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Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"<jats:p>People often cooperate out of concern for their reputation. The corresponding theory of indirect reciprocity predicts that such cooperation can only evolve if people\u2019s opinions of each other are sufficiently correlated. This correlation, however, can be difficult to achieve when individuals form their opinions independently from one another, as in private assessment models. In that case, errors can generate disagreements that propagate throughout a population. Here, we identify a simple mechanism that mitigates this problem. Most prior work assumes that observers revise only the reputations of donors\u2014the individuals who choose whether to cooperate or defect. We instead allow observers to also revise the reputations of recipients\u2014the individuals affected by the donors\u2019 choices. Using analytical calculations and simulations, we show that such dual reputation updates help synchronize opinions and facilitate cooperation. To demonstrate this approach, we focus on a particularly simple rule, which we call Recipient Image Scoring (RIS). Under RIS, recipients are assessed as good whenever donors choose to cooperate with them. We show that this rule for judging recipients effectively complements the classical leading-eight rules for judging donors. Our results establish dual assessment as a simple mechanism for cooperation that relies only on directly observable information.<\/jats:p>","DOI":"10.1073\/pnas.2624656123","type":"journal-article","created":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T17:06:56Z","timestamp":1787850416000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Indirect reciprocity with dual private assessment"],"prefix":"10.1073","volume":"123","author":[{"given":"Yukari Jessica","family":"Tham","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03tgsfw79","id-type":"ROR","asserted-by":"publisher"}],"name":"Graduate School of Humanities, Kobe University","place":["Kobe, Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5116-955X","authenticated-orcid":false,"given":"Christian","family":"Hilbe","sequence":"additional","affiliation":[{"name":"Interdisciplinary Transformation University","place":["Linz, Austria"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5872-420X","authenticated-orcid":false,"given":"Yohsuke","family":"Murase","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/022hvg611","id-type":"ROR","asserted-by":"publisher"}],"name":"RIKEN Center for Interdisciplinary Theoretical and Mathematical Science","place":["Wako, Japan"]},{"id":[{"id":"https:\/\/ror.org\/03r519674","id-type":"ROR","asserted-by":"publisher"}],"name":"RIKEN Center for Computational Science","place":["Kobe, Japan"]},{"id":[{"id":"https:\/\/ror.org\/02evnh647","id-type":"ROR","asserted-by":"publisher"}],"name":"Graduate School of Science and Engineering, Saitama University","place":["Saitama, Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,8,27]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1515\/9781400832255"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1201\/b14069"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1133755"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2302107120"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms1442"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.288.5467.850"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1038\/415424a"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2008.12.006"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1301210110"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1177\/2372732214548426"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1111\/spc3.12255"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.2018.0116"},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature04131"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2018.06.018"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.3390\/g11030027"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2004.06.005"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2005.08.008"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1011271"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1013584"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature07601"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2025.112043"},{"key":"e_1_3_4_22_2","doi-asserted-by":"crossref","unstructured":"H. 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