PiCO: Peer Review in LLMs based on the Consistency Optimization

Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-09 08:21:44

Abstract: Existing large language models (LLMs) evaluation methods typically focus on testing the performance on some closed-environment and domain-specific benchmarks with human annotations. In this paper, we explore a novel unsupervised evaluation direction, utilizing peer-review mechanisms to measure LLMs automatically without any human feedback. 
In this setting, both open-source and closed-source LLMs lie in the same environment, capable of answering unlabeled questions and evaluating each other, where each LLM's response score is jointly determined by other anonymous ones. To obtain the ability hierarchy among these models, we assign each LLM a learnable capability parameter to adjust the final ranking.
We formalize it as a constrained optimization problem, intending to maximize the consistency of each LLM's capabilities and scores. 
The key assumption behind is that high-level LLM can evaluate others' answers more accurately than low-level ones, while higher-level LLM can also achieve higher response scores. 
Moreover, we propose three metrics called PEN, CIN, and LIS to evaluate the gap in aligning human rankings. 
We perform experiments on multiple datasets with these metrics, validating the effectiveness of the proposed approach.

Main paper: 
 introduction: 
 Goodhart's Law: "When a measure becomes a target, it ceases to be a good measure."Large language models (LLMs) [11, 2, 12, 43] have achieved remarkable success across a variety of real-world applications [54, 32, 36, 52] . With the increasingly widespread application of these models, there is an urgent need for an effective evaluation method to ensure that their performance and usability meet the growing demands. To assess the ability level of LLMs, a large number of evaluation benchmarks have been proposed by using some small and domain-specific datasets with human-curated labels, such as MMLU [26] , HELM [30] , Big-Bench [39] , GLUE [45] . However, these benchmarks can only measure LLMs' core capability on a confined set of tasks (e.g. multi-choice knowledge or retrieval questions), which fails to assess their alignment with human preference in open-ended tasks adequately [16, 28, 34] . On the other hand, these evaluations may suffer from benchmark leakage issue, referring that the evaluation data is unknowingly used for model training, which can also lead to misleading evaluations [49, 56] . Therefore, blindly improving scores on these public benchmarks cannot always yield a large language model that truly satisfies human requirements.For assessing human preferences, recent studies have focused on building crowdsourced battle platforms with human ratings as the primary evaluation metric. Typical platforms include Chatbot Arena [55] , MT-Bench [55] , and AlpacaEval [29] . It constructs anonymous battles between chatbots in real-world scenarios, where users engage in conversations with two chatbots at the same time and rate their responses based on personal preferences. While human evaluation is the gold standard for Submitted to 38th Conference on Neural Information Processing Systems (NeurIPS 2024). Do not distribute.Figure 1 : The framework of PiCO. In this framework, both open-source and closed-source LLMs lie in the same environment, capable of answering unlabeled questions and evaluating each other, where each LLM's response score is jointly determined by other anonymous ones. We assign each LLM a learnable capability weight to optimize the score ranking based on the consistency assumption, while reducing the entropy of the peer-review evaluation system. The consistency optimization aims to find a final score ranking that all LLMs "agree" it.measuring human preferences, it is exceptionally slow and costly [55] . In addition, adding a new LLM to the crowdsourced battle platforms also poses a cold-start issue [15] . Thus, a fundamental question arises: can we construct an unsupervised LLMs evaluation system without relying on any human feedback?Actually, in real human evaluation systems, people build their ability hierarchy based on different empirical assumptions. For example, majority voting [22, 10, 40] and rating voting [5] methods are widely used during the decision-making process, which are based on the wisdom of the crowds [40, 13, 50] and have been proven to lead to better results than that of an individual. Moreover, in the established practice of peer-review in academic research, scholars evaluate their academic level rankings based on the consistency assumption, i.e., scholars with stronger abilities have stronger persuasiveness for evaluating others, and can also obtain higher achievements. This paper attempts to explore whether similar phenomena exist in the LLMs evaluation systems.In this work, we propose PiCO, a Peer review approach in LLMs based on Consistency Optimization.In this setting, LLMs themselves act as "reviewers", engaging in mutual assessments to achieve comprehensive, efficient, and performance evaluations without relying on manually annotated data. This method aims to address the limitations of existing evaluation approaches and provide insights into LLMs' real-world capabilities. As shown in Figure 1 , both open-source and closed-source LLMs lie in the same environment and answer the open-ended questions from an unlabeled dataset.Then, we construct anonymous answer pairs, while randomly selecting other LLMs as "reviewers" to evaluate both responses with a learnable confidence weight w. Finally, we employ this weight and calculate the response scores G for each LLM based on the weighted joint evaluation. It is worth noting that the whole peer-review process works in an unsupervised way, and our goal is to optimize the confidence weights that re-rank the LLMs to be closer to human rankings.To achieve this, we formalize it as a constrained optimization based on the consistency assumption. We maximize the consistency of each LLM's capability w and score G while adjusting the final ranking to align with human preference more closely. The key assumption behind this is that high-level LLM can evaluate others' answers more accurately (confidence) than low-level ones, while higher-level LLM can also achieve higher answer-ranking scores. As a result, the entropy (controversy) of the whole peer-review evaluation system can be minimized. In other words, the consistency optimization aims to find a final score ranking that all LLMs have no "disputes" regarding.To evaluate the gap in aligning human rankings, we propose three metrics called PEN (Permutation Entropy), CIN (Count Inversions), LIS (Longest Increasing Subsequence). The experiments are conducted on multiple crowdsourcing datasets and validated on these three metrics. The experimental results demonstrate that the proposed PiCO framework can effectively obtain a large language models' leaderboard closer to human preferences. The contributions of this paper can be summarized as follows.• We explore a novel unsupervised LLM evaluation direction without human feedback, utilizing peer-review mechanisms to measure LLMs automatically. All LLMs can answer unlabeled questions and evaluate each other.• A constrained optimization based on the consistency assumption is proposed to re-rank the LLMs to be closer to human rankings.• We propose three metrics called PEN, CIN, and LIS on the PiCO framework for evaluating the gap with human preferences.• The experiments with these metrics on three crowdsourcing datasets validate the effectiveness of the proposed approach. 
the proposed approach: 
 In this section, we first describe the problem definition and preference alignment evaluation, and then introduce the proposed PiCO framework in detail.Problem Definition. In this subsection, we aim to measure the ability level of LLMs automatically without relying on human annotations. Thus we consider an unsupervised LLM evaluation scenario with an unlabeled dataset Q consisting of n open-ended questions, where Q = {Q i } n i=1 . In addition,we have a large language model pool M = {M j } m j=1 , which includes both open-source and closedsource models. Write M 1 ≻ M 2 to indicate that the LLM M 1 has stronger capabilities than the LLM M 2 . Thus, we can assume that the ground-truth ranking R * alignment with human preferences,EQUATIONand assume that the learned ranking R by different evaluation methods is as follows,EQUATIONThe goal is to build an LLM ranking R that aligns with human ranking R * , making the loss L of the both rankings tend towards 0, i.e., L( R, R * ) → 0 Preference Alignment Metrics. Before building LLM rankings, we first need to discuss how to evaluate aligned human rankings. Intuitively, the metrics we want mainly describe the differences between two arrays composed of ranking indices. Assuming that human ranking R * is defined as being well-ranked in ascending order ([1, 2, 3, ..., m]) as shown in Eq 1. Thus the metric is to quantify the randomness of the learned ranking array ([3, 1, 2, ..., m]) as shown in Eq 2. Based on this, we propose three metrics called PEN, CIN, and LIS, respectively.PEN (Permutation Entropy). Permutation entropy [8] is a concept used to quantify the complexity or randomness of time series data. It provides a measure of the irregularity or unpredictability of the order of values in a sequence. We thus utilize it to measure the gap with human rankings as follows,EQUATIONwhere π denotes different permutations, k is a hyper-parameter recommended to be set to 3 to 7, and we set k = 3 in this paper. Intuitively, it samples some subsequences and calculates the entropy for all permutation types. And the lower the permutation entropy in the learned LLM rankings, the closer it is to the ground-truth human rankings.p(π) = #{t|0 ≤ t ≤ m -k, (M t+1 , ..., M t+k ) ∈ π} m -k + 1 .Counting inversions [27] aims to measure the degree of disorder or "invertedness" in an array or sequence of elements. We thus define it as follows,EQUATIONWhere 1{•} is the indicator function that the value is 1 when the condition is met, otherwise it is 0.Intuitively, the fewer inverse pairs in the learned LLM rankings, the closer it is to the ground-truth human rankings.LIS (Longest Increasing Subsequence). The longest increasing subsequence aims to find the length of the longest subsequence in a given sequence of elements, where the subsequence is in increasing order. We utilize it to measure the degree of match with human rankings as follows,EQUATIONwheredp[i] = 1 + max {dp[j] | 1 ≤ j < i ∧ M j ≺ M i } . dp[i]represents the length of the longest increasing subsequence that ends with M i . LIS allows for a nuanced understanding of the degree to which the learned ranking aligns with the ideal human ranking, with a higher LIS length indicating greater alignment.The PiCO framework, depicted in Figure 3 , involves peer-review and consistency optimization stages.In the peer-review stage, we first collect an unlabeled dataset Q consisting of open-ended questions, and construct a large language model pool M that includes both open-source and closed-source LLMs. Then, we let all LLMs answer each unlabeled question to obtain the response set A. We shuffle the set and construct anonymous answer pairs, while randomly selecting other LLMs as "reviewers" to evaluate both responses with a learnable confidence w. Finally, we can obtain the answer-ranking data D and calculate the response score G for each large language model. In the consistency optimization phase, we maximize the consistency of each LLM's capability w and score G with constrained optimization, while re-ranking the LLMs to be closer to human rankings.Data Collection and LLMs Pool Construction. Benefiting from the creation of crowdsourced battle platforms, we accessed open assessment datasets from Chatbot Arena [55] , MT-Bench [55] ,and AlpacaEval [29] . These open datasets include critical fields such as "question_id" and "question_content." Utilizing the Chatbot Arena dataset, which features pairwise data from twenty LLMs with human preference annotations, we assembled an LLM pool M = {M j } m j=1 . Leveraging 33K human-annotated interactions from this dataset, we established a ground-truth ranking R * andgathered responses A = {{A j i } n i=1 } m j=1 for our dataset Q = {Q i } n i=1 .Answer-Ranking Data Construction Based on Peer Review. After obtaining the responses set A, we aim to generate answer-ranking data D through the peer-review mechanism. Specifically, for the same question Q i ∈ Q, we randomly construct a battle pair < A j i , A k i > for review. Each battle pair will be randomly assigned five models ("reviewers") to determine the winners or declare ties. Note that the model may evaluate its own answers, but the entire process is anonymous. As a result, we can obtain the quadruples (A j i , A k i , > w s ), indicating the "reviewer" M s believes that the answer A j i is better than answer A k i with a confidence w s . Therefore, the answer-ranking data D can be defined as follows,EQUATIONwhere i denotes the question index, and j, k, s indicate the model indices. w s is a learnable confidence of model M s , and > is a partial order relationship from {>, <, =}.As shown in Eq 6, following the peer-review mechanism, we construct anonymous answer pairs and randomly select other LLMs as "reviewers" to evaluate both responses with a learnable confidence w.Next, we expect to optimize the confidence w and re-rank the LLMs to be closer to human rankings.We thus propose the consistency assumption, i.e., high-level LLM can evaluate others' answers more accurately (confidence) than low-level ones, while higher-level LLM can also achieve higher answer-ranking scores. Formally, we maximize the consistency of each LLM's capability w and score G with constrained optimization as follows,EQUATIONs.t. G j = (A j i ,A k i ,>,w s )∼D 1{A j i > A k i } * w s ,where 1{•} is the indicator function that the value is 1 when the condition is met, otherwise, it is 0.G j denotes the response score of model M j , which is calculated by joint evaluation of other models.Moreover, we employ Pearson correlation [38] to measure the consistency between w and G. Note that we only introduce this straightforward implementation to validate our idea of PiCO. Other more advanced strategies may be employed to further improve the performance.Discussion: It is worth noting that the whole process (Eq. 6 and 7) works in an unsupervised way.The only thing we do is to adaptively assign each LLM a score that matches its abilities. An intuitive example is as follows: in a real peer-review system, if the academic level of three scholars a, b, and c satisfies the following relationship, w a > w b > w c . So, in the ultimate ideal scenario, the ranking of the scores submitted by these three scholars should also be,G a > G b > G c .In other words, the sorting of G and w satisfies high consistency. On the other hand, scholars with stronger abilities (i.e., scholar a) evaluate A b > A c have stronger persuasiveness, so scholar b should also receive higher weighted scores 1 * w a .Reviewer Elimination Mechanism. Realizing that not all LLMs have sufficient ability to evaluate the responses of other models. We thus introduce an unsupervised elimination mechanism to remove those LLMs that have low scores. It iteratively removes the lowest-scoring LLM from the "reviewer queue" for the next consistency optimization stage, until 60% of models are eliminated. The whole process of the approach is summarized in Algorithm 1, and the details can be found in Appendix D.Question: Does the paper discuss the limitations of the work performed by the authors?Answer: [No] Justification: Although this paper does not have a separate 'Limitations' section, the consistency assumptions on which the work is based are clearly stated in the introduction, and their validity is experimentally verified in Section 3.5. Moreover, the limitations of our work are discussed in the conclusion, noting that the current study is conducted solely within a text-based llm evaluation environment, and exploring the potential for future expansion into multimodal large model assessments.Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.• The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.• The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.• The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.• The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.• If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.• While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best• The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.• The full details can be provided either with the code, in appendix, or as supplemental material. 
experiments: 
 Datasets. To validate the effectiveness of the proposed approach, we perform experiments on Chatbot Arena [55] , MT-Bench [55] , and AlpacaEval [29] . The MT-Bench dataset assesses six LLMs' responses to 80 multi-category questions. The Chatbot Arena Conversations Dataset, with 33K conversations from 13K IPs during April-June 2023, evaluates real dialogue performance. AlpacaEval dataset Majority Voting [40] 1.27 ±0.05 1.30 ±0.03 1.36 ±0.06 1.37 ±0.03 1.30 ±0.06 1.27 ±0.04 1.26 ±0.02 1.28 ±0.03 1.29 ±0.03 Rating Voting [5] 1.39 ±0.02 1.43 ±0.03 1.42 ±0.07 1.32 ±0.03 1.35 ±0.04 1.38 ±0.04 1.34 ±0.03 1.37 ±0.03 1.34 ±0.08 GPTScore(flan-t5-xxl) [23] 1.68 ±0.01 1.68 ±0.02 1.65 ±0.02 1.72 ±0.02 1.70 ±0.02 1.68 ±0.03 1.55 ±0.02 1.57 ±0.03 1.60 ±0.01 GPTScore(davinci-002) [23] 1.54 ±0.02 1.64 ±0.02 1.68 ±0.05 1.51 ±0.02 1.61 ±0.01 1.61 ±0.04 1.25 ±0.02 1.23 ±0.08 1.26 ±0.14 PandaLM [46] 1.65 ±0.01 1.64 ±0.02 1.63 ±0.05 1.55 ±0.03 1.59 ±0.05 1.52 ±0.08 1.56 ±0.01 1.58 ±0.01 1.64 ±0.05 PRD [28] 1.15 ±0.04 1.12 ±0.05 1.13 ±0.06 1.15 ±0.05 1.17 ±0.06 1.23 ±0.04 1.21 ±0.04 1.22 ±0.06 1.23 ±0.07 PRE [17] 1.07 ±0.01 1.03 ±0.03 1.06 ±0.04 1.17 ±0.04 1.13 ±0.05 1.19 ±0.05 1.18 ±0.03 1.21 ±0.04 1.15 ±0.05 PiCO (Ours) 0.94 ±0.02 0.96 ±0.04 0.95 ±0.08 1.01 ±0.07 1.02 ±0.11 1.06 ±0. 24 1.17 ±0.02 1.17 ±0.08 1.13 ±0.05Majority Voting [40] 22.00 ±0.00 23.25 ±1.09 25.00 ±2. 55 23.00 ±0.00 20.50 ±0.87 21.00 ±1.00 20.00 ±0.00 21.25 ±1. 30 22.25 ±1.30 Rating Voting [5] 24.00 ±0.00 24.50 ±1. 29 25.00 ±1. 15 22.00 ±0.00 22.50 ±1.00 24.25 ±0. 50 22.00 ±0.00 22.50 ±0.58 22.50 ±1.00 GPTScore(flan-t5-xxl) [23] 67.00 ±0.00 66.50 ±0.50 68.25 ±1.09 53.00 ±0.00 55.75 ±2.77 54.50 ±2. 29 35.00 ±0.00 36.00 ±0.71 37.75 ±1.60 GPTScore(davinci-002) [23] 42.00 ±0.00 45.50 ±1.12 51.00 ±5.61 33.00 ±0.00 35.00 ±0.71 36.25 ±1.64 21.00 ±0.00 20.25 ±2.86 21.50 ±4.39 PandaLM [46] 37.00 ±0.00 36.25 ±1.79 36.00 ±3.74 32.00 ±0.00 33.00 ±3. 32 31.50 ±6. 34 31.00 ±0.00 32.25 ±1. 30 35.50 ±2.60 PRD [28] 17.00 ±0.00 16.25 ±0. 43 17.50 ±1. 50 17.00 ±0.00 17.75 ±1.09 19.50 ±1. 50 19.00 ±0.00 19.25 ±1. 48 19.50 ±0.87 PRE [17] 15.00 ±0.00 14.25 ±0.83 14.75 ±1.09 17.00 ±0.00 17.00 ±1.00 18.25 ±1. 30 19.00 ±0.00 19.25 ±1.09 17.75 ±1.30 PiCO (Ours)12.00 ±0.00 12.50 ±0. 50 12.25 ±1.09 14.50 ±0. 50 14.75 ±1.64 16.00 ±6. 36 17.00 ±0.00 18.00 ±1.87 17.25 ±1.09Majority Voting [40] 7.00 ±0.00 6.75 ±0.43 6.75 ±0. 43 7.00 ±0.00 8.25 ±0. 43 8.50 ±1.12 8.00 ±0.00 7.50 ±0.50 7.50 ±0.50 Rating Voting [5] 7.00 ±0.00 7.50 ±0.58 7.75 ±0. 50 7.00 ±0.00 7.25 ±0.50 7.25 ±0.50 8.00 ±0.00 8.00 ±0.00 8.00 ±0.00 GPTScore(flan-t5-xxl) [23] 5.00 ±0.00 5.00 ±0.00 4.00 ±0.71 4.00 ±0.00 4.50 ±0.50 4.75 ±0.43 6.00 ±0.00 6.00 ±0.00 6.00 ±0.00 GPTScore(davinci-002) [23] 8.00 ±0.00 6.25 ±0.43 6.00 ±0.71 6.00 ±0.00 6.50 ±0.50 6.25 ±0. 43 8.00 ±0.00 8.25 ±0.83 8.25 ±1.48 PandaLM [46] 5.00 ±0.00 5.50 ±0.50 6.00 ±0.00 7.00 ±0.00 7.00 ±0.71 7.25 ±0.43 6.00 ±0.00 5.75 ±0. 43 5.50 ±0.50 PRD [28] 8.00 ±0.00 8.75 ±0. 43 9.25 ±0.83 8.00 ±0.00 8.25 ±0. 43 7.75 ±0.83 8.50 ±0.00 8.25 ±0.83 8.25 ±0.43 PRE [17] 9.00 ±0.00 10.25 ±0. 43 10.00 ±0.87 8.00 ±0.00 8.50 ±0. 50 8.25 ±0.83 8.00 ±0.00 8.00 ±0.00 8.25 ±0.43 PiCO (Ours)10.00 ±0.00 10.25 ±0.71 10.50 ±0. 43 8.75 ±0. 43 8.75 ±0.87 9.00 ±1. 22 9.00 ±0.00 8.75 ±0. 43 8.50 ±0.50 integrates 805 evaluations from diverse tests (e.g., Self-Instruct [48] , OASST, Anthropic's helpful [7] ,Vicuna [16] and Koala [25] test sets) to align evaluations real-world interactions [21] . These datasets are collected by crowdsourcing platforms from human feedback, so they have a ground-truth ranking LLMs R * aligned with human preferences.LLMs Pool. In our experiments, we employ 15 LLMs with diverse architectures to construct the LLMs pool, including GPT-3.5-Turbo [35] , WizardLM-13B [51] , Guanaco-33B [1] , Vicuna-7B [16] ,Vicuna-13B [16] , Koala-13B [24] , Mpt-7B [42] , gpt4all-13B [6] , ChatGLM-6B [53] , Oasst-sft-4-pythia-12B [19] , FastChat-T5-3B [55] , StableLM-7B [3] , Dolly-12B [18] , LLaMA-13B [43] , Alpaca-13B [41] .All models use the same evaluation template, they can be found in Appendix B Baselines. To validate the effectiveness of the proposed PiCO approach, we compare the following methods in the experiments.• The wisdom of the crowds: The two methods that perform LLMs evaluation based on the wisdom of the crowds [40, 13, 50] are compared in this experiment. 1) Majority Voting [40] : Multiple review models vote for the better answer for the same response pair, and the model with the most votes gets 1 score; 2) Rating Voting [5] : Multiple review models also vote on the same response pair, and the number of votes obtained is the score.• State-of-the-art methods: The four recent SOTA methods of using either single or multiple models for self-evaluation are compared in this experiment. PandaLM [46] : It is a fine-tuned language model based on Llama-7b designed for the preference judgment tasks to evaluate and optimize LLMs. GPTScore [23] : It employs generative pre-trained models to assess the quality of generated text. It calculates the likelihood that the text was generated in response to specific instructions and context, indicative of high quality. In our implementation, GPT-3 (davinci-002) and flan-t5-xxl serve as the base models. PRD [28] : It transforms the LLMs win rates into weights for competitive ranking, while evaluating each LLM based on its preference for all possible pairs of answers, enabling a tournament-style ranking system.PRE [17] : It employs a supervised process to evaluate LLMs using a qualification exam, aggregates their scores based on accuracy, and assigns weights accordingly. PiCO (Ours):the proposed approach in this paper.Metrics. For all experiments, we employ three metrics to evaluate the aforementioned experimental setups and our Peer Review method: PEN, CIN, and LIS. Moreover, we perform the experiments for 4 runs and record the average results over 4 seeds (seed = 1, 2, 3, 4). We validate the effectiveness of the proposed PiCO method on three datasets by comparing the following two types of methods, i.e., the wisdom of the crowds and recent SOTA LLMs evaluation methods. The average results of PEN, CIN and LIS are demonstrated in Table 1 . The ratios of response sets D are 1, 0.7, and 0.4, respectively.The results presented in Table 1 illustrate the proposed PiCO method consistently surpasses competing approaches across the majority of evaluated metrics Notably, PiCO achieves performance improvements of 0.1, 2.5, and 0.92 on the PEN, CIN, and LIS metrics, respectively, compared to the Runner-up. These results underscore the superiority of aggregating evaluations from multiple models, such as Majority Voting, Rating Voting, PRD, and PRE, as opposed to relying solely on single-model methods like GPTScore and PandaLM. This collective model approach, leveraging 'the wisdom of the crowds', more accurately aligns with human rankings in our open-question evaluation framework.In comparison with existing peer review evaluation methods(i.e., PRD and PRE), it is evident that PiCO exhibits improvements across various evaluation metrics. Despite PRD's adjustment of model weights based on their win rates and PRE's reliance on supervised human feedback data to assign weights through a qualification exam, neither method achieves performance superior to the fully unsupervised PiCO approach. These methods rely on predefined criteria and human feedback, potentially leading to biases or suboptimal performance. In contrast, PiCO leverages unsupervised learning techniques, allowing it to autonomously adapt and discover patterns in the data without explicit human intervention.It is important to highlight that PandaLM, a language model equipped with 7 billion parameters, was fine-tuned using labels generated by GPT-3.5-turbo as the ground truth, achieving stable performance across various datasets. However, in our unsupervised, open-ended experimental setup, which focuses on ranking-based metrics, GPTScore exhibits less robustness regardless of whether the base model is GPT-3 (davinci-002) or flan-t5-xx.In this subsection, we will show that the confidence weight w learned by our consistency optimization can reduce the system evaluation bias. Specifically, we first study whether the "review" model would prefer a particular model's response. Following [17] , we employ the preference gap (PG) to evaluate the bias as follows,EQUATIONwhere P i (i > j) represents the winning rate of model i as the "reviewer" believes that i defeated j. The heatmap distribution of the PG value P G(i, j) among seven LLMs across three datasets is demonstrated in the first row of Figure 4 . It can be observed that the evaluation system exhibits severe bias. Especially on ChatGLM-6B and Mpt-7B models, they often believe that their results are better than other ones, as their PG values are greater than 0 across three datasets.After the consistency optimization, we assign the learned confidence weight w to the corresponding model and ultimately obtain the re-weighting PG value P G(i, j) as follows,EQUATIONThe results of the re-weighting PG value P G(i, j) are displayed on the second row of Figure 4 . It can be observed that the learned confidence weight w can significantly mitigate the preference gaps of the whole evaluation system. In our consistency optimization, LLMs such as ChatGLM-6B and Mpt-7Bhave lower weights, and reducing their confidence can effectively alleviate the system evaluation bias.The PiCO and PRE [17] methods both employ elimination mechanisms to remove those weakest LLMs from the "reviewer queue" during the evaluation process. As shown in Figure 5 , the x-axis quantifies the number of reviewers eliminated, and the y-axis measures the CIN, where lower scores denote higher performance. Due to space limitations, more results on PEN and LIS metrics can be found in Appendix E. It can be observed that both PiCO and PRE exhibit better performance with an increasing number of eliminated "reviewers". The proposed PiCO approach can achieve better performance than PRE in most cases. It is worth noting that the PRE method employs the accuracy of "qualification exams" to eliminate weak LLMs, and this process requires human annotation [17] .On the contrary, the elimination process of our PiCO method is unsupervised and can still achieve better evaluation results than PRE.In this subsection, we conduct the ablation study to validate the effectiveness of the consistency assumption. Specifically, we first manually construct three methods: Forward Weight Voting, Uniform Weight Voting, and Reverse Weight Voting. That is, the ability weights of the model are respectively weighted forward (w = [1, 0.9, ..., 0]), uniformly (w = [1, 1, ..., 1]), and backward (w = [0, 0.1, ..., 1]) according to the ground-truth human ranking. Then, we randomly initialize the ability weights and employ our consistency optimization to adjust the weight. In addition, we also collect the average performance of "reviewer queue", i.e., employing a single LLM as the "reviewer"to evaluate all response pairs and then calculate the average results of all LLMs.As shown in Table 2 , it can be observed that the Forward Weight Voting achieves better results than the Uniform and Backward ones in all cases, while the Backward one achieves worse results. It validates that assigning larger weights to those models with stronger capabilities can obtain better 26 38.80 ±19. 28 1.50 ±0. 23 33.13 ±13.97 Backward Weight Voting 1.43 ±0.04 25.00 ±0.00 1.43 ±0.05 26.00 ±0.00 1.36 ±0.03 24.00 ±0.00 Uniform Weight Voting 1.34 ±0. 23 22.00 ±0.00 1.39 ±0.02 24.00 ±0.00 1.34 ±0.03 22.00 ±0.00 Forward Weight Voting 1.32 ±0.03 21.00 ±0.00 1.33 ±0.03 23.00 ±0.00 1.30 ±0.05 21.00 ±0.00 Random Weight + Consistency Optimization 1.17 ±0.06 17.50 ±0. 50 1.20 ±0.08 18.00 ±1. 22 1.21 ±0.04 19.00 ±0.00 results. Most importantly, employing our consistency optimization algorithm to assign weights to different review models can further improve the performance of the evaluation system, i.e., lower PEN and CIN, as well as higher LIS in all cases. Moreover, it is worth noting that the average performance of the "reviewer queue" is very poor, even worse than the Backward Weight Voting. This means that the answer-ranking data D contains a lot of evaluation noise, while the proposed approach can still optimize weights and obtain better ranking results. In summary, the above experimental results validate the effectiveness of the consistency assumption from various perspectives. 
related work: 
 Evaluation Benchmarks for Diversity. LLMs are designed to handle a variety of tasks, necessitating comprehensive benchmarks [15] . Notable benchmarks include GLUE [45] and SuperGLUE [44] , which simulate real-world scenarios across tasks such as text classification, translation, reading comprehension, and dialogue generation. HELM [30] provides a holistic evaluation of LLMs, assessing language understanding, generation, coherence, and reasoning. BIG-bench [39] pushes LLM capabilities with 204 diverse tasks. MMLU [26] measures multitask accuracy across domains like mathematics and law. However, these evaluations can be compromised by benchmark leakage, where evaluation data inadvertently used for training leads to inflated performance metrics [4, 56] .Human Evaluation. Human evaluation provides reliable feedback that closely aligns with realworld applications [15] . Liang et al. [30] evaluated summary and misinformation scenarios across multiple models. Ziems et al. [57] involved experts to assess model outputs in various domain-specific tasks. Bang et al. [9] examined ChatGPT's performance in summarization, translation, and reasoning using human-annotated datasets. The LMSYS initiative introduced platforms like Chatbot Arena [55] , relying on human ratings as the primary evaluation metric. Despite its effectiveness, human evaluation is costly and subject to bias and cultural differences [37] .Large Language Models for Evaluation. The development of open-source LLMs has led to the use of LLMs as evaluators. GPTScore [23] uses models like GPT-3 to assign probabilities to highquality content through multidimensional evaluation. Bubeck et al. [12] tested GPT-4, finding it rivaling human capabilities. Lin and Chen introduced LLM-EVAL [31] for evaluating dialogue quality with single prompts. PandaLM [46] employs LLMs as "judges" for evaluating instruction tuning.However, reliance on a single model can introduce biases such as positional [20] , verbosity [47] , and self-favoring biases [33, 55] . ChatEval [14] proposes a multi-agent framework to simulate human evaluation processes. Similarly, PRE [17] and PRD [28] use LLMs as evaluators, combining multiple evaluation outcomes for automated assessment. However, the PRE method, which relies on human feedback for supervised evaluation throughout the process, still incurs relatively high costs. 
conclusion: 
 In this paper, we propose the novel Peer Review method based on the Consistency Optimization (PiCO) to automatically evaluate Large Language Models (LLMs) without relying on human feedback.PiCO utilizes peer-review mechanisms to autonomously assess LLMs in a shared environment, where both open-source and closed-source models can respond to unlabeled questions and evaluate each other. In this setup, each LLM's response score is determined collectively by other anonymous models, aiming to maximize consistency across capabilities and scores. We propose three metrics, i.e., PEN, CIN, and LIS, to quantify the disparity from human preferences. The extensive experiment results across multiple datasets and metrics demonstrate that PiCO effectively generates an LLM leaderboard that aligns closely with human preferences. In the future, we plan to extend the peerreview mechanism to evaluate the capabilities of multi-modality large models. interactions involving factual inquiries, such as mathematics or logic problems, where accuracy and reference to correct information are paramount.Template for Multi-Turn Interaction: This template caters to multi-turn conversations between users and LLMs, without predefined answers. It supports extended interactions, enabling users to explore topics in depth through a series of interconnected questions and responses.Referenced Template for Multi-Turn Interaction: Designed for multi-turn dialogues with predefined correct answers, this template is ideal for complex inquiries requiring sequential reasoning or problem-solving, such as mathematical computations or logical deductions.Each template is carefully constructed to match its intended use-case, providing a structured framework that guides the interaction between users and LLMs towards achieving desired outcomes, whether for open-ended exploration or precise problem-solving. 
experiment statistical significance: 
 Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?Answer: [Yes]Justification: We conducted each experiment four times using different seeds (seed = 1, 2, 3, 4) to ensure robustness. The results, presented as averages, are accompanied by standard deviations as error bars in Tables 1 and 2 . This approach captures the variability due to different initializations and confirms the reproducibility of our results. The standard deviations used help clarify the extent of variability in the experiments, ensuring that our statistical analysis aligns with best practices for empirical research.Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.• The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions).• The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)• The assumptions made should be given (e.g., Normally distributed errors).• It should be clear whether the error bar is the standard deviation or the standard error of the mean.• It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified.• For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).• If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text. 
experiments compute resources: 
 Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?Answer: [No] Justification: Although we did not detail the exact compute resources for each experimental setup in the paper, we used NVIDIA A6000 graphics cards for open-source models and API calls for proprietary models. To facilitate reproducibility, we have provided all necessary data, ensuring that the experiments can be replicated on consumer-grade computers. This approach allows readers to reproduce the results without requiring high-end computational resources.Guidelines:• The answer NA means that the paper does not include experiments.• The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.• The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.• The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper). 
code of ethics: 
 Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?Answer: [Yes]Justification: The research conducted in this paper complies with the NeurIPS ethics guidelines in all respects.Guidelines:• The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.• The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 
broader impacts: 
 Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?Answer: [Yes]Justification: In the introduction, we discuss the potential positive impact of our novel unsupervised LLM evaluation approach, which could significantly advance the field of LLM evaluation. However, we also recognize potential negative societal impacts, such as the misuse of this technology to unfairly or inaccurately assess LLM systems, which might lead to biased or misleading outcomes. We suggest potential mitigation strategies, such as implementing robust validation protocols and ethical guidelines to govern the application of this evaluation methodology.Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.• Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.• The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.• The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.• If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?• The paper should discuss whether and how consent was obtained from people whose asset is used.• At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file. 
crowdsourcing and research with human subjects: 
 Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?Answer: [NA] Justification: This paper focuses on an unsupervised evaluation method for LLMs that does not require human feedback or interaction. Consequently, there is no involvement of crowdsourcing or research with human subjects, making details about participant instructions and compensation irrelevant.Guidelines:• The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.• Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper.• According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector. Guidelines:• The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.• Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.• We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.• For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review. 
 
 Appendix: System prompt: Please act as a judge and evaluate the quality of the responses provided by two AI assistants to the user question displayed below. You do not need to explain, just give your judgment. Output your final verdict by strictly following this format: " [[A]]" if assistant A is better, "[[B]]" ifIn Section 2.2.2, Equation 7delineates the methodology for optimizing scores. Within this framework, the function1{A j i > A k i } is more precisely defined as f (A j i , A k i ).Additionally, the functionf (A j i , A k i )is not fixed and can be implemented using various computational strategies. We introduce two distinct methodologies in this context: the Elo mechanism and the Rank mechanism.Within the framework of the Elo mechanism, as specified by Equation 10, the BASE value is set to 10, and the SCALE factor is determined to be 400. This approach facilitates a dynamic adjustment of scores based on the outcomes of pairwise comparisons, allowing for a nuanced reflection of performance variations among models.Conversely, in the context of the Rank mechanism, as outlined by Equation 11, rank(j) signifies the current ranking of model j, with the constant K assigned a value of 200. This mechanism employs a model's ranking within a predefined hierarchy as a pivotal factor in score calculation, thereby providing a straightforward, yet effective, method for evaluating comparative model performance.f (A j i , A k i ) =      1 - 1 1+BASE ((G(k)-G(j))/SCALE) if A j i > A k i 0.5 - 1 1+BASE ((G(k)-G(j))/SCALE) if A j i = A k i 0 - 1 1+BASE ((G(k)-G(j))/SCALE) if A j i < A k i (10) f (A j i , A k i ) =      1 + (rank(j) -rank(k))/K if A j i > A k i 0.5 if A j i = A k i 0 if A j i < A k i (11)The overall algorithm, as delineated in Algorithm for each question q i ∈ Q do 3:Initialize response vector for question q i , A i ← ∅4:for each model m j ∈ M do 5:A i j ← response of model m j to question q i 6:A i ← A i ∪ {A i j } 7:end for 8:Shuffle A i to obtain permuted response vector A iA ← A ∪ {A i } 10: end for 11: Initialize answer-ranking data D ← ∅ 12: Initialize model weights vector w with Gaussian distribution 13: for each permuted response vector A i do 14:for each pair of responses(A j i , A k i ) in A i do 15:for s ← 1 to 5 do ▷ Randomly select 5 models for evaluation 16:Evaluate the pair (A j i , A k i ) with model m s 17:D ← D ∪ {(A j i , A k i , > w s )} 18:end for for each model m j ∈ M do 25:Compute G j using updated formula: 26:G j = i k̸ =j s̸ =k,s̸ =j 1{A j i , A k i } × w s (A j i , A k i , > w s , s ∈ M * ) ∈ D 27:end for 28:Update weight vector w to maximize the consistency of w and Gend whileSort M * by G j to identify M min , the lowest-scoring model 31:if size of M * > threshold then 32:Remove M min from M *end if 34: until size of M * < threshold 35: Compute the final ranking R * based on the optimized scores G j 36: return R *In Section 3.4, we both employ elimination mechanisms to cull the weakest LLMs from the 'reviewer queue' during the evaluation process. In Figures 7 and 8 , we present the results for the PEN and LIS metrics, where lower PEN scores indicate better performance, and higher LIS scores denote superior performance. It is evident that both the 'PiCO' and PRE approaches demonstrate enhanced performance as the number of eliminated 'reviewers' increases. In most cases, the proposed 'PiCO' method outperforms PRE. In Section 3.5, we validate the effectiveness of the consistency assumption and compare it with the Average Performance of the Reviewer Queue, i.e., employing a single LLM as the 'reviewer' to evaluate all response pairs and then calculating the average results of all LLMs. The comprehensive results compared with the Reviewer Queue are illustrated in Table3, Figure 9 , 10 and 11, revealing that in the full Reviewer Queue, the performance of the vast majority of LLMs is very poor, indicating that the evaluations from most LLMs are noise. However, our 'PiCO' approach nearly matches the evaluative prowess of the pool's most capable LLM, GPT-3.5. Remarkably, given its unsupervised nature, the 'PiCO' method demonstrates the capability to mitigate the influence of noise, reaching the For our analysis, we meticulously selected 15 LLMs spanning a variety of architectures, encompassing both open-source and closed-source models, as detailed in the subsequent table. Our curated selection features prominent LLMs including the closed-source "gpt-3.5-turbo," "chatglm" which is predicated on the encoder-decoder framework, "fastchat-t5-3b" that leverages Google's T5 (Text-to-Text Transfer Transformer) architecture, and "llama-13b" founded on the GPT architectural principles.We have comprehensively detailed the ranking outcomes across three distinct datasets for our comparative analysis, incorporating the optimized model rankings, names, and their respective scores. Justification: We clearly state our claims in the abstract and introduction, such as a novel unsupervised LLM evaluation method and a consistency-based constrained optimization approach. These are substantiated in Section 3, demonstrating the alignment between our theoretical contributions and empirical results.Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper.• The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.• The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.• It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. 


Decision: This paper addresses the important issue of evaluating LLMs without relying on human feedback. 

The reviewers acknowledged the novelty and potential of the proposed method, but also raised a number of more serious concerns.

These concerns include clarifying the presentation (including writing, mathematical notation, equations, etc.), providing more evidence in support of the underlying assumptions (related to the existence of larger LLMs that can rate smaller ones consistently well), the computational cost of the approach, and fundamental questions about the evaluation methodology (why not consider more standard rank-based metrics?)

This is promising work and the authors are strongly encouraged to carefully consider the reviewer feedback when preparing an updated version of their paper to improve the clarity and to strengthen the arguments in favor of the proposed method.

Reviews: review: paper_summary: paper_summary: The highlight of the work is the proposed method of evaluating Large Language Models without relying on human feedback.
strength_weakness: strength_weakness: Some of the equations and notations in the paper seems unnecessarily complicated, which can be reorganized when polishing.
questions: questions: 1. How do you define unlabeled questions in line76, as in to what extend is a question unlabeled?
2. How do you differentiate high-level from low-level LLMs? Are they interchangeable or more of a dynamic definition while evaluating on different tasks?
limitations: limitations: The idea is straightforward and make sense to me. But LLMs can be trained to bypass such systems, which may lead to potential fairness or security problems.
paper_summary: paper_summary: In this paper, the authors propose a more reliable evaluation system to rank the abilities of different large language models (LLMs). Previous evaluation methods typically suffer from two main drawbacks: (1) benchmark data leakage and (2) cost-intensive and potentially biased human evaluations. To address these issues, the authors introduce an unsupervised evaluation mechanism to measure the abilities of LLMs and derive their rankings. The core idea of this mechanism is to first collect the answers from each LLM, then treat each LLM as a 'reviewer' to rate the quality of the other LLMs' answers, and finally optimize the internal agreement of the reviews among all LLMs. They also conduct experiments on three datasets to validate the effectiveness of their proposed mechanism.
strength_weakness: strength_weakness: 1. Reliance on Consistency Assumption: The effectiveness of the method relies on the consistency assumption that higher-level LLMs can more accurately evaluate others. However, a natural concern is, "Does this assumption always hold true in practice?" I suggest the authors further discuss the applicability of their method.
2. Complexity of Implementation: The framework involves a complex review process, which requires substantial computational resources to support the LLMs' inference. Can you provide some details on the number of tokens consumed and a comparison of consumption with baseline methods?
3. Consideration of Multi-Agent Methods: Since the proposed method employs multiple LLMs, I think more recent and advanced evaluation methods based on multi-agent systems should also be considered in the experiments, such as AgentVerse.
4. Details of ELO: The ELO system is essential for the proposed mechanism. However, it is only mentioned in the appendix. I suggest the authors add more details about the background of ELO and how it is adopted in the proposed mechanism.
questions: questions: Please see my above comments
limitations: limitations: Yes
paper_summary: paper_summary: This paper studies how to estimate LLMs' performance ranking without human preference annotations. In particular, it proposes to leverage three metrics (PEN, CIN, LIS) to evaluate the estimation quality, gives an estimation mechanism that first asks a list of LLMs (called "reviewers") to rank pairwise answers to user questions independently, and then aggregates their ranking via a weighted sum approach. A consistency optimization determines the weights of each reviewer.
strength_weakness: strength_weakness: While I find the proposed problem interesting, there are still a few limitations, unfortunately.

***Unclear implication of ground truth ranking***: The technical part of the paper starts by introducing a ground truth ranking (equation (1)) without giving its physical meaning. It simply assumes "[...] alignment with human preferences", but it is not clear what human preferences mean in this context. 

***Evaluation metric is strange***: One of my major concerns is on the choices of evaluation metric. All the three proposed metrics, PIN, CIN, LIS, in the authors' own words, seem originally used for time series comparison. However, the goal here is to compare rankings, not time series. Thus, it is unclear why we should not use the standard ranking comparison metrics, e.g., Spearman's rank correlation coefficient or Kendall rank correlation coefficient.

***Consistency optimization algorithm is not provided***: The core of the proposed ranking estimation method is the optimization problem (7). It does not seem to be a standard optimization problem, but I could not find (even a discussion on) any clue on how to solve it in this paper.

***An optimal solution to the consistency optimization formulation can be useless***: I find the following optimal solution to the problem (7): just set weight w to be 0 for all LLMs. It is an optimal solution as G and w are identical and thus the objective is always maximized.  However, this solution is undesired. I probably misunderstood something, but this seems to suggest the formulation is incorrect. 

***Consistency optimization formulation seems brittle to query distribution biases***: Another problem with the formulation is that it seems brittle to data distribution bias. E.g., suppose M1 is indeed better than M2 for some query q. And let us replicate many copies of q in the dataset D. Then the grade G1 can be arbitrarily large. In other words, the grade of an LLM is proportional to the number of battles involving it in the dataset D, which should not be the case.

***Choices of LLMs for evaluation***: In line 547, the authors write "For our analysis, we meticulously selected 15 LLMs". What is the principle of the meticulous selection? Other than open-source and close-source, the selection is quite arbitrary. For example, I am quite surprised to not see GPT-4 and Claude included in the reviewer LLMs.

***Comparison with a simple baseline***: One simple baseline is to ask a powerful LLM(e.g., GPT-4, Cluade-3) to give a preference for each answer question pair, and then take the vote to determine the ranking. I would suggest to compare the proposed method with this simple baseline.
questions: questions: ***Unclear implication of ground truth ranking***: What is the physical meaning of the ground truth ranking? What does that imply?

***Evaluation metric is strange***: What is the motivation of using time series comparison metrics to compare rankings? How does the proposed method work under ranking comparison metrics?

***Consistency optimization algorithm is not provided***: How do you solve problem (7)?

***An optimal solution to the consistency optimization formulation can be useless***: How do you prevent the useless but optimal solution? Does that imply the formulation is incorrect? 

***Query distribution and LLM judgment biases***: How could this formulation resist query distribution and LLM biases?

***Choices of LLMs for evaluation***: What is the principle of the meticulous selection? How does the proposed approach work if strong models such as GPT-4 and Claude are included in the reviewer LLMs? 

***Comparison with a simple baseline***: How does the proposed method compare with the simple baseline?
limitations: limitations: No. The limitations are not well discussed.
paper_summary: paper_summary: The paper introduces a novel unsupervised evaluation method for large language models (LLMs): it uses a peer-review mechanism of a models' anonymized answers by other models. The approach assigns a (learnable) capability parameter to each LLM and solves a constrained optimization problem to maximize the consistency between capabilities and scores. The end result is a ranking of the evaluated models.
strength_weakness: strength_weakness: The paper could be further improved on several directions:
1) you should dedicate a full section to the iterative elimination of models; what is the benefit of eliminating the weaker ones rather than keeping them around? how di you come up with the threshold of 60% to remove? can you learn this threshold automatically? is this threshold optimal for these 15 models? what happens if you start with, say, 100 models? what happens to your results (and the curves in Fig 5) if you stop earlier (all three metrics, not just CIN)? What if you continue to eliminate all models until you are left with one? is there any relationship between the order in which the models are eliminated and their final rank?
2) are there any scaling issues for 100, 1K, 10K, or 100K models? how about cost: is it cheaper to fine-tune a "baseline" model than to pick the best one out of 10K candidates?   
3) while the three metrics you use are meaningful, you should also present results for Precision@1 and -say- RBP@3; after all, we care a lot about identifying the the top models
3) Fig 5 should be extended to nine graphs (3 metrics * 3 datasets); for each of the 9 graphs, you should also show illustrative three ranked lists: PiCO's, PRE's, and the target one. As always, the devil is in the details: not all "CIN = 1" are created equal. Performance-wise, it is almost irrelevant if you have the bottom-2 models inverted; no necessarily so if the inversion is between the top-2 models
questions: questions: 1. line 144 - what is the benefit of a model evaluating itself? why not explicitly disallow it? w/o a full explanation, this detail unnecessarily  complicates the story
2. you repeatedly talk about "higher-level LLM" w/o defining the concept; is it based on the number of parameters (larger --> higher)? 
3. can PiCO (or an extension) also estimate the gap between the performance of two models that are adjacent in the final ranking?   

NITPICKS
- line 72: "closer" ... than whom? existing approaches, I presume
- line 154: the "quadruple" appears to be a "triple"; adding "s" would make it a 4-tuple 
- you talk a few times about "persuasiveness;" this concept makes sense for human reviewers discussing a submitted article, but it is unclear why it matters for LLMs 
- the related work section should be right after the Intro
limitations: limitations: N/A

Comments: title: Thank you for the detailed response
Many thanks to the authors for the detailed answers. After considering both the other reviews and the rebuttals, I maintain the original rating.
comment: May I ask which concerns have not been addressed? Can you provide more details? We are eager to discuss them with you.
Thank you for the detailed response. While the response does not fully address my concerns, I will keep my original score.
Dear Reviewer 8Eov,

We have provided detailed explanations and additional experimental results **(_e.g._ performance comparison in more ranking metrics and comparison with Claude (Table R1 of global author rebuttal))** to address all your concerns. With just **20 hours** left in the discussion period, we would appreciate it if you could review our responses and let us know if there are any final questions or concerns.  Your insights have been invaluable, and we thank you sincerely for your time and effort.

Best regards! 

Authors
Dear Reviewer Ezxz,

We have provided detailed explanations and additional experimental results **(e.g. further validation of the consistency assumptions)** to address all your concerns. With just **20 hours** left in the discussion period, we would appreciate it if you could review our responses and let us know if there are any final questions or concerns.  Your insights have been invaluable, and we thank you sincerely for your time and effort.

Best regards! 

Authors
Dear Reviewer 8Eov,

We would like to once again thank you for your valuable time and constructive comments. This is a gentle reminder that we have diligently addressed your concerns and clarified any confusion. We have not yet heard back from you and would appreciate any further feedback you may have. If there are any concerns that you feel have not been fully addressed, we are eager to discuss them with you.

Best regards!

Authors
Dear Reviewer Ezxz,

We would like to once again thank you for your valuable time and constructive comments. This is a gentle reminder that we have diligently addressed your concerns and clarified any confusion. We have not yet heard back from you and would appreciate any further feedback you may have. If there are any concerns that you feel have not been fully addressed, we are eager to discuss them with you.

Best regards!

Authors
Dear Reviewer mhTC,

We would like to once again thank you for your valuable time and constructive comments. This is a gentle reminder that we have diligently addressed your concerns and clarified any confusion. We have not yet heard back from you and would appreciate any further feedback you may have. If there are any concerns that you feel have not been fully addressed, we are eager to discuss them with you.

Best regards!

Authors
Many thanks to the authors for the detailed answers. After considering both the other reviews and the rebuttals, I maintain the original rating.