Suppose this preference table gives the results of an election among 3 candidate

Question

Suppose this preference table gives the results of an election among 3 candidates, A, B, and C. Who wins using the Plurality method? Does any candidate get a majority of the first-place votes? If so, which one? Who wins using Pairwise Comparisons? Does any candidate beat every other candidate one-on-one? If so, which one? Who wins using the Border Count method? Suppose candidate B drops out but the winner is still chosen using the Border Count method, Is the winner the same as in 'e' above? If not. which candidate does win?

Explanation / Answer

(B)
In Plularity method, majority means getting more than 50% 0f votes. Here total votes are (27+24+2) = 53, out of these A got 27 which is exactly 1 more than 50%. Hence A is the candidate who gets a majority of the first place votes.

(D)
A beats every other candidate in one-on-one.
In column 1, A is preferred over C with 27 votes whereas in column 2 and 3 is preferred over A with cumulative 24 + 2 = 26 votes. As A got more votes than C, A beats C in one-on-one.
Similarly, A beats B with 27 against 26.

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