EXAMPLE 5 Manipulability of Runoff Systems

Both the plurality runoff rule and the Hare system are manipulable. But rather than give the whole story away, we'll just present the sequences of sincere ballots in each case. Exercises 13 and 14 (page 457) ask you to figure out how the leftmost voter in each case can secure a more preferred outcome by a unilateral change of ballot.

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Election 1 for the Hare System
Election 1 for the Plurality
Runoff Rule