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THE CONSTITUTIONAL THEORY OF LEGISLATIVE ORGANIZATION. How the Senate and President Affect the Balance of Power in the House
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| | Unformatted Document Text:
|s-q|
2
-|s-sec(C
H
,s)|
2
≤
0 OR [s=p and |s-q|
2
-|s-sec(C
H
,s)|
2
>0 and |w-q|
2
-|w-
sec(C
H
,s)|
2
≤
0 and|z-q|
2
-|z-sec(C
H
,s)|
2
≤
0] OR [|s-q|
2
-|s-sec(C
H
,s)|
2
>0 and
|p-q|
2
- |p-sec(C
H
,s)|
2
≤
0 and (%P>1/3 or |s-q|
2
-|s-sec(C
H
,s)|
2
–v
≤
0 or |z-
q|
2
-|z-sec(C
H
,s)|
2
)
≤
0.)]
For any set of player ideal points, these equations yield the equilibrium value of cb(C
H
,s). In what
follows, cb(C
H
,s)
∈
{mid(C
H
,s) sec(C
H
,s)} denotes the conference bill. For notational simplicity,
we henceforth drop the superscript 2 from policy utility statements.
Behaviors and Outcomes in the Organizational Stage
In the appendix, we explicitly characterize offers and responses in the organizational
stage. While the technical description of these phenomena is complex, we can describe them
intuitively. For this purpose, consider a decision node in which faction x
∈
{F1, F2, F3} can make
an offer to faction a
≠
x
∈
{F1, F2, F3} or b
≠
x
∈
{F1, F2, F3}. A five-step sequence summarizes the
logic of faction x’s equilibrium strategy. Each step in the sequence is followed by a more precise
statement of its logic.
Step 1: Use the subgame that follows this offer, and responses to it, to determine the consequence for each player if faction x fails to make an acceptable offer.
•
If [conditions under which allowing the game to continue leads to a particular outcome – e.g., L=(cb(s,b)) with faction b subsequently making an offer that faction a accepts], then the policy consequence of x failing to make an acceptable offer is [name the outcome --e.g., mid(s,b)] with [name the offer – e.g., the transfer that faction b will have to make to faction a]. For simplicity, we continue the example started here in subsequent steps.
Step 2: Use step 1 information to determine which offers faction a will accept.
•
Faction a will accept offer c
x
a
≥
Y
∈ℜ
=[(compensation to faction a for loss in policy utility
that it will experience by allowing faction x to be House conferee instead of faction b) plus (the value of the transfer faction a would receive by refusing faction x’s offer and then accepting faction b’s offer)].
Step 3: Use step 1 information to determine which offers faction b will accept.
•
Faction b will accept offer c
x
b
≥
Z
∈ℜ
=[(compensation to faction b for loss in policy utility
that it would experience by allowing faction x, rather than itself, to be House conferee) minus (the value of the transfer that faction b would have to make to a in order for it to be conferee)].
Step 4: Use step 1 information to calculate faction x’s maximum feasible offer.
17
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| | Authors: Sin, Gisela. and Lupia, Arthur. |
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| |
|
|
|s-q|
2
-|s-sec(C
H
,s)|
2
≤
0 OR [s=p and |s-q|
2
-|s-sec(C
H
,s)|
2
>0 and |w-q|
2
-|w-
sec(C
H
,s)|
2
≤
0 and|z-q|
2
-|z-sec(C
H
,s)|
2
≤
0] OR [|s-q|
2
-|s-sec(C
H
,s)|
2
>0 and
|p-q|
2
- |p-sec(C
H
,s)|
2
≤
0 and (%P>1/3 or |s-q|
2
-|s-sec(C
H
,s)|
2
–v
≤
0 or |z-
q|
2
-|z-sec(C
H
,s)|
2
)
≤
0.)]
For any set of player ideal points, these equations yield the equilibrium value of cb(C
H
,s). In what
follows, cb(C
H
,s)
∈
{mid(C
H
,s) sec(C
H
,s)} denotes the conference bill. For notational simplicity,
we henceforth drop the superscript 2 from policy utility statements.
Behaviors and Outcomes in the Organizational Stage
In the appendix, we explicitly characterize offers and responses in the organizational
stage. While the technical description of these phenomena is complex, we can describe them
intuitively. For this purpose, consider a decision node in which faction x
∈
{F1, F2, F3} can make
an offer to faction a
≠
x
∈
{F1, F2, F3} or b
≠
x
∈
{F1, F2, F3}. A five-step sequence summarizes the
logic of faction x’s equilibrium strategy. Each step in the sequence is followed by a more precise
statement of its logic.
Step 1: Use the subgame that follows this offer, and responses to it, to determine the
consequence for each player if faction x fails to make an acceptable offer.
•
If [conditions under which allowing the game to continue leads to a particular outcome –
e.g., L=(cb(s,b)) with faction b subsequently making an offer that faction a accepts], then the
policy consequence of x failing to make an acceptable offer is [name the outcome --e.g.,
mid(s,b)] with [name the offer – e.g., the transfer that faction b will have to make to faction
a]. For simplicity, we continue the example started here in subsequent steps.
Step 2: Use step 1 information to determine which offers faction a will accept.
•
Faction a will accept offer c
x
a
≥
Y
∈ℜ
=[(compensation to faction a for loss in policy utility
that it will experience by allowing faction x to be House conferee instead of faction b) plus
(the value of the transfer faction a would receive by refusing faction x’s offer and then
accepting faction b’s offer)].
Step 3: Use step 1 information to determine which offers faction b will accept.
•
Faction b will accept offer c
x
b
≥
Z
∈ℜ
=[(compensation to faction b for loss in policy utility
that it would experience by allowing faction x, rather than itself, to be House conferee)
minus (the value of the transfer that faction b would have to make to a in order for it to be
conferee)].
Step 4: Use step 1 information to calculate faction x’s maximum feasible offer.
17
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