The most appropriate method that the committee should use to hire sales representatives is the instant runoff method. Instant Runoff Voting (IRV), also known as plurality with an exclusion, is a variation of the plurality voting technique that addresses the problem of disingenuous voting. The candidate receiving the fewest first-place votes is subsequently removed from the race, and any votes cast for them are transferred to the respondents’ next choice (Elkind et al. 605). Therefore, the technique is the most appropriate for the committee to use in its hiring since it satisfies the majority criterion. Using this concept, Z will be eliminated in the first round since it has the least number of votes and its votes are transferred to X. As a result, W has three votes, four votes for Y and 1 for X. Subsequently, because X has the least, it is eliminated, and its votes transferred to Y. Y would now have five first-choice votes, whereas W would have 3. Therefore, under IRV, candidate Y would win the majority with five first-place votes compared to W’s 3.
The Condorcet winner is Christopher Eccleston (CE). CE’s victory is that he had the most one-on-one wins compared to the rest of the participants, as illustrated in the calculations below. CE wins against MS by 69 to 51 points, while he emerges victorious against DT by 61 to 59 points in the second. DT draws PC on 60 points, whereas JW wins against MS by 79 to 41 points. In the fifth cell, CE beats MS again by the same points as in the first cell, while PC takes the lead against JW in the sixth tab by 75 points to 45. Finally, JW steals the show in the last column by beating CE by 76 to 44 votes. CE’s number of one-on-one wins is three, making him the winner.
The Borda count method violates the majority rule criterion and satisfies the monotonicity theorem. The monotonicity requirement states that if results shift exclusively to the advantage of the previous contestant in a rerun, there can be no additional points for the person who previously had the majority scores (Elkind et al. 610). Therefore, the Borda count methods do not hold to the majority paradigm from all the listed voting techniques.
Work Cited
Elkind, Edith, et al. “Properties of Multi winner Voting Rules.” Social Choice and Welfare, Vol. 48, no. 3, 2017, pp. 599-632.