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Gilligan Krehbiel (1987) - Collective Decision Making And Standing Committees (view source)
Revision as of 18:59, 20 May 2010
, 18:59, 20 May 2010no edit summary
Note that it would be efficient for the committee to specialize if <math>k \ge 2K^U\,</math> as well, as this would lead to gains to the floor, but the committee doesn't do so and is therefore 'underspecialized'.
===Closed rule, no specialization===
In this game the committee is not specialized and knows nothing, but it can get an outcome closer to it's ideal point by putting a more attractive bill (than the status quo) on the agenda.
The legislative equilibrium is then:
:<math>
b^*(\omega) =
\begin{cases}
x_c-\overline{\omega} & \mbox{if}\; p_0 \le -x_c-\overline{\omega} \mbox{ or } p_0 \ge x_c-\overline{\omega} \\
-p_0-1 & \mbox{if}\; p_0 \in (-x_c-\overline{\omega}, -\overline{\omega}) \\
b' & \mbox{if}\; P_0 \in \left[ -\overline{\omega}, x_c-\overline{\omega}\right)\mbox{ where } \mathbb{E}u_f(b') \le \mathbb{E}u_f(p_0)
\end{cases}
:<math>
p^*(b) =
\begin{cases}
b & \mbox{if}\;\mathbb{E}u_f(b') \ge \mathbb{E}u_f(p_0) \\
p_0 & \mbox{if}\; \mathbb{E}u_f(b') < \mathbb{E}u_f(p_0)
\end{cases}
\,</math>
:<math>
g^*(b) = \{\omega|\omega \in [0,1]\}
\,</math>
Note that if <math>p_0 = -\overline{\omega}\,</math> then the expected utilities and the Pareto optimality condition are the same as in the open rule with no specialization.
===Closed rule, specialization===
The case of the closed rule with specialization is much like the open rule with specialization except that for extreme values of <math>\omega\,</math> (specifically <math>\omega \le -3x_c - p_0\,</math> and <math>\omega \ge x_c - p_0)\,</math>, the floor can exactly infer the state of the world and is willing to implement the committee's ideal point, as it prefers this to the status quo. For non-extreme values, noisy signalling again occurs, but now the committee can constrain the floor to choosing between its bill and the status quo. The full details of an equilibrium are in the paper on page 318.
Again, we can derive a condition for when the committee would wish to specialize. We can then derive a set of conditions under which the floor would choose an open or closed rule, and in essence which game to play.
