programming tools. Therefore,
careful consideration is still required before directly applying LLM agents as
agents to simulate human behavior.