Lecture VII: Agenda Setting

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Lecture VII Agenda Setting

• Recommended Reading
• Romer Rosenthal (1978)
• Baron Ferejohn (1989)

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Lecture VII Agenda Setting

• Recall standard median voter theorem If
• Voters i n (odd) have single-peaked utility
  functions over a single good, and
• Any voter can freely place a proposal on the
  agenda
• Then, median voters position dominates, i.e., is
  the equilibrium outcome of any sequence of voting

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Lecture VII Agenda Setting

• In most legislatures, access to agenda control is
  limited
• Agenda setter can secure non-median outcomes
• This result contingent on location of status quo
• e.g., given symmetric, single-peaked utility
  functions (e.g. Euclidean, quadratic), agenda
  setter can secure p
• Further SQ is from median voter, closer p can be
  to agenda setters ideal point

Agenda setter
p
SQ
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Lecture VII Agenda Setting

• Romer Rosenthal (1978) generalize this
  situation
• Voters utility functions single-peaked, but not
  necessarily symmetric
• SQ provides different levels of fallback
  utility
• Main Results
• Median voters position no longer dominates
• What agenda setter can secure hinges on utility
  that SQ provides
• Absent agenda-setting, cycles may emerge

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Lecture VII Agenda Setting

• If no SQ, E median voters (2s) ideal point
• But if an SQ offers gt Usq1, 1 3 outvote 2 we
  could get cycles
• If Usq2, setter can obtain E2 Note voter 3 is
  pivotal
• If Usq3, setter cannot obtain E gt sq

V2(E)
V3(E)
V1(E)
Usq1
Usq3
Usq2
E
E2
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Lecture VII Agenda Setting

• Baron Ferejohn (1989)
• Generalization of Rubenstein bargaining model to
  legislative setting where
• Number of players / bargainers gt 2
• Majority rule can be used to impose bargains
• Agenda power a function of recognition and
  amendment rules (open vs. closed)
• Choice of these rules is endogenized
• Main result majority rule closed amendment
  procedures generate less equitable distributions
  but many equilibria are possible.

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Lecture VII Agenda Setting

• Recall
• Ultimatum game agenda setters power to make a
  take-it-or-leave-it offer secures all of the
  pie
• Finite Repetition in Rubenstein model
• First-mover advantage remains (and increases in
  players impatience), but..
• Initial agenda setter has to give other player
  their reservation value

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Lecture VII Agenda Setting

• The Model
• Members 1, , n,
• Utility increasing in x, risk-neutral
• Common discount factor, d
• Recognition rule
• Member i has probability pi of being recognized
• Recognition allows i to propose division of x
• xi (x1i, , xni) s.t. ?x ? 1 sq (01, 0n)
• Amendment rule
• Closed or Open
• Voting rule

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Lecture VII Agenda Setting

• Closed Rule

Leg. 1 Proposes x1
pass
Vote
x11, x21, x31
fail
Recognition
Leg. 2 Proposes x2
pass
x12, x22, x32
Recognition
Vote
fail
Recognition
pass
x13, x23, x33
Vote
Leg. 3 Proposes x3
fail
Recognition
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Lecture VII Agenda Setting

• Open Rule

x11, x21, x31
pass
Put Question
Recognition of 2 or 3
x1 gt x2
Leg. 2 Proposes x2
fail
Leg. 1 Proposes x1
Vote on x1 vs x2
x1 lt x2
Recognition of 2 or 3
Recognition
Vote on x1 vs x2
Leg. 3 Proposes x3
Put Question
x11, x21, x31
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Lecture VII Agenda Setting

• An Illustration
• 3 legislators under closed rule
• pi (1/3, 1/3, 1/3), xsq 0, 0, 0
• pi (.4, .4, .2), xsq .2, .2, .1
• Case 1
• The proposer is indifferent over coalition
  partners
• As pi pj 1/N, all Vi 1/N
• xi 1 1/N, 1/N, 0

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Lecture VII Agenda Setting

• An Illustration
• 3 legislators under closed rule
• pi (1/3, 1/3, 1/3), xsq 0, 0, 0
• pi (.4, .4, .2), xsq .2, .2, .1
• Case 2
• Both 1 2 prefer to coalition with 3 because V3
  lt V3
• Thus 3 knows that she is i) the proposer with p
  .2 or ii) a member of the majority coalition with
  certainty
• Further, 3 is indifferent between 1 2 as
  coalition partners
• Thus, 1 2 know that they are i) the proposer
  with p .4 or ii) a member of the majority
  coalition with Pr .5

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Lecture VII Agenda Setting

• An Illustration
• 3 legislators under closed rule
• pi (1/3, 1/3, 1/3), xsq 0, 0, 0
• pi (.4, .4, .2), xsq .2, .2, .1
• Case 2
• V1 p1(.9) p2(0) p3(½ .2) (½ 0)
• V2 p2(.9) p1(0) p3(½ .2) (½ 0)
• V3 p3(.8) p1(.1) p2(.1)

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Lecture VII Agenda Setting

• An Illustration
• 3 legislators under closed rule
• pi (1/3, 1/3, 1/3), xsq 0, 0, 0
• pi (.4, .4, .2), xsq .2, .2, .1
• Case 2
• V1 .4(.9) 0 .2(½ .2) 0 .38
• V2 .4(.9) 0 .2(½ .2) 0 .38
• V3 .2(.8) .4(.1) .4(.1) .24
• Counterintuitive legislator 3s smaller V
  increases her share of the pie.

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Lecture VII Agenda Setting

• More generally, given equal recognition
  probabilities, the expected payoff for any i is,

Probability of being included in majority
coalition continuation value
Probability of Recognition Residual available
to proposer
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Lecture VII Agenda Setting

• How does change to open rule affect results?
• Initial proposer does not know with certainty who
  will be recognized after their proposal
• Thus, incentive is to propose a distribution that
  accounts for possibility that all remaining
  members may have opportunity to present
  amendments
• Distribution becomes increasingly equitable as
• Players become more patient
• As N increases (because insurance coverage
  against counter-proposals must be spread more
  widely)