In addition to the shortcomings we discussed in this section, several of the voting meth...

In addition to the shortcomings we discussed in this section, several of the voting methods can be manipulated through insincere voting or other means. Insincere voting (not voting in accordance with your true preferences) may be practiced to gain long-run strategic advantage, such as during a sequence of runoffs. For instance, if you know a candidate you really dislike is poised to win, you might change your vote to support a candidate you find less objectionable in the hope of defeating the front runner.

The following table summarizes the preferences for 9 voters faced with 3 alternatives. A majority is needed to win.

Since A has the most votes, but not a majority, a runoff election is held between B and C, with the winner running against A.

a. Determine the winner of the runoff election and the election following the runoff. Show the vote totals.

b. How could voters who support A as their first choice benefit from voting insincerely? What is the minimum number of insincere voters needed to ensure the election of A?