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25 August, 23:17

Suppose that the social choice procedure being used is sequential pairwise voting with a fixed agenda, and that you have agenda-setting power (that is, you get to choose the order). What order should you choose if you want alternative a to be the social choice?

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  1. 26 August, 00:41
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    This question is incomplete; here's the complete question.

    Suppose that we have three voters and four alternatives, and suppose the individual preference lists are as follows:

    Voter 1: a b c d

    Voter 2: c a b d

    Voter 3: b d c a

    Suppose that the social choice procedure being used is sequential pairwise voting with a fixed agenda, and that you have agenda-setting power (that is, you get to choose the order). What order should you choose if you want alternative a to be the social choice?

    Answer: c vs. d, then winner vs. b, then winner vs. a

    Explanation:

    In a Sequential Pairwise Voting, the winner may depend on the order in which the elections are carried, so having agenda-setting power and knowing individual preferences allows us to assure a specific outcome for the social choice.

    If we begin with the election of Alternative C vs. Alternative D, voters 1 and 2 will provide enough votes for Alternative C to win.

    Next, Alternative C being the winner, goes to election vs. Alternative B, and voters 1 and 3 provide enough votes for Alternative B to win.

    Finally, Alternative B being the winner goes to election vs. Alternative A, and voters 1 and 2 provide enough votes for Alternative A to win.
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