Lecture 13 November 8

Lecture 13 November 8 - Africa and Middle East geography...

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Unformatted text preview: Africa and Middle East geography quiz today Notes and books closed Electronic devices off and stowed Pencil or pen only on your desk Today in Comparative Politics Democracy and majority rule Voting rules with two alternatives n individuals 2 alternatives: x and y yP i x, xI i y, xP i y D i = -1, 0, or 1 List of all votes cast: (D 1 , D 2 , D 3 , , D n ) Binary voting rule F (D 1 , D 2 , D 3 , , D n ) = D Voting rules with two alternatives Voting rule F (D 1 , D 2 , D 3 , , D n ) = D How many different voting rules are there? 3 n distinct patterns of individual votes To each one of them we can assign one of the 3 outcomes in {-1, 0, 1}. Voting rules with two alternatives Voting rule F (D 1 , D 2 , D 3 , , D n ) = D How many different voting rules are there? 3 n distinct patterns of individual votes To each one of them we can assign one of the 3 outcomes in {-1, 0, 1}. So there are such voting rules. n 3 3 Voting rules with two alternatives Voting rule F (D 1 , D 2 , D 3 , , D n ) = D How many different voting rules are there? 3 n distinct patterns of individual votes To each one of them we can assign one of the 3 outcomes in {-1, 0, 1}. So there are such voting rules. When n = 3, this number is over 7 trillion. n 3 3 Voting rules with two alternatives Voting rule F (D 1 , D 2 , D 3 , , D n ) = D How many different voting rules are there? 3 n distinct patterns of individual votes To each one of them we can assign one of the 3 outcomes in {-1, 0, 1}. So there are such voting rules. When n = 3, this number is over 7 trillion. To sift through them, it is useful to think in terms of desirable (and undesirable) properties that some of them have. n 3 3 Properties of voting rules Neutrality with respect to alternatives being voted upon: If F (D 1 , D 2 , D 3 , , D n ) = D, then F (-D 1 , -D 2 , -D 3 , , -D n ) = -D. Properties of voting rules Neutrality with respect to alternatives being voted upon: If F (D 1 , D 2 , D 3 , , D n ) = D, then F (-D 1 , -D 2 , -D 3 , , -D n ) = -D. Anonymity : reordering the arguments of F doesnt change its value. Properties of voting rules Neutrality with respect to alternatives being voted upon: If F (D 1 , D 2 , D 3 , , D n ) = D, then F (-D 1 , -D 2 , -D 3 , , -D n ) = -D. Anonymity : reordering the individual ballots in F doesnt change its value. F(1, 1, 0, 1, -1, -1, -1, 0, 1) F(0, -1, 1, 1, -1, 0, -1, 1, 1) Properties of voting rules Neutrality with respect to alternatives being voted upon: If F (D 1 , D 2 , D 3 , , D n ) = D, then F (-D 1 , -D 2 , -D 3 , , -D n ) = -D....
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Lecture 13 November 8 - Africa and Middle East geography...

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