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A slightly simplified version of the model used now follows.
Legislators have ideal points: <math>z \backsim U \left [ - \frac{1}{2},\frac{1}{2} \right ]</math> with the median legislator's ideal point denoted <math>\, z_m = 0</math>.
The utility function of legislators is additively-seperable with a term representing their constituent's preferences and a term for the resources provided to them by the client:
<math>U \left( w , z \right ) = -\alpha(w-z) + r_w, \quad \alpha>0</math> where <math>\alpha</math> represents the intensity of preferences.
The Interest seeks <math>x > 0,\quad x \ge y,\quad A=\{x,y\}</math> where x is the policy, y is the status quo and A is the agenda.
<math></math>
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