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 doesn’t 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 doesn’t 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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