Axlomsfortheaveraginganuaddlng Representatlonsoffunctlonalmeasurement*


NH. Anderson has applied simple averaging and adding representations to numerous bodies of category data (see Anderson (1970,197 1, and 1974) for summaries and further references). The averaging representation, which seems the more useful, is as follows: there are several sets of attributes or factors, Ft. F2, . . . . Fk, and to each set is associated a numerical weight wi and a real-valued function Qi such that the numerical scale assigned to the stimulus complex Ct;, . . . . fk), fi E Fi, is given by $_ I u~i&&)/Cf= ! \t’ie The adding representation does not involve the weights, so the scale assigned to u’,, Ii, . ...&) is of the form Sf= I @im To my knowledge, no one has presented axioms for an ordering of such complexes of attributes that are sufficient to give rise to the averaging representation. and the axioms of additive conjoint measurement apply only to addition over a fiied number of factors. My purpose here is to indicate that, in fact, one such set of conditions for averaging really is known under the guise of conditional expected utility (Krantz et al. (197 1) Ch. 8): Luce and Krantz (1971)), and that a simple modification of it yields the additive representation. It is important at the outset to recognize that the deslired representations are both distinct from that of ordinary additive conj Ant measurement (Krantz et al. (197 1) Ch. 6). the reason being that they apply to different sized subcomplexes of attributes whereas conjoint measurement does not. For example, if 1; and gi are elements of &, then one c:w

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@inproceedings{Kim2001AxlomsfortheaveraginganuaddlngR, title={Axlomsfortheaveraginganuaddlng Representatlonsoffunctlonalmeasurement*}, author={Km Kim}, year={2001} }