The Dice Roll Method: A Standardized Protocol for Repeated-Query Auditing of Large Language Model Brand Recommendations

Background: Researchers increasingly use repeated identical prompts to audit stochastic variation in large language model (LLM) brand recommendations, yet no standardized protocol exists for setting iteration counts, selecting stability metrics, or establishing reliability thresholds. Objective: We formalize the Dice Roll Method as a reusable protocol for repeated-query auditing of LLM brand recommendations, grounded in a generative model of temperature-scaled nucleus sampling. Methods: Total response variance is decomposed into sampling, prompt-phrasing, run-to-run, and model-version components. The stack: a negative-binomial mixed model with iterations as repeated measures; Cliff's delta as the distribution-free effect size; dependence-preserving bootstrap; simulation-based power; a generalizability-theory decomposition; drift diagnostics on pinned snapshots. We reanalyse five brand-recommendation auditing studies: approximately 190,000 observations, 270+ brands, 6 languages, iteration counts 5 to 40. Results: Three tiers of iteration guidance emerge from the D-study: exploratory (n = 5, G = 0.58), confirmatory (n = 10, G = 0.74), and rigorous (n = 15, G = 0.81), tied to effect-size and generalizability targets. The four metric families (count, set, embedding, fairness-adjusted PASOR) are complementary, motivating a compact metric battery over single indicators. A pre-registered external validation on three independent corpora (Motoki et al., 100-round; Rozado, 24 models; llm-stability) reproduces the D-study reliability prediction in 37 of 39 cells with no failures and the n = 5 power value to two decimals; the fixed tiers do not transfer, supporting a pilot-then-solve reading. Conclusion: The protocol gives repeated-query auditing of LLM brand recommendations a statistically principled footing under the conditional, non-Gaussian structure of real autoregressive generation.

AIriskEval-edu: New Dataset for Risk Assessment in AI-mediated K-12 Educational Explanations

This work introduces AIriskEval-edu-db2, a new dataset designed to train and evaluate auditors based on LLMs for an explainable pedagogical risk assessment in instructional content for grades K-12. The dataset comprises 1,639 explanations from 170 curated ScienceQA questions, covering science, language arts, and social sciences. For each question, the dataset includes an explanation written by a human teacher alongside 11 explanations generated by LLM-simulated teacher profiles associated with distinct pedagogical risks. We propose a comprehensive risk rubric aligned with established educational standards that covers five complementary dimensions: factual precision, depth and completeness, focus and relevance, student-level appropriateness, and ideological bias. A key contribution is the addition of 785 explanations with structured explainability annotations, including risk localization and risk description. The annotations are produced through a semi-automatic process with expert teacher validation. Finally, we present validation experiments comparing state-of-the-art proprietary models with a lightweight local Llama 3.1 8B model in both the pedagogical risk detection and the explainability assessment. These experiments evaluate whether supervised fine-tuning on AIriskEval-edu-db2 enables a locally deployable model to approach or outperform stronger frontier models while preserving privacy in educational auditing and assessment tasks.