Showing papers on "Pairwise comparison published in 1970"

Comparison of experiments when the parameter space is finite

Abstract: The convex function criterion for "being more informative" for k-decision problems is-in Section 2-generalized to a convex function criterion for edeficiency for k-decision problems. The particular case of comparison by testing problems is discussed in Section 3. A theorem of Blackwell on comparison of dichotomies is generalized and a problem on products of experiments raised by Blackwell is settled by counter-example. Pairwise comparison of experiments and minimal combinations of experiments are discussed. The problem of composing and decomposing experiments by mixtures is treated in Section 4. It is shown that any experiment with finite parameter space is a mixture of complete experiments, and the complete experiments are characterized.

Unitary equivalence in pairwise spectral analysis

Abstract: A word of Dedication It is a privilege to share in the honoring of Professor Katuzi Ono on this occasion. It would be enough to be simply putting in evidence my high regard for a good and dear friend. But there is so very much more than that here. It is an opportunity for me to declare my esteem for the kind of mathematician who looks at his field from the outside as well as the inside; who sees the richness of all experience and seeks its instruction to know better and better the meaning of mathematics; who by the example of his own life urges young, coming scientists to the more productive path of an uncompartmentalized personality. Katuzi Ono is all of these.

Consumer Distance Transitivity

Abstract: In many marketing experiments or in questionnaires, subjects respond by circling a number on a given scale. Some subjects tend to be "yea" or "nay" sayers, a problem in that those subjects who use only part of the scale will have different variance to their responses. A similar problem exists when subjects are asked to subjectively define a difference between two objects using an unbounded scale. Some report only small differences between all pairs, while others report very large ones between many pairs. The variance of those who only see small differences is by definition smaller than that of those who see large ones. This article presents a method to measure these variances in a relative way, i.e., to measure the variances in terms of a percent of error rather than in absolute terms. In the theory of economic behavior, preferences are supposed to be transitive: if A is preferred to B, and B is preferred to C, then A is preferred to C. The concept of distance transitivity defines a stronger property: if A is preferred to B by an amount a1, and B is preferred to C by an amount a2, then A is preferred to C by an amount a, + a2. If A is preferred to C by an amount different from a, + a2, the relationship is not distance transitive, but even so it can be closer to or farther from it, in the following sense: if A is preferred to B by 4, B to C by 3, and A to C by 9, there is no distance transitivity-but one is closer than one would be if A were preferred to C by only 2, or by no less than 12. This article will present a methodological framework to measure distance transitivity. This is a rather strong property and, a priori, one would not think that preferences are that precise. However, an examination of more than 1,500 preference order transitivities from pairwise experiments showed subjects extremely consistent in preference ordering [5], despite the fact that many subjects had seldom, if ever, tried several brands. Table 1 shows the number of pairwise inconsistent judgments that the subjects made in this experiment.