Part B. There is a group of 5 independent decision makers, A, B, C, D, E, with error rates of

5%, 10%, 10%, 10%, 15%, respectively. If the group is democratic, then the majority of all the 5 individual decisions would be taken as the group decision.

(a) Give formulas for computing the error rate of the democratic group.

(b) Write Matlab code for a computer simulation to determine approximately the error rate of the democratic group.

(c) Use the formulas and the computer simulation, respectively, to determine the error rate of the democratic group.

(d) For this group, who is best to be the dictator and what is the error rate of the dictatorial group?

(e) Which one has a smaller error rate, dictatorship or democracy? Does it make sense?

(f) If A, B, C, D, E have error rates of 5%, 10%, 10%, 10%, 50%, respectively, which one has a smaller error rate, dictatorship or democracy?

(g) If A, B, C, D, E have error rates of 5%, 20%, 20%, 20%, 20%, respectively, which one has a smaller error rate, dictatorship or democracy?