Project 2: Group Decision

This project deals with binary decision making, that is, the problem of deciding on "yes" or "no." It has two parts.

Part A. There is a group of n independent decision makers, each being "normal" with a decision error rate (probability) of 15%. The majority of the individual decisions is taken as the group decision. (a) Give formulas for computing the error rate of the group for an arbitrary n. Use them to determine the error rates of the group of n = 3 and of the group of n = 5. (b) Write Matlab or Python code for a computer simulation to determine approximately the error rate of the group for an arbitrary n. Use it to determine the error rates of the group of n = 3 and of the group of n = 5. (c) Suppose a good decision maker has an error rate of 5%. Is the group a good decision maker for n = 3 or n = 5? Does it make sense?

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