Question
Please help with all parts! Suppose that, for any two candidate positions x and y, each voter either prefers x to y or prefers y
Please help with all parts!
Suppose that, for any two candidate positions x and y, each voter either prefers x to y or prefers y to x (that is, no voter regards any two positions as equally desirable). Also suppose that any individual voters preferences satisfy transitivity: if a voter likes a better than b and likes b better than c, then we know that voter likes a better than c. We say that a position x* is a Condorcet winner if for every position y different from x*, a majority of voters prefer x* to y. Suppose that there are 3 positions (x, y, and z) and three voters. Assume that voter 1 prefers x to y to z. (1 likes x better than y and likes y better than z). Of the remaining two voters, one of them prefers x to y (likes x better than y), while the other of them prefers y to x (likes y better than x). Also, one of the remaining voters prefers x to z (likes x better than z), while one of the remaining voters prefers z to x (likes z better than x). For each of the remaining two voters, specify how they rank x, y, and z such that there is no Condorcet winner.
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