Voting can give people an incentive to lie about their preferences.
Suppose there are three people on city council who collectively must decide whether to spend 100%, 50%, or 0% of their budget.
Spendy Sam, who prefers 100 > 50 > 0
Thrifty Tom who prefers 0 > 50 > 100
Mid Martha who prefers 50>0>100
The outcome will be decided by round-robin voting (pit two choices head to head, with the winner facing choice #3). Sam and Martha are honest people and will always vote their preferences. Tom controls the order of the voting and is not as scrupulous.
a) Does everyone have single-peaked preferences? What option should win if everyone reports preferences honestly?
b) Explain how Tom could manipulate pairwise voting to ensure getting his preferred choice his way.
c) In Congress, sometimes the opponents of a bill will vote in favor of a "killer amendment" that makes the bill even more extreme in their undesired direction. For example, a conservative Democratic senator broaden the 1964 Civil Rights Act at the last minute to include "sex" as a protected class. Given the senator’s history, many argued this was designed to tank the bill (which still passed). Explain killer amendments considering parts (1) and (2) of this problem.