[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84727-en":3,"doc-seo-84727-105":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},84727,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Decentralized Aggregation of LLM Predictions via Wagering Mechanisms","Decentralized Aggregation of LLM Predictions via Wagering Mechanisms studies how to combine probabilistic outputs from multiple LLMs when an aggregator cannot access private model information and when models may strategically misreport. It introduces WALLA, a family of advantage-aligned wagering mechanisms where each model submits a prediction plus a learned wager, using wagers as aggregation weights. WALLA adds a leave-one-out baseline to the net payout to achieve dominant-strategy incentive compatibility, advantage–wager alignment, and prediction-agnostic wager optimization. Two variants balance normality and no-arbitrage while bounding worst-case deficits, and experiments match centralized accuracy with decentralized learning.","arXiv :2607 .04389v 1 [ cs .AI ] 5 Jul 2026  \nDecentralized Aggregation of LLM Predictions via Wagering Mechanisms  \nYuhong Luo ∗ David M. Pennock † Xintong Wang ‡  \nJuly 7, 2026  \nAbstract  \nIt is increasingly common to aggregate predictions from multiple LLMs, each with domain expertise or access to private tools and data, to improve collective prediction performance. In decentralized settings, aggregation weights need to be determined without access to models’ private information and should remain robust to strategic reporting. We propose a family of advantage-aligned wagering mechanisms for LLM aggregation (WALLA), in which each model reports a prediction and a learned wager, and predictions are aggregated using wagers as weights. WALLA introduces a leave-one-out baseline into thenet payout function, yielding three desirable properties: (1) dominant-strategy incentive compatibility of prediction under arbitrary belief structure, (2) advantage–wager alignment, where the optimal wager is proportional to the model’s expected score advantage, and (3) prediction-agnostic wager optimization, enabling decentralized learning of wager policies without requiring optimal predictions. We further instantiate two mechanism variants that trade off normality and no-arbitrage while maintaining a bounded worst-case deficit for the mechanism. Experiments on question-answering and forecasting benchmarks across heterogeneous models and private-information settings show that WALLA matches centralized aggregation methods in predictive performance, while simultaneously achieving decentralized learning, advantage-aligned aggregation weights, uncertainty awareness, and incentive-compatible prediction.1  \n1 Introduction  \nHaving different large language models—each with distinct capabilities, domain expertise, or access to private tools and data—collaborating on complex tasks is becoming increasingly common. When no single model dominates across domains, a natural objective is to combine their complementary strengths. For prediction tasks such as forecasting and question answering, this amounts to aggregating their probabilistic predictions.  \nA central challenge in aggregating LLM predictions is determining how much influence or weight each model should have on each question. In centralized systems, question-dependent aggregation weights can be learned directly from models’ hidden representations or private contexts [1, 2 , 3 , 4 , 5] . In decentralized deployments, however, models’ private signals are unavailable to the aggregator. Existing decentralized approaches either assign fixed weights [6, 7 , 8] or derive weights from reported confidence [9] or input perplexity [10] . However, aggregation weights based on these heuristic signals may be unreliable when models are miscalibrated and may also be strategically exaggerated by independent LLM services seeking greater influence or rewards. We propose designing decentralized mechanisms whose incentives align aggregation weights with models’ expected contribution to the aggregated prediction. Ideally, for each domain-specific question, models that expect to outperform the rest of the pool should participate and receive greater aggregation weights, while models that expect to be outperformed should receive little or no weight in the aggregation.  \nWe propose to address this challenge through wagering mechanisms [11 , 12 , 13 , 14], in which each participant reports a prediction and places a wager—a stake reflecting its confidence in that prediction. The  \n∗ Rutgers University, [y.luo@rutgers.edu](y.luo@rutgers.edu)  \n†DIMACS, Rutgers University, [dpennock@dimacs.rutgers.edu](dpennock@dimacs.rutgers.edu)[ ](dpennock@dimacs.rutgers.edu)‡Rutgers University, [xintong.wang@rutgers.edu](xintong.wang@rutgers.edu)  \n1 The source code is provided in [https://github.com/chailab-rutgers/WALLA](https://github.com/chailab-rutgers/WALLA).  \nmechanism then evaluates predictions using proper scoring rules and alloca","cbCaivcReUlMQ5u2","https://ap.wps.com/l/cbCaivcReUlMQ5u2","pdf",6945567,1,32,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What problem does WALLA address in decentralized LLM aggregation?\",\"answer\":\"It addresses how to set question-specific aggregation weights without access to models’ private information while remaining robust to strategic misreporting. The goal is to align influence with each model’s expected contribution to the aggregated prediction.\"},{\"question\":\"How does WALLA determine aggregation weights for each model?\",\"answer\":\"Each model reports a prediction and a wager, and predictions are aggregated using wagers as weights. The mechanism is designed so that the optimal wager is proportional to the model’s expected score advantage.\"},{\"question\":\"What incentive and optimization properties does the proposed mechanism achieve?\",\"answer\":\"WALLA provides dominant-strategy incentive compatibility for truthful prediction under arbitrary belief structures. It also enables prediction-agnostic wager optimization, allowing decentralized learning of wager policies without requiring models to submit optimal predictions.\"}]",1784197884,81,{"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},"decentralized-aggregation-of-llm-predictions-via-wagering-mechanisms","",{"@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/decentralized-aggregation-of-llm-predictions-via-wagering-mechanisms/84727/",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","2026-07-21","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 problem does WALLA address in decentralized LLM aggregation?","Question",{"text":75,"@type":76},"It addresses how to set question-specific aggregation weights without access to models’ private information while remaining robust to strategic misreporting. The goal is to align influence with each model’s expected contribution to the aggregated prediction.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does WALLA determine aggregation weights for each model?",{"text":80,"@type":76},"Each model reports a prediction and a wager, and predictions are aggregated using wagers as weights. The mechanism is designed so that the optimal wager is proportional to the model’s expected score advantage.",{"name":82,"@type":73,"acceptedAnswer":83},"What incentive and optimization properties does the proposed mechanism achieve?",{"text":84,"@type":76},"WALLA provides dominant-strategy incentive compatibility for truthful prediction under arbitrary belief structures. It also enables prediction-agnostic wager optimization, allowing decentralized learning of wager policies without requiring models to submit optimal predictions.","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},[93,97,101,105,110,115,120,123,128,131,135],{"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":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]