PiCO: Peer Review in LLMs based on Consistency Optimization
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Under review as a conference paper at ICLR 2025
PICO: P EER REVIEW IN LLM S BASED ON CONSIS -
TENCY OPTIMIZATION
Anonymous authors
Paper under double-blind review
ABSTRACT
Existing large language models (LLMs) evaluation methods typically focus on
testing the performance on some closed-environment and domain-speciﬁc bench-
marks with human annotations. In this paper, we explore a novel unsupervised
evaluation direction , utilizing peer-review mechanisms to measure LLMs au-
tomatically 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 LLMs response score is jointly
determined by other anonymous ones. During this process, we found that those
answers that are more recognized by other “reviewers” (models) usually come
from LLMs with stronger abilities, while these models can also evaluate others’
answers more accurately. We formalize it as a consistency assumption, i.e., the
ability and score of the model usually have consistency. We exploit this to opti-
mize each model’s conﬁdence, thereby re-ranking the LLMs to be closer to human
rankings. We perform experiments on multiple datasets with standard rank-based
metrics, validating the effectiveness of the proposed approach.
1 I NTRODUCTION
Goodhart’s Law: “When a measure becomes a target, it ceases to be a good
measure. ”
Large language models (LLMs) [ 11; 2; 12; 45] have achieved remarkable success across a vari-
ety of real-world applications [ 56; 34; 38; 54]. With the increasingly widespread application of
these models, there is an urgent need for an effective evaluation method to ensure that their per-
formance 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 [ 32], Big-Bench [ 41], GLUE [ 46].
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 hu-
man preference in open-ended tasks adequately [ 16; 30; 36]. 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 [ 51; 58]. Therefore, blindly im-
proving 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 plat-
forms with human ratings as the primary evaluation metric. Typical platforms include Chatbot Arena
[57], MT-Bench [ 57], and AlpacaEval [ 31]. 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
measuring human preferences, it is exceptionally slow and costly [ 57]. 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 the human-ability hierarchy based on differ-
ent empirical assumptions. For example, majority voting [ 22; 10; 42] and rating voting [ 5] methods
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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 goal is to ﬁnd a ﬁnal score ranking that all LLMs “agree” it.
are widely used during the decision-making process, which are based on the wisdom of the crowds
[42; 13; 52] and have been proven to lead to better results than that of an individual. Moreover, in the
established practice of peer-reviewin academic research, scholars evaluate their academic level rank-
ings based on the consistency assumption, i.e., scholars with stronger abilities usually have stronger
persuasiveness for evaluating others, and these scholars can also obtain higher achievements. This
paper attempts to explore whether a similar phenomenon exists in the LLMs evaluation systems.
In this paper, 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 an-
notated 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 un-
labeled 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 w 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 (contro-
versy) of the whole peer-reviewevaluation system can be minimized. In other words, the consistency
optimization aims to ﬁnd a ﬁnal score ranking that all LLMs have no “disputes” regarding.
We perform experiments on multiple crowdsourcing datasets with standard rank-based metrics, the
results demonstrate that the proposed PiCO framework can effectively obtain a large language mod-
els’ 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, i.e.,
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.
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Figure 2: The pipeline of the PiCO. It is mainly composed of two components: the peer-review and consistency
optimization stages. Speciﬁcally, in the peer-review stage, the unlabeled dataset Q and the LLMs pool M are
given. 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 to evaluate both responses with a
learnable conﬁdence w. As a result, we can obtain the answer-ranking data D which is a quadruple that records
the partial order between two answers and the evaluator’s conﬁdence weight. In the consistency optimization
stage, we update the parameter w by maximizing the consistency of each LLM’s capability and score, while
re-ranking the LLMs to be closer to human rankings.
• We conduct extensive experiments on three crowdsourcing datasets with three standard
rank-based metrics validating the effectiveness of the proposed PiCO approach.
2 T HE PROPOSED APPROACH
2.1 P ROBLEM DEFINITION
This paper aims to re-rank the ability of LLMs to be closer to human (ground-truth) rankings R∗
in an unsupervised way (without relying on any human annotations). Speciﬁcally, we have a large
language models (LLMs) pool M= {Mj}m
j=1, which includes both open-source and closed-source
models. Write M1 ≻M2 to indicate that the LLM M1 has stronger capabilities than the LLM M2.
Thus, we can assume that the ground-truth ranking R∗ is as follows,
R∗ := [M1 ≻M2 ≻M3 ≻... ≻Mm]. (1)
Assuming that the learned ranking ˆRby different evaluation methods is as follows,
ˆR:= [M3 ≻M1 ≻M2 ≻... ≻Mm]. (2)
The goal is to learn an LLM ranking ˆRthat aligns with human ranking R∗ as much as possible.
2.2 A LGORITHM DETAILS
The pipeline of the proposed PiCO, depicted in Figure 2, involves peer-review and consistency
optimization stages. Next, we will introduce the two stages in detail.
Peer Review Stage. In our peer-review system, we consider an unsupervised LLM evaluation sce-
nario with an unlabeled dataset Qconsisting of n open-ended questions, where Q= {Qi}n
i=1. All
LLMs will answer each unlabeled question to obtain the set A= {{Aj
i }n
i=1}m
j=1, where Aj
i is as
follows,
Aj
i = Mj(Qi) (3)
which infers the model Mj response an answer Aj
i with question Qi. In addition, LLMs themselves
also act as “reviewers” to evaluate other answers. Speciﬁcally, for the same question Qi ∈Q, we
randomly construct a battle pair < A j
i , Ak
i > for review. Each battle pair will randomly assign
“reviewers” to determine the winners or declare ties,
(Ak
i , As
i , >, wj) =Mj(Ak
i ; As
i |Qi). (4)
Under the same question Qi, the quadruples (Ak
i , As
i , >, wj) indicate that the “reviewer” Mj be-
lieves that the answer Ak
i is better than answer Ak
i with a conﬁdence wj. Thus, we can collect the
answer-ranking data Das follows,
D=
{
(Ak
i , As
i , >, wj)
}
i∼Q,j,k,Mj∼M , (5)
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Table 1: Validation of consistency assumption. Performance comparison of Backward, Uniform, Forward
weight voting, and Consistency Optimization methods with two metrics across three datasets.
Methods MT-Bench Chatbot Arena AlpacaEval
S(↑) τ(↑) S(↑) τ(↑) S(↑) τ(↑)
Backward Weight 0.70 0.50 0.72 0.52 0.69 0.50
Uniform Weight 0.74 0.54 0.80 0.58 0.77 0.58
Forward Weight 0.75 0.56 0.82 0.59 0.79 0.60
Random Weight + Consistency Optimization 0.90 0.77 0.89 0.72 0.84 0.68
where i denotes the question index, and j, k, s indicate the model indices. ws ∈(0, 1] is a learnable
conﬁdence weight of model Ms, and > is a partial order relationship from {>, <, =}. After that,
we can calculate the response score Gj of each LLM,
Gj =
∑
(Ak
i ,As
i ,>,wj)∼D
1{Aj
i > Ak
i }·ws, (6)
where 1{·}is the indicator function that the value is 1 when the condition is met, otherwise, it is 0.
We can deﬁne the LLM M1 is better than M2 as its score is larger, i.e., M1 ≻M2 := G1 > G 2.
Thus, we can re-write the learned LLM ranking ˆRas follows,
ˆR:= [G3 > G1 > G2 > ... > G m]. (7)
Thus, the goal is to learn the conﬁdence weights w to adjust the ﬁnal ranking ˆRto be closer to
ground-truth ranking R∗.
Validation of Consistency Assumption. First of all, we start with a toy experiment to study the
role of conﬁdence w in Table 1. Speciﬁcally, we manually construct three methods: Backward
Weight, Uniform Weight, and Forward Weight. That is, the ability weights of the model are re-
spectively 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. In other words, the Forward
Weight means manually assigning higher weights to those models with stronger abilities, and so on
for others. Then, we can calculate the response score Gj for each model using Eq. 6, and obtain
the LLM ranking ˆR. We measure the alignment between ˆRand R∗ with Spearman’s S(↑) and
Kendall’s τ(↑) rank correlation coefﬁcient in Table 1. Note that this is an ideal experiment, as we
only use the ground-truth human ranking to validate the feasibility of our idea.
As shown in Table 1, it can be observed that the Forward Weight achieves better results than the
Uniform and Backward ones in all cases, while the Backward one always achieves worse results.
It validates that assigning larger weights to those models with stronger capabilities can obtain
better results. In other words, those answers that are more recognized by other “reviewers” (models)
usually come from LLs with stronger abilities. We formalize it as a 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, the ability and score of
the model usually have consistency.
Consistency Optimization Stage. Based on this observation, we propose to maximize the consis-
tency of each LLM’s capability w and score G with constrained optimization as follows,
argmax
w
Consistency(G, w) (8)
s.t. Gj =
∑
(Aj
i ,Ak
i ,>,ws)∼D
1{Aj
i > Ak
i }·ws,
where the Pearson correlation [ 40] is used 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. 5 and 8) works in an unsupervised way.
The only thing we do is to adaptively adjust the score of each LLM that match its abilities. Most
importantly, we also validate the effectiveness of the proposed consistency optimizationin Table 1.
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Speciﬁcally, we randomly initialize the ability weights and employ our consistency optimizationto
adjust the weight. It can be observed that the learned w by our consistency optimization algorithm
(Eq.8) can further improve the performance of the evaluation system, making the LLM ranking ˆR
closer to human ranking R∗. Another 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, wa > w b > w c.
So, in the ultimate ideal scenario, the ranking of the scores submitted by these three scholars should
also be, Ga > 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 Ab > A c have stronger
persuasiveness, so scholar b should also receive higher weighted scores 1 ∗wa.
Reviewer Elimination Mechanism. Realizing that not all LLMs have sufﬁcient ability to evalu-
ate 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 discussion of the elimination mechanism can also be found in the Experiment 3.3.
3 E XPERIMENTS
Datasets. To validate the effectiveness of the proposed approach, we perform experiments on Chat-
bot Arena[ 57], MT-Bench[ 57], and AlpacaEval[ 31]. 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. AlpacaE-
val dataset integrates 805 evaluations from diverse tests (e.g., Self-Instruct[ 49], OASST, Anthrop-
ics helpful[ 7], Vicuna[ 16] and Koala[ 24] 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∗ to measure the alignment performance of different evaluation meth-
ods.
LLMs Pool. In our experiments, we employ 15 LLMs with diverse architectures to construct
the LLMs pool, including GPT-3.5-Turbo[ 37], WizardLM-13B[ 53], Guanaco-33B[ 1], Vicuna-
7B[16], Vicuna-13B[ 16], Koala-13B[ 25], Mpt-7B[ 44], gpt4all-13B[ 6], ChatGLM-6B[ 55], Oasst-
sft-4-pythia-12B[19], FastChat-T5-3B[ 57], StableLM-7B[ 3], Dolly-12B[ 18], LLaMA-13B[ 45],
Alpaca-13B[43]. All models use the same prompt template, which can be found in Appendix C.
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 [ 42; 13; 52] are compared in this experiment. 1) Majority Voting
[42]: 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[48]: 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 gen-
erated 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[30]:
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 ac-
cordingly. Claude-3 (API): Another SOTA closed-source LLM developed by Anthropic.
PiCO (Ours): the proposed approach in this paper.
Metrics. For all experiments, we employ three popular rank-based metrics to evaluate the aforemen-
tioned experimental setups and our PiCO method: Spearman’s Rank Correlation Coefﬁcient S(↑)
[28], Kendall’s Rank Correlation Coefﬁcient τ(↑) [27] and Permutation Entropy H(↓) [8]. The
details of these metrics can be found in the Appendix A. Moreover, we perform the experiments for
4 runs and record the average results over 4 seeds ( seed = 1, 2, 3, 4).
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Table 2: Comparison of all methods on three datasets under data volumes of 1, 0.7 and 0.4, where the top value
is highlighted by blod font. Higher S and τ scores indicate better performance, while a lower H score signiﬁes
improved performance.
Datasets Chatbot Arena MT-Bench AlpacaEvalMethods 1 0.7 0.4 1 0.7 0.4 1 0.7 0.4
Spearman’s Rank Correlation CoefﬁcientS(↑)
Majority V oting [42] 0.76±0.00 0.75±0.01 0.73±0.03 0.73±0.00 0.77±0.01 0.75±0.01 0.80±0.00 0.79±0.01 0.78±0.01
Rating V oting [5] 0.74±0.00 0.72±0.02 0.71±0.02 0.80±0.00 0.78±0.02 0.74±0.03 0.77±0.00 0.77±0.01 0.78±0.01
GPTScore(ﬂan-t5-xxl)[23] −0.09±0.00−0.09±0.01−0.12±0.02 0.05±0.00 0.01±0.07 0.04±0.09 0.34±0.00 0.34±0.00 0.34±0.01
GPTScore(davinci-002)[23] 0.15±0.00 0.13±0.02 −0.02±0.14 0.52±0.00 0.42±0.05 0.45±0.05 0.76±0.00 0.77±0.07 0.75±0.06
PandaLM[48] 0.43±0.00 0.44±0.03 0.44±0.10 0.50±0.00 0.50±0.08 0.52±0.17 0.57±0.00 0.55±0.01 0.48±0.08
PRD[30] 0.84±0.00 0.84±0.00 0.82±0.03 0.86±0.00 0.84±0.03 0.81±0.03 0.81±0.00 0.81±0.01 0.81±0.02
PRE[17] 0.86±0.00 0.86±0.01 0.86±0.01 0.86±0.00 0.84±0.03 0.82±0.04 0.83±0.00 0.81±0.01 0.83±0.02
Claude-3 (API) 0.90±0.01 0.88±0.03 0.87±0.04 0.85±0.06 0.82±0.08 0.80±0.07 0.79±0.03 0.78±0.02 0.75±0.04
PiCO (Ours) 0.90±0.000.89±0.010.89±0.01 0.89±0.010.89±0.010.84±0.110.84±0.000.83±0.030.85±0.01
Kendall’s Rank Correlation Coefﬁcientτ(↑)
Majority V oting [42] 0.58±0.00 0.56±0.02 0.52±0.05 0.56±0.00 0.61±0.02 0.60±0.02 0.62±0.00 0.60±0.02 0.58±0.02
Rating V oting [5] 0.54±0.00 0.53±0.02 0.52±0.02 0.58±0.00 0.57±0.02 0.54±0.01 0.58±0.00 0.57±0.01 0.57±0.02
GPTScore(ﬂan-t5-xxl) [23] −0.06±0.00−0.06±0.02−0.09±0.02−0.05±0.00−0.07±0.05−0.02±0.06 0.25±0.00 0.26±0.01 0.26±0.01
GPTScore(davinci-002) [23] 0.20±0.00 0.23±0.02 0.03±0.11 0.36±0.00 0.30±0.05 0.31±0.05 0.60±0.08 0.61±0.05 0.59±0.08
PandaLM [48] 0.30±0.00 0.31±0.03 0.31±0.07 0.39±0.00 0.37±0.06 0.40±0.12 0.41±0.00 0.39±0.02 0.32±0.05
PRD [30] 0.68±0.00 0.69±0.01 0.67±0.03 0.68±0.06 0.66±0.02 0.63±0.03 0.64±0.00 0.63±0.03 0.63±0.02
PRE [17] 0.71±0.00 0.73±0.02 0.72±0.02 0.68±0.00 0.68±0.02 0.65±0.03 0.64±0.00 0.66±0.01 0.66±0.03
Claude-3 (API) 0.76±0.04 0.72±0.05 0.70±0.07 0.67±0.07 0.66±0.11 0.61±0.10 0.64±0.06 0.61±0.04 0.66±0.06
PiCO (Ours) 0.77±0.000.76±0.010.77±0.02 0.72±0.010.72±0.030.70±0.120.68±0.000.66±0.040.67±0.02
Permutation EntropyH(↓)
Majority V oting [42] 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 V oting [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[48] 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[30] 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±0.020.96±0.040.95±0.08 1.01±0.071.02±0.111.06±0.241.17±0.021.17±0.081.13±0.05
3.1 P ERFORMANCE COMPARISON
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 with different rank-based metrics and datasets are demonstrated in
Table 2. The ratios of response sets Dare 1, 0.7, and 0.4, respectively.
The results presented in Table 2 demonstrate that the proposed PiCO method consistently outper-
forms competing approaches across most evaluated metrics, including surpassing all baselines, such
as Claude-3 (API) . Speciﬁcally, PiCO achieves improvements of 0.027, 0.047, and 0.14 on Spear-
man’s Rank Correlation Coefﬁcient, Kendall’s Rank Correlation Coefﬁcient, and Permutation En-
tropy metrics, respectively, compared to the runner-up. These results underscore the superiority of
aggregating evaluations from multiple models, such as Majority V oting, Rating V oting, PRD, and
PRE, as opposed to relying solely on single-model methods like GPTScore and PandaLM. This col-
lective model approach, leveraging ’the wisdom of the crowds’, aligns with human rankings more
accurately in our open-question evaluation framework.
In comparison with existing SOTA 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, po-
tentially 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 per-
formance 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.
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(a) ChatBot Arena (PG)
 (b) MT-Bench (PG)
 (c) AlpacaEval (PG)
(d) ChatBot Arena (weighted PG)
 (e) MT-Bench (weighted PG)
 (f) AlpacaEval (weighted PG)
Figure 3: Heatmap distribution of preference gap (PG) metric among seven LLMs across three datasets. Higher
values (above 0) indicate greater evaluation bias[ 17]. The ﬁrst row shows original PG values in three datasets,
while the second row displays PG values re-weighted using our learned conﬁdence weights.
3.2 E XPLORING THE ROLE OF CONFIDENCE WEIGHT
In this subsection, we 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, PG(i, j) =Pi(i > j ) −Pj(i > j ), (9)
where Pi(i > j ) represents the winning rate of model i as the “reviewer” believes that i defeated
j. The heatmap distribution of the PG value PG(i, j) among seven LLMs across three datasets is
demonstrated in the ﬁrst row of Figure 3. 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 ˆPG(i, j) as follows,
ˆPG(i, j) =wi ×Pi(i > j ) −wj ×Pj(i > j ). (10)
The results of the re-weighting PG value ˆPG(i, j) are displayed on the second row of Figure 3.
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-7B have lower weights, and reducing their conﬁdence can effectively alleviate the system
evaluation bias.
3.3 S TUDY OF ELIMINATION MECHANISM
Performance Comparison of Elimination Mechanisms. 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 4, the x-axis quantiﬁes the number of reviewers elimi-
nated, and the y-axis measures the PEN, where lower scores denote higher performance. It can be
observed that both PiCO and PRE exhibit better performance with an increasing number of elimi-
nated “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 elim-
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Figure 4: Performance comparison of the PiCO (Ours) and PRE[ 17] methods on the Chatbot Arena, MT-Bench,
and AlpacaEval datasets, with the number of eliminated reviewers on the x-axis. The y-axis is PEN, where
lower values indicate better performance.
inate 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.
Figure 5: The average loss for different
numbers of eliminated reviewers( ↓). It
shows how the iterative elimination of
weaker reviewers affects the overall
loss in the peer-review system.
Automatic Learning of Elimination Thresholds. We ob-
served that weaker LLMs tend to have poorer evaluation abil-
ities, introducing signiﬁcant noise into the peer-review sys-
tem. Therefore, eliminating weaker models instead of retain-
ing them enhances the robustness of the system. We employed
an unsupervised approach to automatically learn the elimina-
tion threshold, as shown in Figure 5, by using the average train-
ing loss curve as the number of eliminated reviewers increases.
It can be seen that removing weaker reviewers reduces the aver-
age loss of the entire system, indicating that eliminating noisy
evaluations beneﬁts the overall process. Notably, when 60 %
(or 9) of the weaker reviewers are removed, the system’s loss
reaches its minimum. This trend is consistent across all three
datasets, suggesting that the elimination threshold is learned
automatically. However, removing more than 9 stronger re-
viewers harms the evaluation process.
3.4 O THER RESULTS
Validation on more metrics (Precision@K and RBP@K). We demonstrated the results of preci-
sion and RBP (K=8,9,10) with other baselines in Table 3 (left). The results show that the proposed
PiCO approach can achieve better precision and RBP performance in all cases. These results once
again validate that PiCO can predict the LLM ranking more accurately than other baselines.
Comparison of tokens consumed. We compute the token consumption of each method in Table 3
(right). It can be observed that the proposed PiCO approach has a similar token consumed with other
baselines ( e.g., PRD and PRE) while achieving better evaluation performance. Although Chatbot
Arena has a smaller token consumption, it requires 33k human annotations, while PiCO does not
require any human annotations.
Stability validation of consistency optimization. We repeated the experiment with different seeds
for 1000 times, and plotted the training loss curve and weight distribution in Figure 6. The results
show that the proposed consistency optimization process is stable and the learned w is convergence.
4 R ELATED WORK
Evaluation Benchmarks for Diversity. LLMs are designed to handle a variety of tasks, necessi-
tating comprehensive benchmarks [ 15]. Notable benchmarks include GLUE[ 46] and SuperGLUE
[47], which simulate real-world scenarios across tasks such as text classiﬁcation, translation, read-
ing comprehension, and dialogue generation. HELM [ 32] provides a holistic evaluation of LLMs,
assessing language understanding, generation, coherence, and reasoning. BIG-bench [ 41] pushes
LLM capabilities with 204 diverse tasks. MMLU [ 26] measures multitask accuracy across domains
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Table 3: Comparison of more metrics (Precision@K and RBP@K) and token consumption on Chatbot Arena.
Methods RBP@K(↑) Precision@K(↑) Input Token Output Token Annotation Cost8 9 10 8 9 10
Chatbot Arena Platforms [57] - - - - - - ∼7500k ∼10944k ∼32k
GPTScore(ﬂan-t5-xxl) [23] 26.2% 29.6% 45.1%50.0% 55.6% 70.0%∼22882k ∼12260k 0
GPTScore(davinci-002) [23] 42.0% 50.6% 53.3%62.5% 77.8% 80.0%∼22882k ∼12260k 0
PandaLM [48] 63.5% 63.5% 66.2%62.5% 55.6% 60.0%∼22882k ∼10355k 0
PRD [30] 67.2% 73.8% 81.3%87.5% 88.9% 80.0%∼25087k ∼10935k 0
PRE [17] 78.0% 81.3% 81.3%87.5% 88.9% 80.0%∼24120k ∼11115k ∼7k
PiCO (Ours) 83.2% 83.2% 85.9%100.0% 100.0% 90.0%∼23823k ∼11685k 0
Figure 6: Stability validation of consistency optimization. We repeated the experiment with different seeds
for 1000 times, and plotted the training loss curve and weight distribution. The results show that the learning
process is stable and the learned w is convergence.
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; 58].
Human Evaluation. Human evaluation provides reliable feedback that closely aligns with real-
world applications [ 15]. Liang et al. [ 32] evaluated summary and misinformation scenarios across
multiple models. Ziems et al. [ 59] 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 [ 57], relying on human ratings as the primary evaluation metric. Despite its effectiveness,
human evaluation is costly and subject to bias and cultural differences[ 39].
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 high-
quality content through multidimensional evaluation. Bubeck et al.[ 12] tested GPT-4, ﬁnding it
rivaling human capabilities. Lin and Chen introduced LLM-EV AL[ 33] for evaluating dialogue qual-
ity with single prompts. PandaLM[ 48] employs LLMs as "judges" for evaluating instruction tuning.
However, reliance on a single model can introduce biases such as positional[ 20], verbosity[50], and
self-favoring biases[ 35; 57]. ChatEval[ 14] proposes a multi-agent framework to simulate human
evaluation processes. Similarly, PRE[ 17] and PRD[ 30] use LLMs as evaluators, combining mul-
tiple 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.
5 C ONCLUSION
In this paper, we propose PiCO, a novel unsupervised evaluation method 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. The extensive experiment results across multiple datasets
and standard rank-based metrics demonstrate that PiCO effectively generates an LLM ranking that
aligns closely with human preferences. In the future, we plan to extend the peer-review mechanism
to evaluate the capabilities of multi-modality large models.
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A D ETAILED EXPLANATION OF METRICS
In this section, we provide a comprehensive explanation of the metrics used to evaluate the alignment
between learned LLM rankings and human rankings. These metrics assess the strength of correla-
tions, complexity, and the level of agreement between rankings. Speciﬁcally, we discuss ﬁve key
metrics: Spearman’s Rank Correlation Coefﬁcient, Kendall’s Rank Correlation Coefﬁcient, Permu-
tation Entropy, Count Inversions, and Longest Increasing Subsequence, detailing their formulations
and intuitive interpretations.
i) Spearman’s Rank Correlation Coefﬁcient S(↑) [28] measures the strength and direction of the
monotonic relationship between two ranked variables. It is computed as:
S( ˆR, R∗) = 1− 6 ∑m
i=1 d2
i
m(m2 −1), (11)
where di = rank ˆR(Mi)−rankR∗(Mi) is the difference between the ranks of LLM Mi in the learned
ranking ˆRand the human ranking R∗, and m is the total number of LLMs. A higher Spearman
coefﬁcient indicates a stronger correlation between the rankings.
ii) Kendall’s Rank Correlation Coefﬁcient τ(↑) [27] evaluates the similarity between two rankings
by counting the number of concordant and discordant pairs. It is given by:
τ( ˆR, R∗) = C −D
1
2 m(m −1), (12)
where C represents the number of concordant pairs, and D represents the number of discordant pairs.
A pair (Mi, Mj) is concordant if Mi and Mj have the same order in both ˆRand R∗, meaning if
Mi ≻Mj in ˆR, then Mi ≻Mj in R∗. Conversely, a pair is discordant if their relative order differs
between the two rankings. A higher τ value indicates a closer alignment between the rankings.
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iii) Permutation Entropy H(↓) [8] measures the complexity or randomness of sequences, which is
formulated as follows:
H( ˆR, R∗) :=−
∑
p(π) logp(π), (13)
where
p(π) = #{t|0 ≤t ≤m −k, (Mt+1, ..., Mt+k) ∈π}
m −k + 1 .
π denotes different permutations, k is a hyper-parameter recommended to be set to 3 to 7, and we
set k = 3in 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.
iv) Count Inversions C(↓). Counting inversions [ 29] aims to measure the degree of disorder or
"invertedness" in an array or sequence of elements. We thus deﬁne it as follows,
C( ˆR, R∗) :=
∑
Mi,Mj∼M
1{Mi ≻Mj ∧i < j }. (14)
Where 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.
v) Longest Increasing Subsequence L(↑). 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,
L( ˆR, R∗) := max{dp[i] |1 ≤i ≤m}, (15)
where
dp[i] = 1 + max{dp[j] |1 ≤j < i ∧Mj ≺Mi}.
dp[i] represents the length of the longest increasing subsequence that ends with Mi. 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.
B D ATASET FORMAT
Focusing on the MT-Bench dataset, we demonstrate the ensuing data format utilizing dataset Q.
As Figure 7 illustrates, the Question dataset Qcontains "Question id," "Category," "Question," and
"Reference." In categories with deﬁnitive answers like "reasoning" or "math," the "Reference" ﬁeld
is populated with standard answers; otherwise, it remains blank. Each model M in our pool processes
the Question dataset Qto generate the LLMs answer data A, consisting of "Question id," "Answer
id," "Model id," and "Answer." Finally, we combine pairs in Aand appoint judges to evaluate,
creating the Answer-Ranking data D, featuring "Question id," "Model 1," "Model 2," "G1 winner,"
"G2 winner," and "Judge." Here, "G1 winner" and "G2 winner" indicate the outcomes of inputting
reversed order responses of Model 1 and Model 2 into the judge model, a method employed to
mitigate biases stemming from models’ preferences for input order.
C D ETAILED PROMPT FOR REVIEWERS
The evaluation prompts, as detailed in Section 2.2.1, are employed during the Peer Review Stage.
These prompts are provided to the Reviewer Language Model Systems (LLMs), enabling them to
generate evaluative preferences. In our experimental framework, we devised four distinct prompt
settings. For each setting, a tailored prompt template was meticulously crafted as illustrated below:
Template for Single-Turn Interaction: This template is designed for single-turn interactions be-
tween users and LLMs, where there is no predetermined correct answer. It facilitates open-ended
dialogue, allowing for a wide range of user inquiries without the expectation of speciﬁc responses.
Referenced Template for Single-Turn Interaction: Tailored for single-turn dialogues between
users and LLMs, this template incorporates predeﬁned correct answers. It is particularly suited for
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Figure 7: Format of the Question dataset Q, LLMs responses data A, and the Answer-Ranking data D for Peer
Review
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 prede-
ﬁned 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 frame-
work that guides the interaction between users and LLMs towards achieving desired outcomes,
whether for open-ended exploration or precise problem-solving.
Template for Single-Turn Answer
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]]" if assistant B is better, and "[[C]]" for a tie.
User Question: {question}
Assistant A’s Answer: {answer a}
Assistant B’s Answer: {answer b}
Referenced Template for Single-Turn Answer
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, with reference to the provided
reference answers. 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]]" if assistant B
is better, and "[[C]]" for a tie.
User Question: {question}
Reference Answer: {reference answer}
Assistant A’s Answer: {answer a}
Assistant B’s Answer: {answer b}
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Template for Multi-Turn Answer
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]]" if assistant B is better, and "[[C]]" for a tie
Assistant A’s Conversation with User:
User: {question 1}
Assistant A: {answer a1}
User: {question 2}
Assistant A: {answer a2}
Assistant B’s Conversation with User:
User: {question 1}
Assistant B: {answer b1}
User: {question 2}
Assistant B: {answer b2}
Referenced Template for Multi-Turn Answer
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, in comparison to the reference
answers. 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]]" if assistant B is better,
and "[[C]]" for a tie.
Reference Answer
User: {question 1}
Reference answer: {ref answer 1}
User: {question 2}
Reference answer: {ref answer 2}
Assistant A’s Conversation with User:
User: {question 1}
Assistant A: {answer a1}
User: {question 2}
Assistant A: {answer a2}
Assistant B’s Conversation with User:
User: {question 1}
Assistant B: {answer b1}
User: {question 2}
Assistant B: {answer b2}
D S CORING METHODOLOGY
In Section 2.2.2, Equation 8 delineates the methodology for optimizing scores. Within this frame-
work, the function 1{Aj
i > Ak
i }is more precisely deﬁned as f(Aj
i , Ak
i ). Additionally, the function
f(Aj
i , Ak
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 16, 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 17, 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.
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f(Aj
i , Ak
i ) =



1 − 1
1+BASE((G(k)−G(j))/SCALE) if Aj
i > Ak
i
0.5 − 1
1+BASE((G(k)−G(j))/SCALE) if Aj
i = Ak
i
0 − 1
1+BASE((G(k)−G(j))/SCALE) if Aj
i < Ak
i
(16)
f(Aj
i , Ak
i ) =



1 + (rank(j) −rank(k))/K if Aj
i > Ak
i
0.5 if Aj
i = Ak
i
0 if Aj
i < Ak
i
(17)
E O VERALL ALGORITHM OF PEER REVIEW
The overall algorithm, as delineated in Algorithm 1, encapsulates the comprehensive process out-
lined in Section 2.2. This sequence commences with "Data Collection and LLMs Pool Construc-
tion," progresses through "Answer-Ranking Data Construction Based on Peer Review," advances to
"Consistency Optimization," and culminates with the "Unsupervised Elimination Mechanism."
F C OMPLETE EXPERIMENTAL RESULTS
In Section 3.4, we both employ elimination mechanisms to cull the weakest LLMs from the ’reviewer
queue’ during the evaluation process. In Figures 8 and 9, 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.
Figure 8: Performance comparison of the PiCO (Ours) and PRE[ 17] methods on the MT-Bench, Chatbot Arena,
and AlpacaEval datasets, with the number of eliminated reviewers on the x-axis. The y-axis is CIN, where lower
values indicate better performance.
In Section 3.5, we validate the effectiveness of the consistency assumptionand 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 Table 4, Figure 10, 11 and 12, reveal-
ing 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 un-
supervised nature, the ’PiCO’ method demonstrates the capability to mitigate the inﬂuence of noise,
reaching the evaluation upper bound (the strongest LLM) within any given unknown LLM pool M,
even in the absence of prior ranking information.
G S ELECTED MODELS AND OPTIMIZED RANKING
For our analysis, we meticulously selected 15 LLMs spanning a variety of architectures, encompass-
ing both open-source and closed-source models, as detailed in the subsequent table. Our curated
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Algorithm 1 Overall Framework Algorithm of Peer Review
Require: Unlabeled dataset Q, Pool of LLMs M, Active LLM pool M∗ = M
Ensure: Consistency-optimized ranking of LLMs R∗
1: Initialize response matrix A ←∅
2: for each question qi ∈Q do
3: Initialize response vector for question qi, Ai ←∅
4: for each model mj ∈M do
5: Ai
j ←response of model mj to question qi
6: Ai ←Ai ∪{Ai
j}
7: end for
8: Shufﬂe Ai to obtain permuted response vector Ai
9: A ←A ∪{Ai}
10: end for
11: Initialize answer-ranking data D ←∅
12: Initialize model weights vector w with Gaussian distribution
13: for each permuted response vector Ai do
14: for each pair of responses (Aj
i , Ak
i ) in Ai do
15: for s ←1 to 5 do ▷ Randomly select 5 models for evaluation
16: Evaluate the pair (Aj
i , Ak
i ) with model ms
17: D ←D ∪{(Aj
i , Ak
i , > w s)}
18: end for
19: end for
20: end for
21: Initialize scores Gj for each model mj ∈M to the Elo initial score
22: repeat
23: while not converged do
24: for each model mj ∈M do
25: Compute Gj using updated formula:
26: Gj = ∑
i
∑
k̸=j
∑
s̸=k,s̸=j 1{Aj
i , Ak
i }×ws (Aj
i , Ak
i , > w s, s ∈M∗) ∈D
27: end for
28: Update weight vector w to maximize the consistency of w and G
29: end while
30: Sort M∗ by Gj to identify Mmin, the lowest-scoring model
31: if size of M∗ > threshold then
32: Remove Mmin from M∗
33: end if
34: until size of M∗ < threshold
35: Compute the ﬁnal ranking R∗ based on the optimized scores Gj
36: return R∗
Figure 9: Performance comparison of the PiCO (Ours) and PRE[ 17] methods on the MT-Bench, Chatbot Arena,
and AlpacaEval datasets, with the number of eliminated reviewers on the x-axis. The y-axis is LIS, where upper
values indicate better performance.
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Table 4: Comparison of performance across three datasets using Unsupervised methods versus using single
models in reviewer queue.
Methods MT-Bench Chatbot Arena AlpacaEval
PEN(↓)CIN(↓)LIS(↑) PEN(↓)CIN(↓)LIS(↑) PEN(↓)CIN(↓)LIS(↑)
Gpt-3.5 0.97 12.00 10.00 0.85 11.00 11.00 1.15 16.00 9.00
Guanaco-33B 1.25 21 .00 8 .00 1.50 28 .00 7 .00 1.26 20 .00 9 .00
Vicuna-13B 1.31 20 .00 7 .00 1.27 23 .00 8 .00 1.20 17 .00 8 .00
WizardLM-13B 1.15 17 .00 9 .00 1.27 19 .00 8 .00 1.17 17 .00 9 .00
Vicuna-7B 1.27 21 .00 8 .00 1.30 20 .00 7 .00 1.34 23 .00 8 .00
Koala-13B 1.67 43 .00 6 .00 1.34 23 .00 8 .00 1.54 31 .00 7 .00
gpt4all-13B 1.74 45 .00 6 .00 1.60 35 .00 6 .00 1.73 42 .00 6 .00
Mpt-7B 1.67 39 .00 6 .00 1.72 52 .00 6 .00 1.63 34 .00 7 .00
Oass-pythia-12B 1.77 50 .00 5 .00 1.74 42 .00 5 .00 1.70 47 .00 6 .00
Alpaca-13B 1.77 49 .00 7 .00 1.60 73 .00 4 .00 1.63 34 .00 7 .00
FastChat-T5-3B 1.45 29 .00 7 .00 1.53 30 .00 7 .00 1.30 22 .00 7 .00
ChatGLM-6B 1.59 33 .00 7 .00 1.71 55 .00 5 .00 1.63 34 .00 6 .00
StableLM-7B 1.68 63 .00 5 .00 1.75 44 .00 5 .00 1.72 56 .00 4 .00
Dolly-12B 1.76 46 .00 6 .00 1.57 71 .00 6 .00 1.75 54 .00 6 .00
LLaMA-13B 1.60 35 .00 7 .00 1.76 56 .00 6 .00 1.70 50 .00 5 .00
Average Performance of All Review LLMs1.51 34 .87 6 .93 1.50 38 .80 6 .60 1.50 33 .13 6 .93
PRD[30] 1.15 17 .00 8 .00 1.15 17 .00 8 .00 1.21 19 .00 9 .00
PRE[17] 1.17 17 .00 8 .00 1.07 15 .00 9 .00 1.18 19 .00 8 .00
PiCO (Ours) 1.01 14.50 8.75 0.94 12.00 10.00 1.17 17.00 9.00
Figure 10: Comparison of performance on the CIN metric across three datasets using Unsupervised methods
versus using single models, with Unsupervised methods on the left and Supervised methods on the right. The
dotted line represents the average value using single models.
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 princi-
ples.
We have comprehensively detailed the ranking outcomes across three distinct datasets for our com-
parative analysis, incorporating the optimized model rankings, names, and their respective scores.
As delineated in Appendix D, the PiCO (Ours) is capable of employing various scoring mechanisms,
thereby facilitating the presentation of ranking outcomes on three datasets utilizing both the Elo and
Rank mechanisms. Furthermore, we have also enumerated the ranking results for PRD and PRE
methodologies across the three datasets, offering a holistic view of the competitive landscape.
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Figure 11: Comparison of performance on the PEN metric across three datasets using Unsupervised methods
versus using single models, with Unsupervised methods on the left and Supervised methods on the right. The
dotted line represents the average value using single models.
Figure 12: Comparison of performance on the LIS metric across three datasets using Unsupervised methods
versus using single models, with Unsupervised methods on the left and Supervised methods on the right. The
dotted line represents the average value using single models.
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G.1 P ICO
Grade-Elo-Chatbot
#1 Gpt-3.5 | Grade: 9205.162109375
#2 WizardLM-13B | Grade: 9143.46875
#3 Guanaco-33B | Grade: 5886.92626953125
#4 Vicuna-7B | Grade: 5368.9462890625
#5 Vicuna-13B | Grade: 5216.79541015625
#6 Koala-13B | Grade: 3545.1171875 | Eliminated
#7 Mpt-7B | Grade: 962.99462890625 | Eliminated
#8 Gpt4all-13B | Grade: 652.4602661132812 | Eliminated
#9 Chatglm-6B | Grade: 417.1375427246094 | Eliminated
#10 Oasst-pythia-12B | Grade: -898.2676391601562 | Eliminated
#11 Fastchat-t5-3B | Grade: -1251.7183837890625 | Eliminated
#12 StableLM-7B | Grade: -2232.66943359375 | Eliminated
#13 Dolly-12B | Grade: -3163.540283203125 | Eliminated
#14 Llama-13B | Grade: -3648.37841796875 | Eliminated
#15 Alpaca-13B | Grade: -14204.3984375 | Eliminated
Grade-Elo-AlpacaEval
#1 WizardLM-13B | Grade: 8662.7158203125
#2 Vicuna-13B | Grade: 5586.46630859375
#3 Guanaco-33B | Grade: 5445.341796875
#4 Vicuna-7B | Grade: 5374.2314453125
#5 Gpt-3.5 | Grade: 4845.91552734375
#6 Koala-13B | Grade: 4338.77783203125 | Eliminated
#7 Chatglm-6B | Grade: 2293.4208984375 | Eliminated
#8 Gpt4all-13B | Grade: 2080.511962890625 | Eliminated
#9 Mpt-7B | Grade: 1694.4945068359375 | Eliminated
#10 Fastchat-t5-3B | Grade: 1371.94287109375 | Eliminated
#11 Oasst-pythia-12B | Grade: -665.8685302734375 | Eliminated
#12 StableLM-7B | Grade: -1343.5838623046875 | Eliminated
#13 Dolly-12B | Grade: -5377.13427734375 | Eliminated
#14 Llama-13B | Grade: -5847.59130859375 | Eliminated
#15 Alpaca-13B | Grade: -13459.6162109375 | Eliminated
Grade-Elo-MT_Bench
#1 WizardLM-13B | Grade: 2178.10302734375
#2 Vicuna-13B | Grade: 1720.1114501953125
#3 Guanaco-33B | Grade: 1704.1832275390625
#4 Vicuna-7B | Grade: 1659.2799072265625
#5 Gpt-3.5 | Grade: 1535.8819580078125
#6 Mpt-7B | Grade: 1338.5235595703125 | Eliminated
#7 Koala-13B | Grade: 1267.9747314453125 | Eliminated
#8 Chatglm-6B | Grade: 1011.7701416015625 | Eliminated
#9 Gpt4all-13B | Grade: 976.5963745117188 | Eliminated
#10 Oasst-pythia-12B | Grade: 779.3573608398438 | Eliminated
#11 StableLM-7B | Grade: 512.1678466796875 | Eliminated
#12 Alpaca-13B | Grade: 334.9879455566406 | Eliminated
#13 Fastchat-t5-3B | Grade: 303.5980529785156 | Eliminated
#14 Dolly-12B | Grade: 72.63818359375 | Eliminated
#15 Llama-13B | Grade: -395.19921875 | Eliminated
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Under review as a conference paper at ICLR 2025
Grade-Rank-Chatbot
#1 WizardLM-13B | Grade: 0.30809280276298523
#2 Gpt-3.5 | Grade: 0.293962299823761
#3 Guanaco-33B | Grade: 0.28587597608566284
#4 Vicuna-7B | Grade: 0.28212910890579224
#5 Vicuna-13B | Grade: 0.27900218963623047
#6 Koala-13B | Grade: 0.2672431766986847 | Eliminated
#7 Mpt-7B | Grade: 0.2500302195549011 | Eliminated
#8 Gpt4all-13B | Grade: 0.24746862053871155 | Eliminated
#9 Chatglm-6B | Grade: 0.2466953843832016 | Eliminated
#10 Oasst-pythia-12B | Grade: 0.23637069761753082 | Eliminated
#11 Fastchat-t5-3B | Grade: 0.2350562959909439 | Eliminated
#12 StableLM-7B | Grade: 0.22843806445598602 | Eliminated
#13 Dolly-12B | Grade: 0.22219440340995789 | Eliminated
#14 Llama-13B | Grade: 0.2165679931640625 | Eliminated
#15 Alpaca-13B | Grade: 0.13975904881954193 | Eliminated
Grade-Rank-AlpacaEval
#1 WizardLM-13B | Grade: 0.4019235074520111
#2 Vicuna-13B | Grade: 0.36745429039001465
#3 Guanaco-33B | Grade: 0.3664878010749817
#4 Vicuna-7B | Grade: 0.36541733145713806
#5 Gpt-3.5 | Grade: 0.36000365018844604
#6 Koala-13B | Grade: 0.3544933795928955 | Eliminated
#7 Chatglm-6B | Grade: 0.3319571018218994 | Eliminated
#8 Gpt4all-13B | Grade: 0.3306528627872467 | Eliminated
#9 Mpt-7B | Grade: 0.32641729712486267 | Eliminated
#10 Fastchat-t5-3B | Grade: 0.32173293828964233 | Eliminated
#11 Oasst-pythia-12B | Grade: 0.2999681532382965 | Eliminated
#12 StableLM-7B | Grade: 0.2932431995868683 | Eliminated
#13 Dolly-12B | Grade: 0.24777530133724213 | Eliminated
#14 Llama-13B | Grade: 0.24381506443023682 | Eliminated
#15 Alpaca-13B | Grade: 0.16114839911460876
Grade-Rank-MT_Bench
#1 WizardLM-13B | Grade: 0.2994651198387146
#2 Vicuna-13B | Grade: 0.2809261679649353
#3 Guanaco-33B | Grade: 0.2767307460308075
#4 Vicuna-7B | Grade: 0.2758147716522217
#5 Gpt-3.5 | Grade: 0.27261608839035034
#6 Mpt-7B | Grade: 0.26338690519332886 | Eliminated
#7 Koala-13B | Grade: 0.2613368630409241 | Eliminated
#8 Gpt4all-13B | Grade: 0.24908888339996338 | Eliminated
#9 Chatglm-6B | Grade: 0.24898234009742737 | Eliminated
#10 Oasst-pythia-12B | Grade: 0.2415400892496109 | Eliminated
#11 StableLM-7B | Grade: 0.2299075722694397 | Eliminated
#12 Alpaca-13B | Grade: 0.22171474993228912 | Eliminated
#13 Fastchat-t5-3B | Grade: 0.221677765250206 | Eliminated
#14 Dolly-12B | Grade: 0.21185410022735596 | Eliminated
#15 Llama-13B | Grade: 0.192665234208107 | Eliminated
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Under review as a conference paper at ICLR 2025
G.2 PRD
PRD-Chatbot
#1 WizardLM-13B | Grade: 5565.28271484375
#2 Gpt-3.5 | Grade: 4613.22900390625
#3 Guanaco-33B | Grade: 3423.588134765625
#4 Vicuna-7B | Grade: 2985.4892578125
#5 Vicuna-13B | Grade: 2972.15673828125
#6 Koala-13B | Grade: 2237.70751953125
#7 Chatglm-6B | Grade: 875.373779296875
#8 Mpt-7B | Grade: 602.46923828125
#9 Gpt4all-13B | Grade: 356.06243896484375
#10 Fastchat-t5-3B | Grade: 184.89663696289062
#11 Dolly-12B | Grade: 52.10746765136719
#12 Oasst-pythia-12B | Grade: -307.49908447265625
#13 StableLM-7B | Grade: -691.4453735351562
#14 Llama-13B | Grade: -848.1654052734375
#15 Alpaca-13B | Grade: -7020.923828125
PRD-AlpacaEval
#1 WizardLM-13B | Grade: 5469.75634765625
#2 Guanaco-33B | Grade: 3707.014892578125
#3 Vicuna-13B | Grade: 3618.63427734375
#4 Vicuna-7B | Grade: 3569.389892578125
#5 Gpt-3.5 | Grade: 3197.755615234375
#6 Koala-13B | Grade: 2893.642578125
#7 Chatglm-6B | Grade: 1847.1300048828125
#8 Fastchat-t5-3B | Grade: 1585.66943359375
#9 Gpt4all-13B | Grade: 1561.145751953125
#10 Mpt-7B | Grade: 1332.3753662109375
#11 StableLM-7B | Grade: -33.00855255126953
#12 Oasst-pythia-12B | Grade: -92.68387603759766
#13 Dolly-12B | Grade: -3013.588623046875
#14 Llama-13B | Grade: -3211.0302734375
#15 Alpaca-13B | Grade: -7432.3701171875
PRD-MT_Bench
#1 WizardLM-13B | Grade: 1811.64697265625
#2 Vicuna-13B | Grade: 1537.8084716796875
#3 Guanaco-33B | Grade: 1481.1739501953125
#4 Vicuna-7B | Grade: 1401.5194091796875
#5 Gpt-3.5 | Grade: 1272.8072509765625
#6 Mpt-7B | Grade: 1186.5518798828125
#7 Chatglm-6B | Grade: 1166.6246337890625
#8 Koala-13B | Grade: 1124.2513427734375
#9 Gpt4all-13B | Grade: 871.2874755859375
#10 Oasst-pythia-12B | Grade: 855.3653564453125
#11 StableLM-7B | Grade: 782.702880859375
#12 Fastchat-t5-3B | Grade: 636.966064453125
#13 Alpaca-13B | Grade: 414.9374694824219
#14 Dolly-12B | Grade: 377.5018005371094
#15 Llama-13B | Grade: 78.90127563476562
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Under review as a conference paper at ICLR 2025
G.3 PRE
PRE-Chatbot
#1 WizardLM-13B | Grade: 1113.7034715479742
#2 Gpt-3.5 | Grade: 1076.1116664199608
#3 Guanaco-33B | Grade: 1067.441581415147
#4 Vicuna-13B | Grade: 1057.702184441485
#5 Vicuna-7B | Grade: 1043.4840340151043
#6 Koala-13B | Grade: 1030.4455842017508 | Eliminated
#7 Chatglm-6B | Grade: 1012.4487557424748 | Eliminated
#8 Mpt-7B | Grade: 1000.487230109001 | Eliminated
#9 Gpt4all-13B | Grade: 1000.4111397038492 | Eliminated
#10 Fastchat-t5-3B | Grade: 992.3732179832363 | Eliminated
#11 Oasst-pythia-12B | Grade: 977.5217305871272 | Eliminated
#12 StableLM-7B | Grade: 970.3665926795535 | Eliminated
#13 Llama-13B | Grade: 929.6268868888149 | Eliminated
#14 Dolly-12B | Grade: 929.1943463130976 | Eliminated
#15 Alpaca-13B | Grade: 798.6815779514078 | Eliminated
PRE-AlpacaEval
#1 WizardLM-13B | Grade: 1127.822808841937
#2 Vicuna-7B | Grade: 1077.1823389450524
#3 Vicuna-13B | Grade: 1075.4338443616266
#4 Guanaco-33B | Grade: 1074.8043135229418
#5 Gpt-3.5 | Grade: 1065.305736105376
#6 Gpt4all-13B | Grade: 1039.4091630861865 | Eliminated
#7 Koala-13B | Grade: 1038.205749976473 | Eliminated
#8 Mpt-7B | Grade: 1032.2893401162178 | Eliminated
#9 Chatglm-6B | Grade: 1027.1937496918501 | Eliminated
#10 Fastchat-t5-3B | Grade: 992.3481168791307 | Eliminated
#11 StableLM-7B | Grade: 979.3894141445692 | Eliminated
#12 Oasst-pythia-12B | Grade: 940.6438439723215 | Eliminated
#13 Dolly-12B | Grade: 886.1412110662756 | Eliminated
#14 Llama-13B | Grade: 880.0797724297793 | Eliminated
#15 Alpaca-13B | Grade: 763.7505968602533 | Eliminated
PRE-MT_Bench
#1 WizardLM-13B | Grade: 1065.5843776639435
#2 Vicuna-13B | Grade: 1062.3934138040302
#3 Guanaco-33B | Grade: 1052.2206466556906
#4 Vicuna-7B | Grade: 1035.1112817247572
#5 Gpt-3.5 | Grade: 1029.8316754711038
#6 Koala-13B | Grade: 1024.9307662983267 | Eliminated
#7 Chatglm-6B | Grade: 1020.5238960907612 | Eliminated
#8 Mpt-7B | Grade: 1014.0683255081057 | Eliminated
#9 Gpt4all-13B | Grade: 991.7142639623017 | Eliminated
#10 StableLM-7B | Grade: 979.8443261256327 | Eliminated
#11 Oasst-pythia-12B | Grade: 977.9930430111322 | Eliminated
#12 Fastchat-t5-3B | Grade: 953.0776159143571 | Eliminated
#13 Alpaca-13B | Grade: 949.129770731626 | Eliminated
#14 Dolly-12B | Grade: 928.511065779112 | Eliminated
#15 Llama-13B | Grade: 915.0655312591185 | Eliminated
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