André C. R. Martins (2008)
Replication in the Deception and Convergence of Opinions Problem
Journal of Artificial Societies and Social Simulation
vol. 11, no. 4 8
<https://www.jasss.org/11/4/8.html>
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Received: 19-Jan-2008 Accepted: 27-Sep-2008 Published: 31-Oct-2008
P(S|p,e,d,a,b)=ed+(1-e)[pa+(1-p)(1-b)] | (1) |
P(S|p,e,d,a,b)=e[0.5h+(1-h)d]+(1-e)[pa+(1-p)(1-b)] | (2) |
P(SR)= e{[e(0.5h+(1-h)d)+(1-e)(pa+(1-p)(1-b))] [0.5h+(1-h)d]}
+(1-e){[pa+(1-p)(1-b)][e(1-h)d+(1-e(1-h))(pa+(1-p)(1-b))]} P(S~R)= e{[e(0.5h+(1-h)d)+(1-e)(p(1-a)+(1-p)b)] [0.5h+(1-h)(1-d)]} +(1-e){[ pa+(1-p)(1-b)][e(1-h)(1-d)+(1-e(1-h))(p(1-a)+(1-p)b)]} P(~SR)= e{[e(0.5h+(1-h)(1-d))+(1-e)(pa+(1-p)(1-b))] [0.5h+(1-h)d]} +(1-e){[ p(1-a)+(1-p)b][e(1-h)d+(1-e(1-h))(pa+(1-p)(1-b))]} and P(~S~R)= e{[e(0.5h+(1-h)(1-d))+(1-e)(p(1-a)+(1-p)b)] [0.5h+(1-h)(1-d)]} +(1-e){[ p(1-a)+(1-p)b][e(1-h)(1-d)+(1-e(1-h))(p(1-a)+(1-p)b)]} |
(3) |
n = 4o(S)(1-o(S)) / [o(R)-o(S)]2 | (4) |
where it was assumed, for the numerator that o(R) and o(S) were very close and that o(S)(1-o(S)) was basically the same as o(R)(1-o(R)).
Figure 1. Posterior opinion as a function of the average proportion, 0.5(o(S)+o(R)). Each curve corresponds to a different number of pairs of articles (original experiment and replication). The results correspond to a=b=0.6. For 200 and 1,000 pairs, the results correspond to averages over 20 different realizations |
Figure 2. Posterior opinion as a function of the average proportion, 0.5(o(S)+o(R)). Each curve corresponds to a different number of pairs of articles (original experiment and replication). These results were obtained with a=b=0.7 |
Figure 3. Posterior opinion as a function of the average proportion, 0.5(o(S)+o(R)), for different values of a and b. The results correspond to 200 pairs of articles (original experiment and replication) and are averages over 20 different realizations |
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