A M onte- C arlo Sampling Framework For Reliable Evaluation of Large Language Models Using Behavioral Analysis (2025)

Abstract: Scientific evaluation of Large Language Models is an important topic that quantifies any degree of progress we make with new models. Even though current LLMs show high level of accuracy on benchmark datasets, the single-sample approach to evaluating them is not sufficient as it ignores high entropy of LLM responses. We introduce a Monte-Carlo evaluation framework for evaluating LLMs that follows behavioral science methodologies and provides statistical guarantees for estimates of performance. We test our framework on multiple LLMs to see if they are susceptible to cognitive biases. We find significant effect of prompts that induce cognitive biases in LLMs, raising questions about their reliability in social sciences and business. We also see higher susceptibility of newer and larger LLMs to cognitive biases, which shows a development towards more human-like and less rational LLM responses. We conclude by calling for the use of Monte-Carlo sampling as opposed to pass@1 for the broader LLM evaluations.

## introduction large language models (llms) have demonstrated remarkable capabilities across a wide range of natural language tasks, from question answering to creative writing, reasoning, and code generation. despite the strong focus of current literature on mathematics, coding, and general question answering capabilities of large language models, llm use is expanding well beyond these areas. llms are increasingly integrated into critical applications across diverse fields such as healthcare @xcite @xcite , education @xcite @xcite , and decision support systems @xcite @xcite . in particular, there is growing interest in the application of large language models in social sciences. consumer behavior researchers are exploring how llms can simulate and replace human participants @xcite . there is unprecedented reliance on ai agents in making consumption decisions @xcite . despite this interest from researchers and consumers, the scientific literature has not addressed two major gaps in our understanding of llm behavior in social sciences settings. first, there is an absence of a proper evaluation framework for social sciences problems that properly accounts for high entropy of llm responses. second, there is a lack of llm evaluation beyond the standard benchmark datasets on coding, mathematics, and general questions answering. to address the first gap, we define a monte-carlo evaluation framework to gain a reliable estimate of llm performance. this framework accounts for the high level of entropy @xcite in llm responses, which is neglected by the standard evaluation practice. to address the second gap, we formulate an experimental setup inspired from consumer behavior literature that allows scientific testing of llms' performance in consumption settings. we focus specifically on the problem of pricing in economics and business. in our investigation, we ground our analysis in consumer choice theory by drawing on established models from behavioral economics, namely stochastic utility theory @xcite and prospect theory @xcite , which predict that consumer decisions stem from underlying latent utilities and that choices vary according to risk preferences, perceived value, and budget constraints. by analogously modeling the magnitude of maximum willingness-to-pay (wtp) elicited from llms, we evaluate whether these models, which have traditionally been applied to human decision-makers, hold predictive power for artificial decision-making systems. we further interrogate whether llm responses reflect systematic deviations from traditional rational behavior, such as anomalies in consistency and anchoring effects @xcite , by comparing the simulated choice patterns against norms predicted by economic theory. simultaneously, our study delves into emergent behavior using complex decision patterns that arise from the high-dimensional, data-driven learning process of llms, despite the absence of an explicitly programmed decision-making module. specifically, we aim to uncover whether the llms, when tasked with consumer-like evaluations (e.g., google's project mariner; deepmind (2025)), produce non-linearities or clustering in willingnessto-pay that mirror cognitive biases or contextual influences observed in human subjects. this article makes two main contributions. first, we identify and formalize the limitations of singlesample evaluation approaches for high-entropy llms, and introduce a monte-carlo sampling framework for llm evaluation that provides statistical reliability metrics beyond accuracy, which can be applied to general llm evaluation as well as social sciences and business. second, we show limitations of llms in uncertain decision making, by quantifying the between-and within-llm variance as well as their susceptibility to cognitive biases. ## related work consumer behavior and artificial intelligence consumers are increasingly utilizing artificial intelligence (ai) models in their everyday consumption. there is a rich literature on how consumers' respond to ai-generated outputs. artificially intelligent voice assistants (aivas) are commonly used in everyday purchase decisions @xcite . in their decision-making, consumers tend to trust ai models to the point of "overdepending" on them even when those the responses are suboptimal @xcite . specifically, in the context of online shopping, consumers rely on ai decision making without much thought @xcite . there is also an increase in intelligent llm-based agents that seek to replace humans in making purchase decision (e.g., google's project mariner (deepmind, 2025)) large language model bias as large language models continue to improve in natural language generation and consumers increase their trust and reliance on ai-generated decisions, it is imperative to understand potential llm biases when it comes to decision making. in recent years, there has been an emergence and growth in research on algorithmic bias. algorithmic bias refers to a phenomenon where a machine learning model displays similar social patterns as the ones embedded in the data used to train the model @xcite . prior research has investigated various cases where llms show social biases @xcite . this phenomenon has been mostly attributed to the implicit and explicit biases present in the training data of the llms (johnson, 2021) and the uncurated nature of the training data @xcite . another factor identified as the source of social biases in llms is the benchmark datasets used to fine-tune these models. gallegos et al. (2024) argue that llms are optimized on datasets that do not represent the broad population that will end up using these models. cognitive biases in large language models cognitive biases have long been one of the main points of focus for social sciences researchers @xcite . they refer to systematic biases that deviate from rational decision making @xcite . many behavioral biases have been studied in consumer behavior including framing effects @xcite @xcite @xcite @xcite , overgeneralization @xcite , overconfidence @xcite and anchoring effects @xcite . prior research has investigated the presence of cognitive biases in large language models @xcite @xcite . for code generation, @xcite tested two llms on some of the most common cognitive biases including anchoring bias and framing effects. the article provides indication of cognitive biases in llms for coding by showing how prompting llms can negatively affect their performance by introducing cognitive biases. even though these articles provide helpful indication of the presence of cognitive biases in llms, their methodological approach uses single-sample estimation to analyze llm behavior, which ignores high entropy of llms and does not provide a complete picture for stochasticity of llm responses. ## methodology the standard approach to evaluating llms involves measuring the "pass@1" accuracy (i.e., the correctness of a single response to a given prompt) across benchmark datasets @xcite @xcite @xcite . while this methodology provides a basic assessment of model capabilities, it fundamentally ignores the intrinsic variability in llm outputs. modern llms operate with nonzero temperature settings that introduce controlled randomness into their generation process @xcite , allowing them to produce more natural, creative, and human-like responses. this randomness is desirable for many applications, to the point that almost all llms use non-zero temperature. this non-zero temperature creates a critical challenge for model evaluation. the same model, given identical inputs, can produce substantially different outputs from one inference to the next. to illustrate this, consider an llm that sometimes exhibits strong anchoring bias in pricing judgments but at other times provides rational marketbased valuations in response to identical prompts. standard single-sample evaluation of the llm would categorize this model as either biased or rational depending solely on which single response was sampled. using our monte-carlo framework (algorithm 2), we sample multiple responses using the same llm and prompt. by analyzing the aggregated behavior of the llm, we statistically measure the reliability and the rationality of the llm, by obtaining the model's true probabilistic behavioral profile. this approach would allow us to make informed decisions when utilizing llms as decision aids in sensitive consumption choices. ## statistical framework here we present the statistical framework. the proofs to the theorem are presented in the appendix a.2. let f (p, y, r) denote an evaluation function that maps a prompt @xmath0, the correct response y, and a sampled response r ∼ m(p; t ) from a stochastic language model m at non-zero temperature t , to a real-valued score. define the true model behavior as the expectation: then, the monte-carlo evaluation framework has three main properties. first, the monte-carlo sample evaluation, vk (m; p, y), is an unbiased estimator of the true population evaluation. in the context of llm evaluation, this means that averaging multiple model responses to the same prompt provides an unbiased estimate of the model's true behavior, accounting for the inherent variability introduced by non-zero temperature sampling. second, the between-sample variance decays to 0 as k becomes large enough. third, the monte-carlo sample asymptotes to a normal distribution, n µ, σ 2 k . this allows us to define confidence intervals for llm predictions and evaluation metrics. corollary the normalized estimator follows a normal distribution as @xmath1: ## hypothesis development a large number of consumers rely on ai agents to help them with their pricing choice decision, in many cases without giving the response of the ai agent much thought @xcite . in this case, we know little about how llms behave in face of market-related decisions. do they act rationally, or do they fall prey to the same marketing manipulations as humans? to address these questions, we develop the following hypotheses. ## experiments this section details our experimental methodology for evaluating llm susceptibility to anchoring bias in consumer decision-making contexts using our monte-carlo framework. to demonstrate the effectiveness of our framework, we introduce a cognitive bias experiment drawn from consumer behavior and behavioral economics literature (tversky and @xcite @xcite . this experiment challenges llms with prompts designed to elicit anchoring @xcite @xcite . this experiment serves as an effective case study for the proposed evaluation framework, revealing how models may exhibit susceptibility to cognitive biases depending on sampling randomness.