[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81953-en":3,"doc-seo-81953-105":31,"detail-sidebar-cat-0-en-105":93},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},81953,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","When Do Prophets Profit in Prediction Markets","Prediction markets aggregate dispersed beliefs into trade prices that serve as probabilistic forecasts. Classical theory links forecasting accuracy to trading profit for a specific automated market maker (AMM) design, yet major exchanges today use central limit order books where informed forecasters often lose while uninformed heuristics can profit. This paper resolves the gap by proving a formal equivalence between predictive accuracy and profitability under any strictly proper scoring rule, provided the market has sufficient liquidity.","When do prophets profit in prediction markets? ∗  \nAnri Gu  \nUniversity of Chicago [anrigu@uchicago.edu](anrigu@uchicago.edu)  \nNicole Kagan  \nKalshi Research  \n[nkagan@kalshi.com](nkagan@kalshi.com)  \nAlec Sun  \nUniversity of Chicago [alecsun@uchicago.edu](alecsun@uchicago.edu)  \nJibang Wu  \nNew York University, Shanghai [wujibang@nyu.edu](wujibang@nyu.edu)  \nHaifeng Xu  \nUniversity of Chicago [haifengxu@uchicago.edu](haifengxu@uchicago.edu)  \narXiv :2607 .06 166v 1 [ cs .AI ] 7 Jul 2026  \nAbstract  \nPrediction markets aggregate dispersed beliefs into prices that act as probabilistic forecasts of uncertain events. Classical theory establishes a clean equivalence between forecasting accuracy and trading profit, but only for the specific automated market maker (AMM) design. However, the largest exchanges today are based on central limit order books in which informed forecasters routinely lose money while uninformed strategies can profit on simple heuristics. We resolve this discrepancy by establishing a formal equivalence between predictive accuracy and profitability.  \nFor any strictly proper scoring rule S, we exhibit a “proper” betting strategy that depends only on the forecaster’s prediction p and the market price q, and earns positive expected profit whenever p outperforms q under S and the market has sufficient liquidity. Moreover, this proper betting is essentially the only strategy with such robust profitability guarantee. The proof rests on a decomposition of expected profit that strictly generalizes the classical AMM guarantee and also explains how strategies can profit without an accuracy edge. Empirically, across thousands of forecasts by AI models, proper betting is the only strategy that reliably converts accuracy into profit, and we further identify systematic forecasting personas and show how the optimal proper strategy varies across them. A monthlong live deployment on Kalshi achieves +80 .33% return on investment with a Sharpe ratio of 3.35.  \n1 Introduction  \nPrediction markets let people trade contracts whose prices reflect the market’s estimated probability of an event, aggregating dispersed beliefs in the spirit of Hayek [1945]’s “marvel of the price system.”Empirical studies confirm that real prediction-market prices are well calibrated and often outperform polls and expert panels [Berg et al., 2008, Rothschild, 2009, Wolfers and Zitzewitz, 2004, Arrow et al., 2008] . The market scoring rule literature [Hanson, 2003, 2007, Chen and Pennock, 2007, Abernethy et al., 2013] formalizes the underlying incentive: an informed forecaster profits by trading against the market, and that trade pushes the price closer to the truth, so information aggregation and individual reward would go hand in hand.  \nThis picture, however, was developed for one specific market design: an automated market maker (AMM) [Hanson, 2003], in which an informed forecaster ensures profit by moving the market  \n∗ Authors are ordered alphabetically. The work by Jibang Wu is performed while visiting the University of Chicago.  \nPreprint.  \nprice exactly to their own forecast, with expected profit equal to their accuracy edge. The largest prediction markets today (e.g., Kalshi, Polymarket) instead use central limit order books [Kalshi, 2025, Polymarket, 2023, Ng et al., 2026], favored over AMMs for their scalability, adaptability, and regulatory fit (see Section A) . Prices arise from matching opposing limit orders, and a forecaster can pick any bet size but faces whatever price impact the order book happens to deliver, plus bid-ask spreads, finite liquidity, and platform fees. The link between accuracy and profit is no longer pinned down by the price-formation rule, and converting accuracy into profit becomes a separate problem.  \nRecent empirical work makes this gap visible. Forecasters whose predictions outperform the market on average routinely fail to convert that edge into trading profit [Della Vedova, 2026, Jang et al., 2025] . On the AI","cbCaifwV4qhJ5MiA","https://ap.wps.com/l/cbCaifwV4qhJ5MiA","pdf",882303,5,1,30,"English","en",105,"# Introduction\n## Market design: AMM vs central limit order books\n## Motivation from empirical discrepancies\n## Main contributions and theorem sketch","[{\"question\":\"What problem does the paper address about prediction markets?\",\"answer\":\"It addresses why accuracy and trading profitability are tightly linked in classical AMM theory, but appear disconnected in today’s order-book-based exchanges.\"},{\"question\":\"Under what condition does the paper establish a link between predictive accuracy and profit?\",\"answer\":\"For any strictly proper scoring rule, it shows that expected profit becomes positive whenever the forecaster outperforms the market under that scoring rule and the market has sufficient liquidity.\"},{\"question\":\"What strategy does the paper propose to convert accuracy into profit?\",\"answer\":\"It constructs a “proper” betting strategy that depends only on the forecaster’s prediction p and the market price q, and it provides a robustness guarantee tied to the scoring-rule framework.\"}]","When Do Prophets Profit in Prediction Markets | 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problem does the paper address about prediction markets?","Question",{"text":77,"@type":78},"It addresses why accuracy and trading profitability are tightly linked in classical AMM theory, but appear disconnected in today’s order-book-based exchanges.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"Under what condition does the paper establish a link between predictive accuracy and profit?",{"text":82,"@type":78},"For any strictly proper scoring rule, it shows that expected profit becomes positive whenever the forecaster outperforms the market under that scoring rule and the market has sufficient liquidity.",{"name":84,"@type":75,"acceptedAnswer":85},"What strategy does the paper propose to convert accuracy into profit?",{"text":86,"@type":78},"It constructs a “proper” betting strategy that depends only on the forecaster’s prediction p and the market price q, and it provides a robustness guarantee tied to the scoring-rule 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