LLMs as a Jury: Cross-Model Consensus Can Outperform Process Reward Models for LLM Reasoning

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Next we'll be talking about the paper "LLMs as a Jury: Cross-Model Consensus Can Outperform Process Reward Models for LLM Reasoning".

Jane: The paper was written by Ning Liu from.

Tom: Stay tuned as we take you through the paper and discuss its implications.

Jane: We also have Lu with us today — senior AI researcher at Tsinghua.

Tom: We also have Meng with us today — lead engineer at a mysterious AI startup.

Jane: We also have Lalam with us today — the in-house Large Language Model.

Tom: Alright, let's get started.

Title: Tom: Welcome back to the show, everyone. Today we’re looking at a paper that’s got a wonderfully simple title: “LLMs as a Jury: Cross-Model Consensus Can Outperform Process Reward Models for LLM Reasoning.” Jane, I have to say, that title alone tells you most of the story.

Jane: It really does, Tom. The idea is that instead of having one model check its own work, you get several different models to solve the problem independently, and then you take a vote. If they all agree on an answer, that’s a strong signal it’s correct. The paper calls this an “LLM-jury,” which is such a vivid way to think about it.

Tom: And the punchline is that this simple voting scheme beats the fancy trained reward models that people have been building. Those are the process reward models, or PRMs, that score each step of a solution. The paper shows that on competition math, the jury closes the entire gap to an oracle selector, while a model scoring its own candidates captures almost none of that gap.

Jane: Right, and that’s the part I find so striking. The paper says a model scoring its own twelve candidates captures essentially zero percent of the achievable selection gain over self-consistency. But three models that never see each other’s work capture one hundred percent of it. So the signal that separates a correct answer from a wrong one lives between models, not inside any single one.

Tom: That’s a profound observation, Jane. It’s like the classic idea that diverse perspectives catch errors that a single perspective misses. The paper formalizes this with something they call error decorrelation. When models are independently trained, their mistakes tend to be different, so wrong answers scatter while the correct answer accumulates agreement.

Jane: Exactly. And that’s why self-consistency, which resamples the same model over and over, inherits that model’s systematic errors. If the model has a blind spot, every sample will have that same blind spot, and the majority vote will confidently pick the wrong answer.

Tom: So the jury is a label-free, training-free verifier. You don’t need annotated data, you don’t need to train a reward model. You just need a few different models that you probably already have access to. That’s a big deal for practitioners.

Jane: It is. And the paper goes further. They derive a mathematical law that predicts when the jury will work and when it won’t. That’s the part we should dig into next, because it gives you a ceiling, a floor, and a way to know in advance whether you can trust the verdict.

Tom: I’m hooked. Let’s get into that law and what it means for actually using this in practice.

Summary: Jane: So Tom, we’ve established the basic idea of the LLM-jury. Now let’s talk about what the paper actually found across their seven benchmarks. They tested on competition math like AIME, on MATH-five hundred on OlympiadBench, on grade-school math, on graduate science with GPQA, and on broad knowledge with MMLU-Pro.

Tom: And the results are pretty consistent. The jury beats self-consistency on every benchmark that has headroom. On AIME-two thousand twenty-four it’s a twenty-point jump, from thirty-six point seven to fifty-six point seven percent accuracy. That’s enormous. And it beats the single-model LLM-verifier on all seven benchmarks.

Jane: The single-model verifier is the weakest selector, which is really telling. That’s the setup where one model scores each candidate solution and picks the highest score. The paper’s point is that a model cannot adjudicate its own candidates, because it shares the same blind spots that produced the errors in the first place.

Tom: Right. And the advantage holds even when they switch the generator. They repeated the whole comparison with DeepSeek-V3 point 2 as the generator instead of Qwen3-235B, and the jury still wins on every unsaturated benchmark. So it’s not about one specific model’s pool of candidates.

Jane: Now, the part I find most exciting is the predictive law. The paper derives a closed-form equation that predicts the jury’s accuracy from just three measured statistics: the mean member accuracy, the pairwise error correlation, and the shared-misconception rate. And it predicts consensus accuracy to a mean absolute error of zero point zero three across all seven benchmarks.

Tom: That’s remarkably precise for a parameter-free law. And it also predicts the method’s ceiling, which they call the shared-error floor. That’s the rate at which the whole panel agrees on the same wrong answer. On math, that floor is near zero. But on GPQA science questions, it’s about three percent, because independently trained models share some graduate-level misconceptions.

Jane: So the law tells you when to trust the jury and where it will fail. That’s the kind of characterization you rarely get for a heuristic method. It’s not just “voting helps.” It’s a precise statement about the conditions under which voting helps and the irreducible error that remains.

Tom: And that irreducible error is a real thing. They found cases on GPQA where all four models were unanimously wrong, and they were wrong for the same reason. For example, all four reported a thermochemical quantity in the textbook-default unit instead of the per-gram basis the question asked for. That’s a shared convention, not a random slip.

Jane: That’s a beautiful example, Tom. It shows the floor is structured, not noise. And it means the jury is blind exactly where models have internalized the same convention. The law quantifies that blindness in advance.

Tom: So we have a verifier that’s free, label-free, and predictable. But the big question for me is how it stacks up against the trained reward models that people are actually using. That’s the comparison that matters for adoption.

Improvements: Tom: So Jane, we’ve seen the jury beat self-consistency and the single-model verifier. But the real test is against trained reward models. The paper compares against four of them: two discriminative process reward models, Qwen2 point 5-Math-PRM at 7B and 72B, an outcome reward model called AceMath-72B, and a generative verifier called ThinkPRM-14B.

Jane: And the results are striking. On MATH-five hundred which is exactly the kind of math these reward models were trained on, the jury matches the strongest of them. It gets ninety-six point six percent, versus ninety-five point six for AceMath. That difference isn’t statistically significant, but the point is the free jury is right there with the best trained verifier.

Tom: And out of domain, on GPQA, the jury is the top selector. It gets thirty-five point nine percent, beating all four trained verifiers, some of them significantly. That’s the key advantage. Trained reward models don’t transfer well outside their training distribution, but cross-model agreement is domain-agnostic.

Jane: That’s the improvement the paper suggests, in a nutshell. Instead of spending resources training a reward model that only works on math, you can use a panel of models you already have. The jury is immediately deployable, with no training cost, and it generalizes to new domains.

Tom: And there’s a clever engineering trick too. They propose an agreement-gated cascade. You run a cheap two-model panel on every problem. If they agree, you accept their answer. If they disagree, you escalate to the full four-model panel. This recovers the full panel’s accuracy at close to two-model cost.

Jane: The escalation rate self-scales with difficulty. On GSM8K, only three percent of problems escalate. On AIME, it’s sixty to seventy percent. So you spend the extra compute exactly where it matters. At matched average cost, this cascade beats self-consistency by a wide margin on AIME-two thousand twenty-four seventy percent versus thirty-six point seven.

Tom: And the signal generalizes beyond math. On code, they define consensus behaviorally. Two programs agree if they produce identical outputs on a shared battery of test inputs. That predicts correctness at an AUROC of zero point seven four eight, and unanimous programs pass held-out tests ninety-five point two percent of the time versus fifty-two point nine percent when the panel splits.

Jane: So the same principle works across modalities. And they even show it can be used as a label-free reward for fine-tuning. A policy trained with cross-model consensus as the reward captures most of the gain that gold labels provide, at both 1 point 5B and 7B scale.

Tom: That’s a full toolkit, Jane. Verification, abstention, routing, and training signal, all from the same simple idea. But I want to hear what Lu and Meng think about the practical side. Lu, does this change how you think about building reasoning systems?

Lu: It absolutely does, Tom. The paper’s framing of a “shared-error floor” is the part I find most profound. It tells us that the ceiling of this method isn’t a property of the method itself, but of how alike current models are. If we train models that fail differently, the floor drops and the jury gets stronger. That’s a research direction in itself.

Meng: And from an engineering standpoint, the cost story is what sells it. You’re not hosting a separate reward model. You’re using the models you already query. The cascade makes the compute story even better. I’d want to see how this holds up with more diverse panels and different model families, but the open-weight results in the appendix are encouraging.

Jane: Great points from both of you. The paper really does span theory, experiments, and practical deployment. Let’s wrap up with our final thoughts.

Conclusion: Tom: We’ve covered a lot of ground on “LLMs as a Jury: Cross-Model Consensus Can Outperform Process Reward Models for LLM Reasoning.” Let’s pull it together. The core idea is that agreement among independently trained models is a powerful verification signal, one that’s free at inference time and needs no training data.

Jane: And the evidence is strong. On competition math, the jury closes the entire gap to an oracle selector. It matches the strongest trained reward models inside their training domain and beats them outside it. And the parameter-free law predicts its behavior to within zero point zero three mean absolute error.

Tom: The law also gives you the method’s ceiling, the shared-error floor. On math, that floor is near zero. On science, it’s measurable, because models share some misconceptions. That’s not a flaw in the method, it’s a measurement of how alike current models are.

Lu: And that measurement points to a concrete path forward. If we want stronger verification, we should train models that fail differently. The law quantifies the value of that investment.

Meng: From my side, the practical takeaway is that you can deploy this today with models you already have. The cascade keeps the cost down, and the abstention dial gives you a calibrated way to decide when to answer and when to escalate.

Jane: So we’ll say goodbye to this paper with a sense of excitement. It’s rare to find a method that’s simple, free, predictable, and competitive with trained systems. The LLM-jury is all of those things.

Tom: And the implications go beyond verification. The same signal can train models, route compute, and even work for code. That’s a versatile tool. Thanks for joining us, and we’ll see you next time with another paper.