Voter preferences for a committee. A “Condorcet” committee of, say, 3 members is a committee that is preferred by voters over any other committee of 3 members. A scoring function was used to determine “Condorcet” committees in Mathematical Social Sciences (Nov. 2013). Consider a committee with members A, B, and C. Suppose there are 10 voters who each have a preference for a 3-member committee.

For example, one voter may prefer a committee made up of members A, C, and G. Then this voter’s preference score for the {A, B, C} committee is 2, because 2 of the members (A and B) are on this voter’s preferred list.

For a 3-member committee, voter preference scores range from 0 (no members on the preferred list) to 3 (all members on the preferred list). The table below shows the preferred lists of 10 voters for a 3-member committee selected from potential members A, B, C, D, E, F, and G.

a. Find the preference score for committee {A, B, C} for each voter.

b. For a randomly selected voter, let x represent the preference score for committee {A, B, C}. Determine the probability distribution for x.

c. What is the probability that the preference score, x, exceeds 2?

d. Is {A, B, C} a “Condorcet” committee?

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Voter: 1 2 3 4 5 6 A B C C B D E A C D F BCH DEF C E G 7 8 9 10 ACA ABC BCD ACY G G