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Comput."],"published-print":{"date-parts":[[2022,12,31]]},"abstract":"<jats:p>Peer prediction mechanisms incentivize self-interested agents to truthfully report their signals even in the absence of verification by comparing agents\u2019 reports with their peers. We propose two new mechanisms, Source and Target Differential Peer Prediction, and prove very strong guarantees for a very general setting.<\/jats:p>\n          <jats:p>\n            Our Differential Peer Prediction mechanisms are\n            <jats:italic>strongly truthful<\/jats:italic>\n            : Truth-telling is a strict Bayesian Nash equilibrium. Also, truth-telling pays strictly higher than any other equilibria, excluding permutation equilibria, which pays the same amount as truth-telling. The guarantees hold for\n            <jats:italic>asymmetric priors<\/jats:italic>\n            among agents, which the mechanisms need not know (\n            <jats:italic>detail-free<\/jats:italic>\n            ) in the\n            <jats:italic>single question setting<\/jats:italic>\n            . Moreover, they only require\n            <jats:italic>three agents<\/jats:italic>\n            , each of which submits a\n            <jats:italic>single item report<\/jats:italic>\n            : two report their signals (answers), and the other reports her forecast (prediction of one of the other agent\u2019s reports). Our proof technique is straightforward, conceptually motivated, and turns on the logarithmic scoring rule\u2019s special properties.\n          <\/jats:p>\n          <jats:p>\n            Moreover, we can recast the Bayesian Truth Serum mechanism\u00a0[\n            <jats:xref ref-type=\"bibr\">20<\/jats:xref>\n            ] into our framework. We can also extend our results to the setting of\n            <jats:italic>continuous signals<\/jats:italic>\n            with a slightly weaker guarantee on the optimality of the truthful equilibrium.\n          <\/jats:p>","DOI":"10.1145\/3565560","type":"journal-article","created":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T12:37:16Z","timestamp":1669898236000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Two Strongly Truthful Mechanisms for Three Heterogeneous Agents Answering One Question"],"prefix":"10.1145","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6878-0670","authenticated-orcid":false,"given":"Grant","family":"Schoenebeck","sequence":"first","affiliation":[{"name":"University of Michigan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3697-8807","authenticated-orcid":false,"given":"Fang-Yi","family":"Yu","sequence":"additional","affiliation":[{"name":"George Mason University"}]}],"member":"320","published-online":{"date-parts":[[2023,2,21]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1703486114"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2"},{"key":"e_1_3_3_4_2","article-title":"Measurement integrity in peer prediction: A peer assessment case study","author":"Burrell Noah","year":"2021","unstructured":"Noah Burrell and Grant Schoenebeck. 2021. 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