On the construction of weak orders from fragmentary information

An iterative method is proposed for constructing a weak order from a partial order on a set of stimuli that is based on individual pairwise comparison data. The method generalizes Duncan Luce's construction of the weak order induced by a semiorder. Various aspects of the iterative procedure are discussed, including its rationale, the number of iterations required to obtain a weak order, and the extent to which the data support additions to the initial partial order as a function of the number of iterations performed before the additions occur.This work was supported in part by a grant from the Alfred P. Sloan Foundation to The Institute for Advanced Study.The computer simulation programs for this study were written and run by William Gehrlein. I am grateful to him for his assistance.