{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T02:38:50Z","timestamp":1787279930832,"version":"3.56.0"},"reference-count":57,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>The sequential probability ratio test (SPRT) and related drift-diffusion model (DDM) are optimal for choosing between two hypotheses using the minimal (average) number of samples and relevant for modeling the decision-making process in human observers. This work extends these models to group decision making. Previous works have focused almost exclusively on group accuracy; here, we explicitly address group decision time. First, we derive explicit solutions for the error rate and probability distribution function of decision times for a group of independent, (possibly) nonidentical decision makers using one of three simple rules: Race, Majority Total, and Majority First. We illustrate our solutions with a group of N i.i.d. decision makers who each make an individual decision using the SPRT-based DDM, then compare the performance of each group rule under different constraints. We then generalize these group rules to the $\\eta$-Total and $\\eta$-First schemes, to demonstrate the flexibility and power of our approach in characterizing the performance of a group, given the performance of its individual members.<\/jats:p>","DOI":"10.1137\/10079700x","type":"journal-article","created":{"date-parts":[[2012,2,8]],"date-time":"2012-02-08T18:16:49Z","timestamp":1328725009000},"page":"121-138","source":"Crossref","is-referenced-by-count":7,"title":["Group Decision-Making Models for Sequential Tasks"],"prefix":"10.1137","volume":"54","author":[{"given":"Margot","family":"Kimura","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeff","family":"Moehlis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,8]]},"reference":[{"key":"R1","unstructured":"M. M. 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Condorcet,\n                      Essai sur l'application de l'analyse \u00e0 la probabilit\u00e9 des d\u00e9cisions rendues \u00e0 la pluralit\u00e9 des voix, Paris\n                      , 1785. English translation: I. McLean and F. Hewitt, eds., Condercet: Foundations of Social Choice and Political Theory, Edward Elgar, Brookfield, VT, 1984."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1038\/471040a"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1109\/7.481268"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0749-5978(92)90044-8"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.2307\/249563"},{"key":"R17","unstructured":"B. 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Swets,\n                      Signal Detection Theory and Psychophysics\n                      , John Wiley & Sons, New York, 1966."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1007\/BF00125672"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1093\/ietfec\/e88-a.10.2496"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1109\/7.303740"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1006\/game.1997.0587"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1007\/s003550200190"},{"key":"R29","unstructured":"M. Kimura,\n                      Group Decision-Making Models\n                      , Ph.D. thesis, University of California, Santa Barbara, 2011. (Please contact the authors to request a copy.)"},{"key":"R30","doi-asserted-by":"crossref","unstructured":"M. W. Koch and K. T. 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Lehmann,\n                      Testing Statistical Hypotheses\n                      , John Wiley & Sons, New York, 1959."},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2003.815774"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1016\/j.tree.2004.02.004"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2006.890821"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1002\/bdm.464"},{"key":"R39","unstructured":"N. A Macmillan and C. D. Creelman,\n                      Detection Theory: A User's Guide\n                      , Cambridge University Press, New York, 1991."},{"key":"R40","doi-asserted-by":"crossref","unstructured":"J. D. Papastavrou and M. 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