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Showing papers on "Pairwise comparison published in 1974"


Journal ArticleDOI
TL;DR: In this paper, the authors compile and systematize published and dispersed results on two aspects of balancing in incomplete block designs, i.e., pairwise balance and variance balance, and put them in a form which is useful for further work in this area.
Abstract: The purpose of this paper is three-fold. The first purpose is to compile and to systematize published and dispersed results on two aspects of balancing in incomplete block designs, i.e., pairwise balance and variance balance. This was done in order to establish the status of these two concepts of balance in published literature and to put them in a form which is useful for further work in this area. Also, the results in this form are necessary for the development of the remainder of the paper.

50 citations



01 Jan 1974
TL;DR: A tribute must also go to my talented typist, Mrs. Delores Gold as discussed by the authors, who was a friend and advisor to this work, as well as to Professor P. K. Sen.
Abstract: MARCH 1974 ii ACKNOWLEDGMENTS I wish to express my gratitude to Professor P. K. Sen who, as my adviser, efficiently guided this work. A tribute must also go to my talented typist Mrs. Delores Gold.

3 citations


Journal ArticleDOI
TL;DR: VOTEPOW uses combinatiorial mathematics to generate three a posteriori measures for the power in voting bodies, based on a model created by Brams (l972) of New York University, to produce a measure of individual voting power and two measures of conditional or relational voting power.
Abstract: VOTEPOW uses combinatiorial mathematics to generate three a posteriori measures for the power in voting bodies, based on a model created by Brams (l972) of New York University. Using roll-call data as input, the program produces a measure of individual voting power and two measures of conditional or relational voting power (Kushner & Urken, 1973). Output. The first piece of output generated by VOTEPOW is a listing of individual voting power ratings for all actors of a voting body. The individual voting power of an actor is defined as that probability that the preference of an actor, i, will agree with the majority outcome across a set of roll calls, i.e., P(i). For example, an actor who votes with the majority on nine out of nine roll calls would have an individual voting power of 1.00, since the voter's chance agrees with the majority outcome on all roll calls. The second measure [pairwise probabilistic power (PDIFF)] generated by VOTEPOW is a conditional or relational measure of voting power. This measure represen ts the influence of pairwise agreement or disagreement with other actors on an actor's chances of being on the winning side, i.e., voting with the majority. Thus, conditional probability gauges the extent to which the actors i and j sustain majority outcome, given that they agree (AG) with each each other [P(i,j I AGi,i)] ; and conditional probabilities that, given that i and j disagree (DG) with each other, i votes with the majority [P(i I DGi,i)], or j votes with the majority [PO I DGi,i)] . These conditional probabilities enable us to obtain a measure which represents the difference that agreement or disagreement makes on each actor's chances of being on the winning side. For example, for Actor i,

1 citations


Journal ArticleDOI
T. Tsuda1
01 Dec 1974-Calcolo
TL;DR: In this article, a pairwise sampling technique is considered, where one draws two samples at a time when required, one from each of the two sums of terms, each of which suffers stochastic fluctuations accompanying samplings.
Abstract: The difficulty is first pointed out concerning the nonlinear interpolation of functions defined in a space of very many dimensions. There is a method using a sampling technique that works well fork≈10–20 (k=number of dimensions). The sampling errors, however, increase in powers ofk, so that fork greater than the above-quoted values the computation is no more feasible. This is due to the subtraction between two large sums of about the same magnitude, each of which suffers stochastic fluctuations accompanying samplings. To avoid this unfavorable effect, a pairwise sampling technique is considered where one draws two samples at a time when required, one from each of the two sums of terms. By this new avenue of approach, the probabilistic interpretation becomes much more straighforward than hitherto conceived and the reduction of standard errors is also remarkable especially for the cases of very many dimensions.