[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85825-en":3,"doc-seo-85825-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85825,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","LLMS AS A JURY: CROSS-MODEL CONSENSUS CAN OUTPERFORM PROCESS REWARD MODELS FOR LLM REASONING","Selecting correct answers among candidate reasoning chains is central to test-time scaling, but common selectors impose trade-offs: self-consistency inherits systematic errors from the same sampled model, while trained process or outcome reward models need labeled data and generalize poorly off distribution. This work introduces cross-model consensus, a label-free verifier where independently trained models solve once and agreement structure becomes the signal. Across seven benchmarks, it surpasses self-consistency and model self-scoring, closing most gap to an oracle selector via error decorrelation. A closed-form, parameter-free law predicts consensus accuracy from panel statistics and identifies a shared-error ceiling.","arXiv :2607 . 10 139v 1 [ cs .LG] 11 Jul 2026  \nLLMS AS A JURY: CROSS-MODEL CONSENSUS CAN OUTPERFORM PROCESS REWARD MODELS FOR LLM REASONING  \nNing Liu  \nIndependent Researcher [ningliu@umich.edu](ningliu@umich.edu)  \nABSTRACT  \nSelecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: selfconsistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution. We study a third signal, free at inference time: cross-model consensus, the degree to which independently trained models, each solving the problem once, agree on a final answer. We treat the panel as an LLM-jury, in which the structure of agreement, not any model’s score of another, is the verification signal. Across seven benchmarks it selects correct answers better than self-consistency and far better than a model scoring its own candidates: on competition math it closes the entire gap to an oracle selector, while self-scoring closes almost none. The mechanism is error decorrelation: independently trained models err differently, so their wrong answers scatter while the correct one accumulates agreement. We make this precise with a parameter-free law, derived in closed form, that predicts consensus accuracy from three measured panel statistics to a mean absolute error of 0 .03 and exposes the method’s ceiling: a shared-error floor where models share a misconception, near zero on math but non-trivial on science. Against four trained verifiers spanning discriminative, outcome, and generative reward models, the free LLM-jury matches the strongest inside their math training domain and is the topselector outside it. Cross-model consensus is thus a verifier we can characterize in advance: a law that says when to trust it, and a floor that marks where it cannot.  \n1 INTRODUCTION  \nModern reasoning systems spend compute at inference time by sampling many candidate solutionsand selecting among them (Wei et al., 2022; Brown et al., 2024; Snell et al., 2025; Muennighoffet al., 2025) . As the sample count grows a correct answer almost always appears somewhere in the pool, so the bottleneck shifts from generation to selection: the verifier that picks which candidate to return, not the generator, increasingly bounds end-to-end accuracy (Zhao et al., 2025; Liu et al., 2025a) . Yet the two verifiers that dominate practice each carry a structural cost. Self-consistency takes a majority vote over repeated samples of a single model (Wang et al., 2023); because every sample comes from the same model, it inherits that model’s systematic errors, so a confidently wrong model errs on most samples and votes its own error into the majority. Trained reward models (outcome and process reward models, or PRMs) (Lightman et al., 2023; Wang et al., 2024b; Zhang et al., 2025c; Liu et al., 2025b) score candidates with a learned network, but require annotated training data and, as we show, transfer poorly outside the distribution they are trained on. Both leave a gap: a verifier that is at once label-free, general, and able to catch the errors a single model is blind to.  \nWe study a third signal that fills this gap, needing neither extra samples of one model nor any training: cross-model consensus, the degree to which several independently trained models, each solving the problem once, agree on a final answer. We call this panel an LLM-jury (Figure 1): like jurors who deliberate independently before a verdict, each model solves the problem on its own and the structure of their agreement is the signal, a unanimous panel marking a trustworthy answer and a split one a problem to escalate. Crucially, our jurors never see the candidates or one another’s work,  \nCandidate Generation Independent Verification Panel (LLM-Jury) Selection  \n\n|  |  |  |  |  |  |  |  |  | Best-of-NSelector Selected:\u003Cbr>􀝕ො = 17 ✓\u003Cbr>\u003Cbr>➢ Predictable: law predicts c","cbCaifWk2usizKKv","https://ap.wps.com/l/cbCaifWk2usizKKv","pdf",540183,1,24,"English","en",105,"# Introduction\n## Problem setup: test-time verification\n## Cross-model consensus (LLM-jury)\n## Why agreement tracks correctness\n## Predictable law and bounded ceiling","[{\"question\":\"What is the proposed “LLM-jury” verification method?\",\"answer\":\"An independent panel of separately trained LLMs each solves the same problem once without seeing candidates or each other’s work, and the selected answer is the modal agreement class. Agreement structure serves as the verification signal.\"},{\"question\":\"How does cross-model consensus address the weaknesses of self-consistency and reward models?\",\"answer\":\"Self-consistency repeats correlated errors from a single model, which can produce confident wrong majorities. Reward models require labeled training data and transfer poorly off distribution, while cross-model consensus is label-free and relies on decorrelated mistakes.\"},{\"question\":\"What determines when the method should be trusted?\",\"answer\":\"The paper derives a parameter-free closed-form law that predicts consensus accuracy from three measured panel statistics, and it reveals a ceiling caused by shared-error floors when models share the same misconception.\"}]",1784206490,60,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"llms-as-a-jury-cross-model-consensus-can-outperform-process-reward-models-for-llm-reasoning","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/llms-as-a-jury-cross-model-consensus-can-outperform-process-reward-models-for-llm-reasoning/85825/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the proposed “LLM-jury” verification method?","Question",{"text":75,"@type":76},"An independent panel of separately trained LLMs each solves the same problem once without seeing candidates or each other’s work, and the selected answer is the modal agreement class. Agreement structure serves as the verification signal.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does cross-model consensus address the weaknesses of self-consistency and reward models?",{"text":80,"@type":76},"Self-consistency repeats correlated errors from a single model, which can produce confident wrong majorities. Reward models require labeled training data and transfer poorly off distribution, while cross-model consensus is label-free and relies on decorrelated mistakes.",{"name":82,"@type":73,"acceptedAnswer":83},"What determines when the method should be trusted?",{"text":84,"@type":76},"The paper derives a parameter-free closed-form law that predicts consensus accuracy from three measured panel statistics, and it reveals a ceiling caused by shared-error floors when models share the same misconception.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":28,"slug":108},5,"Comic","comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]