Gilligan Krehbiel (1987) - Collective Decision Making And Standing Committees

• This page is referenced in BPP Field Exam Papers

Reference(s)

Gilligan, T. and K. Krehbiel (1987), Collective Decision-making and Standing Committees: An Informational Rationale for Restrictive Amendment Procedures, Journal of Law, Economics and Organization 3, 287 pdf

Abstract

Specialization is a predominant feature of informed decisionmaking in collective bodies. Alternatives are often initially evaluated by standing committees comprised of subsets of the membership. Committee members may have prior knowledge about policies in the committee's jurisdiction or may develop expertise on an ongoing basis. Specialization by committees can be an efficient way for the parent body to obtain costly information about the consequences of alternative policies. Indeed, some scholars have argued persuasively that acquisition of information is the raison d'etre for legislative committees (Cooper).

Summary

The solution concept is perfect Bayesian equilibrium.

The Model

There are two bodies:

• A committee
• The legislature, or parent chamber, or 'floor', that uses a majority rule

There are two proceedures:

• [math]P^R\,[/math] is the restrictive proceedure (closed rule) where no amendments are allowed and the policy is voted against the status quo
• [math]P^U\,[/math] is the unrestrictive proceedure (open rule) where the parent body may choose any alternative to the policy.

The outcome ([math]x\,[/math]) is linear in both the policy ([math]p\,[/math]) and random variable ([math]\omega \sim U[0,1]\,[/math], such that [math]\mathbb{E}(\omega) = \overline{\omega}\,[/math] and [math]\mathbb{V}(\omega) = \sigma_{\omega}^2\,[/math]) concerning the state of the world. That is:

[math]x = p+ \omega\,[/math]

Utilities are negative quadratice about ideal points ([math]x_f = 0\,[/math] and [math]x_c \gt 0\,[/math]). The committee can incur a cost [math]k\,[/math] to learn the state of the world if it chooses to specialize ([math]s \in \{0,1\}\,[/math]). The floor knows if the committee has specialized but not what it has learnt.

[math]u_f = -(x-x_f)^2 = -x^2\,[/math]

[math]u_c = -(x-x_c)^2 - sk\,[/math]

The sequence of the game is as follows:

1. The floor chooses [math]P \in \{P^U,P^R\}\,[/math] (Note not to be confused with the policy space [math]P\,[/math])
2. The committee chooses [math]s \in \{0,1\}\,[/math] (i.e. symmetric or asymmetric uncertainty)
3. Nature chooses the state of the world [math]\omega \sim U[0,1]\,[/math]
4. The committee reports a bill [math]b \in P \subset R^1\,[/math]
5. The floor updates its beliefs [math]g \in [0,1]\,[/math]
6. A policy is choosen [math]p \in P \subset R^1 \mbox{ if } P^U\,[/math] or [math]p \in \{p_0,b\} \mbox{ if } P^R\,[/math]
7. There are consequences and payoffs: [math]x, u_f, u_c\,[/math] all determined

There are four games:

1. Open rule and no specialization
2. Open rule and specialization
3. Closed rule and no specialization
4. Closed rule and specialization

An equilibrium is a set of strategies [math]p^*(\cdot)\,[/math], [math]b^*(\cdot)\,[/math] and beliefs [math]g^*(\cdot)\,[/math] such that:

• [math]b^*(\omega)\,[/math] maximizes [math]\mathbb{E}u_c\,[/math], given [math]p^*(b)\,[/math]
• [math]p^*(b)\,[/math] maximizes [math]\mathbb{E}u_f\,[/math], given [math]g^*(b)\,[/math]
• [math]g^*(b) \subseteq [0,1]\,[/math] for all [math]b\,[/math] and [math]g^*(b)=\{\omega | b = b^*(\omega)\}\,[/math] whenever [math]g^*(b)\,[/math] is non-empty

Furthermore the decision to specialize must maximise the committee's expected utility and likewise the decision to choose a proceedure must maximise the floor's expect utility. (Both are formalized in the paper).

The paper makes two efficiency distinctions:

1. The outcome is only Pareto optimal iff [math]x \in [0,x_c]\,[/math]
2. The game is expertise efficient iff the choice to specialize maximizes the expected total surplus.

Open rule, no specialization

The equilibrium is:

[math]b^* \in P, \quad p*(b) = -\overline{\omega}, \quad g^*(b) = \{w|w \in [0,1]\}\,[/math]

The expected utilities are:

[math]\mathbb{E}u_f = -\sigma_{\omega}^2\,[/math]

[math]\mathbb{E}u_c = -\sigma_{\omega}^2 - x_c^2\,[/math]

To find the equilibrium do the following:

1. The floor maximizes its utility given its priors about the distribution. Its best guess is the mean and it believes the outcome is in the range of the distribution. [math]p^* = x_f - \overline{w} = - \overline{w}\,[/math].
2. The committee knows that it can't affect the floors posterior, and so proposes any bill.

This is found by taking [math]\mathbb{E}u_f = \mathbb{E}(-(\overline{\omega}+\omega)^2) = -(\mathbb{E}(\omega^2)-\overline{\omega}^2) = -\sigma_{\omega}^2\,[/math]. And likewise for the committee. Note that both have informational losses, and the committee has a distributional loss.

Outcomes are Pareto Optimal iff:

[math]\omega \in [\overline{\omega}, x_c + \overline{\omega}]\,[/math]

Open rule, specialization

Exact inference by the floor is not possible - it is not in the committee's interest to allow this. But inference in a partition of the range of the distribution is possible, much like a cheap talk model. (Specifically, see Crawford and Sobel (1982), covered in Grossman and Helpman (2001)).

Let [math]a_i\,[/math] denote the partition boundaries, with [math]a_0 = 0\,[/math] and [math]a_N = 1\,[/math].

A legislative equilibrium is then:

[math]b^*(\omega) \in [x_c-a_{i+1}, x_c - a_i] \quad \mbox{if}\; \omega \in [a_i,a_{i+1}]\,[/math]

[math] p^*(b) = \begin{cases} -\frac{(a_{N-1} + a_N)}{2} & \mbox{if}\; b \lt x_c -1 \\ -\frac{(a_{i} + a_{i+1})}{2} & \mbox{if}\; b \in [x_c-a_{i+1}, x_c - a_i] \\ -\frac{(a_{0} + a_1)}{2} & \mbox{if}\; b \gt x_c \end{cases} \,[/math]

[math] g^*(b) = \begin{cases} \{\omega|\omega \in [a_{N-1} + a_N]\} & \mbox{if}\; b \lt x_c -1 \\ \{\omega|\omega \in [a_{i} + a_{i+1}]\} & \mbox{if}\; b \in [x_c-a_{i+1}, x_c - a_i] \\ \{\omega|\omega \in [a_{0} + a_1]\} & \mbox{if}\; b \gt x_c \end{cases} \,[/math]

Where [math]a_i = a_1 i + 2i(1-i)x_c\,[/math] and [math]N\,[/math] is the largest interger such that [math]|2N(1-N)x_c| \lt 1\,[/math].

The expected utilities are:

[math]\mathbb{E}u_f = -\frac{\sigma_{\omega}^2}{N^2} - \frac{x_c^2(N^2-1)}{3}\,[/math]

[math]\mathbb{E}u_c = -\frac{\sigma_{\omega}^2}{N^2} - \frac{x_c^2(N^2-1)}{3}- x_c^2 - k\,[/math]

Outcomes are Pareto Optimal iff:

[math]\omega \in \left[\frac{(a_i+a_{i+1})}{2}, x_c + \frac{(a_i+a_{i+1})}{2}\right]\quad i = 0,\ldots,N-1\,[/math]

See figure 4, p310 of the paper for a graphic intuitiion.

As in cheap talk models, the number of partitions that can be sustained is a function of the bias of the reporting agent. If [math]x_c \ge 3\sigma_{\omega}^2\,[/math] only one partition can be supported and the model reverts to the unspecialized case. Likewise, as the bias decreases the number of partitions increases and the floor is able to make more refined inferences about [math]\omega\,[/math], and there is less loss due to uncertainty.

The committee chooses to specialize if its expected utility is higher. Put another way, it specializes if the cost of specialization [math]k\,[/math] is less or equal to than some cut off [math]k^U\,[/math], where:

[math]K^U = \sigma_{\omega}^2 \left( 1- \frac{1}{N^2}\right) - \frac{x_c^2(N^2-1)}{3}\,[/math]

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} :\lt math\gt 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') \lt \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.