In the 1998 Minnesota gubernatorial election, there were three main candidates: Norm Coleman (the Republican), Jesse “The Body” Ventura (an Independent), and Hubert Humphrey III (the Democrat). Although we can’t know for certain, the vot­ers probably ranked the candidates in a way similar to that found in the following table. The table tells us, for example, that 35% of the voters ranked Coleman first, Humphrey second, and Ventura third; and 20% of the voters ranked Ventura first, Coleman second, and Humphrey third; and so forth.

a. Suppose the election is by plurality rule, which means that the candidate with the most first-place votes wins the election. Who wins in this case?

b. In Challenges question 19, you were introduced to the Marquis de Condorcet. Today, voting theorists call a candidate a Condorcet winner if he or she can beat every other candidate in a series of 1:1 or “face-off” elections. Question 19 showed you that in some cases, there is no Condorcet winner. What about in the Minnesota guber­natorial election of 1998?

c. A Condorcet winner beats every other candidate in a face-off. A Condorcet loser loses to every other candidate in a face-off. Was there a Condorcet loser in the 1998 Minnesota gubernatorial election (given the preferences we have estimated)?

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Rank 123 2 Minnesota Gubernatorial Election, 1998 35% 28% 20% Coleman Humphrey Ventura Ventura Humphrey Humphrey Coleman 17% Ventura Ventura Coleman Humphrey Humphrey Humphrey Coleman