Cooke, Roger M.; Draaisma, Henk A method of weighing qualitative preference axioms. (English) Zbl 0557.92014 J. Math. Psychol. 28, 436-447 (1984). Summary: A method is developed for determining the absolute and relative strengths of qualitative preference axioms in normative Bayesian decision theory. These strengths are calculated for the three most common qualitative axioms; transitivity, the sure-thing principle, and dominance. The relative strength of the latter two axioms with respect to transitivity is calculated for special cases, and a bound is derived which is applicable to a larger class of decision problems. Possible implications of this theoretical work for decision heuristics are discussed. MSC: 91D99 Mathematical sociology (including anthropology) 91B08 Individual preferences 91B06 Decision theory 62C10 Bayesian problems; characterization of Bayes procedures 91E99 Mathematical psychology Keywords:qualitative preference axioms; transitivity; sure-thing principle; dominance; bound PDFBibTeX XMLCite \textit{R. M. Cooke} and \textit{H. Draaisma}, J. Math. Psychol. 28, 436--447 (1984; Zbl 0557.92014) Full Text: DOI References: [1] Allais, M., Le comportement de l’homme rationnel devant le risque, Econometrica, 21, 503-546 (1953) · Zbl 0050.36801 [2] Allais, M., The so-called Allais paradox and rational decisions under uncertainty, (Allais, M.; Hagen, O., The Expected Utility Hypothesis and the Allais Paradox (1979), Reidel: Reidel Dordrecht), 437-683 [3] Arbuckle, J.; Larimer, J., The number of two-way tables satisfying certain additivity axioms, Journal of Mathematical Psychology, 13, 89-100 (1976) · Zbl 0323.62052 [4] Ellsberg, D., Risk, ambiguity and the savage axioms, Quarterly Journal of Economics, 75, 643-669 (1961) · Zbl 1280.91045 [5] Kahneman, D.; Tversky, A., Prospect theory, Econometrica, 47, No. 2, 263-269 (1979) · Zbl 0411.90012 [6] Machina, M., ‘Rational’ decision making versus ‘rational’ decision modelling?, Journal of Mathematical Psychology, 24, 163-175 (1981) [7] MacCrimmon, K. R., Descriptive and normative implications of the decision-theory postulates, (Risk and Uncertainty (1968), Macmillan & Co: Macmillan & Co London), 3-24 [8] McClelland, G., A note on Arbuckle and Larimer, The number of two-way tables satisfying certain additivity axioms, Journal of Mathematical Psychology, 15, 292-295 (1977) [9] Savage, L. J., (The Foundations of Statistics (1972), Dover: Dover New York) · Zbl 0276.62006 [10] Tversky, A., Intransitivity of preference, Psychological Review, 76, No. 1, 31-48 (1969) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.