论文信息 - Towards consensus: some convergence theorems on repeated averaging

Towards consensus: some convergence theorems on repeated averaging

The problem of tendency to consensus in an information-exchanging operation is connected with the ergodicity problem for backwards products of stochastic matrices. For such products, weak and strong ergodicity, defined analogously to these concepts for forward products of inhomogeneous Markov chain theory, are shown (in contrast to that theory) to be equivalent. Conditions for ergodicity are derived and their relation to the consensus problem is considered.

E. Seneta | S. Chatterjee | S. Chatterjee

[1] Eugene Seneta,et al. Non‐Negative Matrices , 1975 .

[2] Harry Cohn. A ratio limit theorem for the finite nonhomogeneous Markov chains , 1974 .

[3] M. Degroot. Reaching a Consensus , 1974 .

[4] E. Seneta,et al. On the historical development of the theory of finite inhomogeneous Markov chains , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[5] Norman Crolee Dalkey,et al. An experimental study of group opinion , 1969 .

[6] Robert L. Winkler,et al. The Consensus of Subjective Probability Distributions , 1968 .

[7] M. Bartlett,et al. Weak ergodicity in non-homogeneous Markov chains , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[8] J. L. Mott. XXIV.—Conditions for the Ergodicity of Non-homogeneous Finite Markov Chains , 1957, Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences.

[9] W. Feller. An Introduction to Probability Theory and Its Applications , 1959 .

[10] D. Blackwell. Finite Non-Homogeneous Chains , 1945 .

[11] A. Kolmogoroff. Zur Theorie der Markoffschen Ketten , 1936 .