An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
An Experimental Investigation of
Malapportionment in Bicameral Legislatures
Emanuel Vespa
NYU
January 3, 2010
Malapportionment of Voting Power
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Voting power of each member not proportional to the
population she represents.
Examples:
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Bicameralism:
I US Congress: One legislator every 230,000 Alaskans
and 660,000 Californians.
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Unicameral Weighted Voting:
I Council of the EU: One vote every 140,000 Maltese
and 2.2 million Italians.
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Proposal Power and Allocation of Resources
I
Bicameralism and Unicameral Weighted Voting: Voting
Power is Malapportioned.
Institution
Bicameralism
Weighted Voting
I
Proposal Power
Properly Apportioned Malapportioned
Equality
Inequality
Inequality
Inequality
Experimental Test of theory.
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Proposal Power and Bicameralism
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Proposal Power and Weighted Voting
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Outline of the Presentation
I
Theory:
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Bicameralism: Ansolabehere, Snyder and Ting (APSR
2003)
Weighted Voting: Extension to Snyder, Ting and
Ansolabehere (AER 2005)
Experiments:
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Bicameralism.
Weighted Voting (Preliminary).
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Theory: Bicameralism
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House and Senate allocate a xed Budget to districts.
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Proposer: One legislator chosen to submit a Proposal.
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House and Senate approve a division by majority rule.
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Preferences of Representatives and Senators are
connected.
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Bicameralism: Example
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Bicameralism: Proposal power and allocations
I
Proposal power
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Properly apportioned (in the House): 1/5 for each
representative.
Malapportioned (in the Senate): 1/3 for each senator.
MAIN STATEMENT (AST 2003):
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Proposal power properly apportioned, then equality.
Proposal power malapportioned, then inequality.
Details
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Theory: Weighted Voting
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Unicameral setting with one legislator per state.
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The legislator of state
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t has w votes and z voters.
W : total number of votes, Z : total population.
t
t
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Simple majority of votes for a proposal to pass.
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Malapportionment:
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There is a
t such that
wt < zt .
W
Z
Weighted Voting: Proposal power and allocations
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p
Proposal power ( t )
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MAIN STATEMENT:
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Properly apportioned: pt = zt /Z .
Malapportioned: pt = wt /W .
Proposal power properly apportioned, then inequality.
Proposal power malapportioned, then inequality.(STA
2005)
Continuation value:
Details
v = w /W
t
t
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Experimental Design: Bicameralism
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Run at CESS Lab (NYU).
I
Treatments (Between subjects design):
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House treatment: proposal power in the House.
Senate treatment: proposal power in the Senate.
Legislatures of size 8: As in example.
Allocate 50 dollars among 5 zones.
15 Rounds, 16 subjects per session.
3 Sessions per treatment (96 Subjects).
Payment: One random round. Average pay 25 dollars.
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Results: Malapportionment
I
Continuation Values
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Weighted Voting: Experimental Design
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Country:
Z = 10
W =8
Number of Legislators = 6
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Weighted Voting: Experimental Design
Proposal Power
Super Malapportioned
Malapportioned
Properly Apportioned
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p1
16.7%
12.5%
10.0%
q1
40.0%
57.1%
66.7%
Big State
p2
16.7%
25.0%
30.0%
q2
70.0%
50.0%
35.7%
Treatments (Between Subjects Design):
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Small State
Super Malapportioned (2 Session)
Malapportioned (2 Session)
Properly Apportioned (0 Sessions)
12 subjects per session. (24 subjects per treatment)
15 Rounds.
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Results: Probability of Joining the Coalition
(preliminary)
Proposal Power
Super Malapportioned
Observed
Malapportioned
Observed
Properly Apportioned
Small State
p1
16.7%
12.5%
10.0%
q1
40.0%
32.6%
57.1%
43.2%
66.7%
Big State
p2
16.7%
25.0%
30.0%
q2
70.0%
77.4%
50.0%
66.3%
35.7%
Summary: Malapportionment
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Bicameralism:
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No Small State Advantage when Proposer is chosen
among Representatives.
Signicant Small State Advantage when Proposer is
chosen among Senators.
Weighted Voting:
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Small state advantage regardless of proposal power.
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Bicameralism: Intuition
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MWC in House ⇔ MWC in Senate.
Proposal power in House: No district has an advantage.
Proposal power in Senate: Small state districts have an
advantage.
Statement
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures
Weighted Voting: Intuition
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p z /Z or p = w /W continuation
In SSSPE for t =
value is the same:
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t
t
vt = wW .
t
How can this be sustained?
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Vt : Amount paid to other coalition members.
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qt : Prob. of being in coalition given not the proposer.
I If
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t
vt
is the same,
Continuation value:
Vt
is also the same.
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vt = pt (1 − Vt ) + (1 − pt )qt vt .
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qt = v −(p1−(1p−)V )
Statement
t
t
t
t
An Experimental
Investigation of
Malapportionment in
Bicameral
Legislatures