4. (6) Consider a five-member society (call its members 1, 2, 3, 4, and 5) whose members have preferences over three alternatives (call the alternatives A, B, and C). Suppose that preferences for each individual are randomly determined. Using pairwise majority rule, what is the probability that there is a preference cycle? Hint: try to do this without brute force counting. You can write some Python or R code to solve this problem. 4. (6) Consider a five-member society (call its members 1, 2, 3, 4, and 5) whose members have preferences over three alternatives (call the alternatives A, B, and C). Suppose that preferences for each individual are randomly determined. Using pairwise majority rule, what is the probability that there is a preference cycle? Hint: try to do this without brute force counting. You can write some Python or R code to solve this