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#Nature chooses the state of the world <math>\omega \sim U[0,1]\,</math>
Gilligan Krehbiel (1987) - Collective Decision Making And Standing Committees (view source)
Revision as of 19:02, 16 September 2011
, 19:02, 16 September 2011→The Model
==The Model==
<b>Players</b>: There are two bodies:. *c: A committee *f: The legislature, or parent chamber, or 'floor', that uses a majority rule
<b>Choice space</b>: There are two proceeduresprocedures:
*<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.
* ... and a policy diminson <math>p\in P=R</math> the
<b>Policy outcomes</b>: 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>
<b>Utilities </b> are negative quadratice about ideal points (<math>x_f = 0\,</math> and <math>x_c > 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>
<b>Information</b>: S is known (everybody knows whether specialization happened). Specific realization of <math>\omega</math> is unknown. Priors about <math>\omega</math> are common.
The sequence of the game is as follows:
#Nature chooses the state of the world <math>\omega \sim U[0,1]\,</math>
#The floor chooses <math>P \in \{P^U,P^R\}\,</math> (Note not to be confused with the policy space <math>P\,</math>)
#The committee chooses <math>s \in \{0,1\}\,</math> (i.e. symmetric or asymmetric uncertainty -- whether to specialize or not.)
#The committee reports a bill <math>b \in P \subset R^1\,</math>
#The floor updates its beliefs <math>g \in [0,1]\,</math>
#A policy is choosen chosen <math>p \in P \subset R^1 \mbox{ if } P^U\,</math> or <math>p \in \{p_0,b\} \mbox{ if } P^R\,</math>. If the floor can offer amendments, it does.
#There are consequences and payoffs: <math>x, u_f, u_c\,</math> all determined
