(to appear) : [7] P. E. Kloeden, H. Keller and B. SchmalfuB, Towards a theory of random numerical dynamics. In Random Dynamical . Editors: M. Gundlach and W. Kliemann. Springer-Verlag, 1998 . P.E. Kloeden and B. SchmalfuB, Lyapunov functions and

doi:10.1201/b16999-33

ABSTRACT

Denote by Xi (t) � 0 the assessment made by expert i E { I , . . . , n} at time t E N = {O, 1 , 2, . . . } of the nonnegative magnitude under consider ation. Suppose that expert i arrives at a revision Xi (t + 1) by taking the assessments Xj (t) of the other experts into account with certain weights aij . If A denotes the row-stochastic matrix of the weights aij , i .e . , aij � 0 and

n L: aij = 1 , and x(t) the column vector of the Xi (t) this amounts to j=l

( 1 )

This model has been put foward in [6] where standard limit theorems for Markov chains are used to formulate conditions on the weights under which a consensus c will be reached, that is lim Xi (t) = c for all i E { I , . . . , n} .