C. Genest et Lp. Rivest, A STATISTICAL LOOK AT SAATYS METHOD OF ESTIMATING PAIRWISE PREFERENCES EXPRESSED ON A RATIO SCALE, Journal of mathematical psychology, 38(4), 1994, pp. 477-496
Citations number
36
Categorie Soggetti
Psychologym Experimental","Social Sciences, Mathematical Methods","Mathematical, Methods, Social Sciences
This article is concerned with the problem of estimating n greater tha
n or equal to 2 object or attribute weights from a set of n(n - 1)/2 p
airwise preferences expressed on a ratio scale. Saaty's classical solu
tion to this problem (Saaty, 1977, Journal of Mathematical Psychology,
15, 234-281) is to use as an estimate the normalized positive eigenve
ctor corresponding to the Perron eigenvalue of the binary comparison m
atrix. An alternative procedure, rooted in the statistical theory of l
inear models, involves minimizing the total sum of square deviations m
easured on the logarithmic scale (de Jong, 1984, Journal of Mathematic
al Psychology, 28, 467-478; Crawford and Williams, 1985, Journal of Ma
thematical Psychology, 29, 387-405). In recent years, extensive simula
tion studies have revealed that the two methods have a tendency to pro
duce similar estimates. This observation is theoretically strengthened
here. In addition, a statistically valid interpretation is provided f
or Saaty's eigenvalue-based index of cardinal consistency in a set of
responses. This makes it possible to derive an approximate distributio
n for this quantity under reasonable assumptions and ultimately leads
to a critical examination of the assumptions underlying the so-called
10% cut-off rule recommended by Saaty for identifying response matrice
s that exhibit too large a degree of cardinal inconsistency. (C) 1994
Academic Press, Inc.