Lecture+16+November+23

Lecture+16+November+23 - Today in Comparative Politics...

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Today in Comparative Politics Problem 4: tradeoffs in designing electoral rules Political parties Social cleavages and party systems

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Problem Set 5 CGG 13.3 CGG 14.1 CGG 14.2 CGG 14.6 Due in recitation section next week
The former homework problem 4 xR i y i regards x as at least as good as y Assumptions about R i xR i x for all outcomes x R i is reflexive Either xR i y or yR i x or both for all outcomes x and y. R i is complete If xR i y and yR i z, then xR i z for all outcomes x, y, and z. R i is transitive

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Preferences of person i xR i y i regards x as at least as good as y xP i y i strictly prefers x to y xI i y i is indifferent between x and y Thus xR i y means xP i y or xI i y . xP i y means xR i y and not yR i x . xI i y means xR i y and yR i x .
Transitivity of indifference If R i is transitive, so is I i . Why? If xI i y and yI i z, then xR i y and yR i z. Since R i is transitive, xR i z. If xI i y and yI i z, then zR i y and yR i x. Since R i is transitive, zR i x. Since xR i z and zR i x, we know that xI i z.

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Transitivity of strict preference If R i is transitive, so is P i . If xP i y and yP i z, then xR i y and yR i z. Since R i is transitive, xR i z. What if xI i z? Then we would have zR i x and xR i y, and hence zR i y since R i is transitive. Thus we have zR i y and yR i z, so yI i z. But we had assumed yP i z, so it can’t after all be true that xI i z. Since xR i z and not xI i z, we conclude xP i z.
Evading dictatorship Collective rationality : the group’s preferences R are transitive …and reflexive and complete. What happens if we relax collective rationality? Rule of consensus: xPy if and only if xP i y for all i Does the rule of consensus obey R-transitivity? 12 yx xz zy xIy and yIz, but xPz so no, it does not.

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Evading dictatorship Rule of consensus: xPy if and only if xP i y for all i Does the rule of consensus at least satisfy P-transitivity? Suppose xPy and yPz. Then xP i y for all i and yP i z for all i. Since individuals are P-transitive, xP i z for all i. Thus xPz, so this CCR is P-transitive.
P-transitive Satisfies Arrow’s other conditions Universal Scope Rather trivially, since the RoC is clearly well defined for all profiles of individuals’ preferences Unanimity Arrow’s requirement makes unanimous agreement sufficient for strict social preference; under the RoC, unanimity is necessary as well as sufficient for strict social preference Pairwise Determination Clearly under the RoC, social preferences over {x,y} depend only on individual’s preferences over {x,y}. Egalitarian

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This note was uploaded on 11/10/2011 for the course POLI SCI 790:103 taught by Professor Blair during the Fall '09 term at Rutgers.

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Lecture+16+November+23 - Today in Comparative Politics...

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