Sequential Pairwise Voting Dilemma

 

Suppose we have 3 voters and 4 alternatives (candidates) and suppose the sequence of preference list is as follows:

 

 

Number of voters (3)

Rank

1

1

1

First

A

C

B

Second

B

A

D

Third

D

B

C

Fourth

C

D

A

 

Show that if the voting system being used is sequential pairwise voting with a fixed agenda, and if you have agenda-setting power (ie you get to choose the order), then you can arrange for whichever alternative you want to win the election.  (In other words, create four agendas: one in which A wins, an agenda in which B wins, C wins, and D wins.)