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Instutional Analysis Lecture 5: Legislative Organization How a bill becomes a law Arrow’s Theorem Completeness - (Transitivity) If x beats y and y beats z in the social ordering then x beats z. Universal Domain - the rules must apply to all possible combinations of individual preference orderings. Pareto Optimality- x beats y whenever everyone individually prefers x to y. Independence of irrelevant alternatives - The collective preferences between two alternatives never depend on individual preferences regarding other alternatives. Non-Dictatorship. No individual is so powerful that, for every pair of alternatives x and y, x beats y socially even if she prefers x to y while everyone else prefers y to x. CUPID Implications Arrow showed that these 5 criteria are incompatible with any system of preference aggregation. Example: Simple Majority Rule Simple Voting Paradox Majority Rule Violates Transitivity Suppose we have a preference ordering as follows: A x y z B y z x C z x y Problem: Collective preferences are cyclic and every feasible alternative is unstable, such that: x>y, y>z; and z>x. No unique stable outcome: x z y Significance We can't predict what will be the outcome under a majority rule setting. There is no true social welfare maximizing outcome Then majority government cannot be modeled as maximizing anything, if any outcome is possible no matter how unrepresentative. When Does Stability Occur? Black’s Theorem: One-dimensional issue space Ideal (bliss) points: the one point on the line they prefer to all others The only stable point on the line is the median x1 x2 x3 xm x5 x6 x7 Xm is the Condorcet winner because it is the point that beats all others. Median Voter Result In general, for any distribution of voters with single peakedness there will be a median voter. If we assume that 1) Individuals have single peaked preference in a one-dimensional space and 2) A proposal can be freely amended Then the outcome is always the ideal point of the median voter. Plott Conditions In more than one dimension, however, no single equilibrium point exists. Unless… the Plott Conditions are met: Each individual’s ideal point can be paired with another that is exactly on the opposite side of the Median XM. x5 x7 x1 x6 xM x3 x2 Chaos Theory Divide the Dollar Game Distributive politics has no unique outcome Devil Agenda Setter… things are getting worse: If no Condorcet winner exists, then majority rule voting can lead to anywhere in the policy space. x2 x1 x3 Strategic Voting Assume individuals vote sophisticatedly: A bill is proposed along with an amendment • a = amended bill • b = bill • q = status quo Preference are: Sequence: 1 a b q 2 b q a 3 q a b An amendment is voted on against the bill Then which ever wins is pitted against the status quo. Strategic Voting (continued) In sincere or myopic voting: 2 1, 3 b b a q 1 2,3 a q In sophisticated voting: 1,2 3 b 1,2 b a 3 q a q Structure Induced Equilibrium Question: Why do we observe so much stability? Governmental institutions are stable Policy change in incremental Answer: Institutions Create Stability If a policy space is divided among legislators And these legislators have agenda control and special rights Then outcomes will not be chaotic Procedures induce Institutional Equilibrium Committee System & Stability issue 2 x = outcome committe 2 committe 1 Issue 1 Committees are given monopoly power over a jurisdiction. Policy may be unrepresentative of median chamber, but it is stable.