Deception and Convergence of Opinions Part 2: the Effects of Reproducibility

Recently Martins (Martins 2005) published an article in this journal analyzing the opinion dynamics of a neutral observer deciding between two competing scientific theories (Theory A and Theory B). The observer could not perform any experiments to verify either theory, but instead had to form its opinion solely by reading published articles reporting the experimental results of others. The observer was assumed to be rational (modeled with simple Bayesian rules) and the article examined how the observer's confidence in the correctness of the two theories changed as a function of number of articles read in support of each theory, and how much, if any, deception was believed to be present in the published articles. A key (and somewhat disturbing) result of this work was that for even relatively small amounts of perceived deception in the source articles, the observer could never be reasonably sure of which theory (A or B) was correct, even in the limit of the observer reading an infinite number of such articles. In this work we make a small extension to the Martins article by examining what happens when the observer only considers experimental results which have been reproduced by multiple parties. We find that even if the observer only requires that the articles he or she reads be verified by one additional party, its confidence in one of the two theories can converge to unity, regardless of the amount of amount of deception believed to be present in the source articles.