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Instutional Analysis Lecture 5: Legislative Organization

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How a bill becomes a law

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Arrow’s Theorem zCompleteness - (Transitivity) If x beats y and y beats z in the social ordering then x beats z. zUniversal Domain - the rules must apply to all possible combinations of individual preference orderings. zPareto Optimality- x beats y whenever everyone individually prefers x to y. zIndependence of irrelevant alternatives - The collective preferences between two alternatives never depend on individual preferences regarding other alternatives. zNon-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

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Implications zArrow showed that these 5 criteria are incompatible with any system of preference aggregation. zExample: Simple Majority Rule

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Simple Voting Paradox zMajority Rule Violates Transitivity xSuppose we have a preference ordering as follows: zProblem: xCollective preferences are cyclic and every feasible alternative is unstable, such that: x>y, y>z; and z>x. xNo unique stable outcome: z x y

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Significance zWe can't predict what will be the outcome under a majority rule setting. zThere is no true social welfare maximizing outcome zThen majority government cannot be modeled as maximizing anything, if any outcome is possible no matter how unrepresentative.

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When Does Stability Occur? zBlack’s Theorem: yOne-dimensional issue space yIdeal (bliss) points: the one point on the line they prefer to all others yThe only stable point on the line is the median xmxm x6x6 x7x7 x3x3 x2x2 x1x1 x5x5 yX m is the Condorcet winner because it is the point that beats all others.

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Median Voter Result zIn general, for any distribution of voters with single peakedness there will be a median voter. zIf we assume that x1) Individuals have single peaked preference in a one-dimensional space and x2) A proposal can be freely amended yThen the outcome is always the ideal point of the median voter.

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Plott Conditions zIn more than one dimension, however, no single equilibrium point exists. zUnless… the Plott Conditions are met: yEach individual’s ideal point can be paired with another that is exactly on the opposite side of the Median X M. x5x5 x7x7 x6x6 x3x3 x2x2 x1x1 xMxM

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Chaos Theory zDivide the Dollar Game xDistributive politics has no unique outcome zDevil Agenda Setter… things are getting worse: xIf no Condorcet winner exists, then majority rule voting can lead to anywhere in the policy space. x1x1 x3x3 x2x2

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Strategic Voting zAssume individuals vote sophisticatedly: yA bill is proposed along with an amendment a = amended bill b = bill q = status quo yPreference are: ySequence: xAn amendment is voted on against the bill xThen which ever wins is pitted against the status quo.

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Strategic Voting (continued) zIn sincere or myopic voting: zIn sophisticated voting:

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Structure Induced Equilibrium zQuestion: Why do we observe so much stability? xGovernmental institutions are stable xPolicy change in incremental zAnswer: Institutions Create Stability xIf a policy space is divided among legislators xAnd these legislators have agenda control and special rights xThen outcomes will not be chaotic zProcedures induce Institutional Equilibrium

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Committee System & Stability yCommittees are given monopoly power over a jurisdiction. yPolicy may be unrepresentative of median chamber, but it is stable.

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Voting for Public Goods (Fisher, Ch. 3) © Allen C. Goodman 2009.

Voting for Public Goods (Fisher, Ch. 3) © Allen C. Goodman 2009.

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