APPLICATION:
SHERMAN AT THE CONSTITUTIONAL
CONVENTION
Application: Sherman at the Convention
A. Background
1.
2.
3.
4.
Robertson (2005), and to a lesser extent Rakove (1996), argue that
Roger Sherman was surprisingly influential at the Constitutional
Convention.
Roger Sherman was a small shop owner, and one of the few
delegates who were in debt.
Nevertheless, he was a member of the confederation congress
for 9 years, had 27 years experience in the Connecticut state
assembly, 21 years experience as a judge, and signed the
Declaration of Independence. Pretty experienced.
Robertson (2005) does not make it clear why he thinks Sherman was
influential. Perhaps it was his political experience or charisma.
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Application: Sherman at the Convention
• William Peirce, a delegate from GA, described Sherman this
way:
Mr. Sherman exhibits the oddest shaped character I ever remember
to have met with. He is awkward, unmeaning, and unaccountably
strange in his manner. But in his train of thinking there is something
regular, deep and comprehensive; yet the oddity of his address, the
vulgarisms that accompany his public speaking, and that strange
New England cant which runs through his public as well as his
private speaking make everything that is connected with him grotesque
and laughable: - and yet he deserves infinite praise - no Man has a better
Heart or a clearer Head. If he cannot embellish he can furnish thoughts
that are wise and useful. He is an able politician, and extremely artful in
accomplishing any particular object; - it is remarked that he seldom fails.
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Application: Sherman at the Convention
B. Dougherty and Heckelman
1.
Claim Sherman was influential because he was a pivotal delegate
from a pivotal state.
a.
A different explanation than suggested by Robertson.
C. Pivotal
1.
A delegate is pivotal if he can change the assembly’s choice by
changing his vote.
D. Bloc Voting
1.
2.
3.
Votes were tallied by states with each state having one vote
A majority of states carried a motion.
Each state’s vote was determined by a majority of the delegates from
that state.
majority of states
CT:
y Ellsworth
y Sherman
Johnson
NH MA CT NY NJ PA DE MD VA NC SC GA
3 4
3
3
5 8 5 5
7
5
4
4
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Application: Sherman at the Convention
E. Shapley-Owen Value
1.
The percentage of all possible minimum winning coalitions in which
an actor is a member.
Hypothetical:
9 delegates from
3 states: A, B, C.
Median Delegate:
not defined.
Idea:
find median delegate
for each possible vote.
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Application: Sherman at the Convention
E. Shapley-Owen Value
1.
The percentage of all possible minimum winning coalitions in which
an actor is a member.
Cut Line.
First possible vote:
Q vs X
Draw a line between X
and Q.
X
*
Q
*
Because distances are
Euclidean, each
delegate’s vote for X
vs Q is identical to
their vote if they were
projected onto an XQ
line across the space.
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Application: Sherman at the Convention
E. Shapley-Owen Value
1.
The percentage of all possible minimum winning coalitions in which
an actor is a member.
Cut Line.
First possible vote:
Q vs X
Draw a line between X
and Q.
Because distances are
Euclidean, each
delegate’s vote for X
vs Q is identical to
their vote if they were
projected onto an XQ
line across the space.
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Application: Sherman at the Convention
E. Shapley-Owen Value
1.
The percentage of all possible minimum winning coalitions in which
an actor is a member.
In fact, this is true for
any line parallel to XQ.
Cut Line.
median
X
*
X X
* *
X
*
Q
*
X
*
Q
*
Q Q
* *
Q
*
And it is true for any
XQ pair equidistant
from the cut line.
This means that the
projection represents
a whole class of votes.
Voting by individuals:
C1 is the median
delegate for this class.
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Application: Sherman at the Convention
E. Shapley-Owen Value
1.
The percentage of all possible minimum winning coalitions in which
an actor is a member.
Voting by State blocs:
The pivotal delegates
are B3 and B4.
See why?
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Application: Sherman at the Convention
E. Shapley-Owen Value
1.
The percentage of all possible minimum winning coalitions in which
an actor is a member.
To get all possible
coalitions, we rotate the
normal vector (i.e. XQ
line) through the space.
make projections,
calculate pivots for those
projections, and record
percentage of times an
actor is pivotal.
Fortunately, the
CyberSenate software
does this for us (for
individual voting only).
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Application: Sherman at the Convention
E. Shapley-Owen Value
1.
The percentage of all possible minimum winning coalitions in which
an actor is a member.
CyberSenate reports the
percentage of time an
actor pivots for all possible
coalitions in the space.
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Application: Sherman at the Convention
F. States at the Convention
1.
Dougherty and Heckelman use a shortcut.
They estimate ideal points
for each state.
Calculate Shapley-Owen
values for each state,
using CyberSenate, and
determine CT is most
often pivotal.
Then try to determine
which delegate is most
often pivotal among the
CT delegates, which is
Sherman.
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Application: Sherman at the Convention
G. Conclusion
1.
2.
3.
4.
This might explain why a lesser known delegate, like Roger Sherman,
was influential at the Constitutional Convention.
Sherman was most often in the pivotal position.
Biographers find Sherman less influential in the first U.S. House.
Ironically, Sherman was not in a pivotal position there.
H. Discussion
1.
2.
What do you think?
Shapley-Owen values are for all possible votes given the estimated
ideal points. Would it be better to do the analysis for observed votes?
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