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This implies that interests that are moderate or centralist (defining centralist as interests whose preferred policy fall in the range <math>z_g \in [0,z_g^-(x,y)]\,</math>) will not act, leading to inertia in policies.
 
Likewise one can calculate the upper limit of the range <math>z_g^+\,</math> for when <math>y > 0\,</math>. The interest will then recruit votes iff:
 
<math>z_g \ge z_g^+(x,y) \equiv \frac{x+y}{2} \left (1+\frac{\alpha(x+y)^2}{4 \beta (x-y)}\right) - \frac{\alpha y^2}{2 \beta (x-y)}</math>
 
A crucial contribution of this model is that it allows some basic comparative statics. Examination of the effects of changes in exogenous parameters for the case where <math>y \le 0\,</math> shows that:
 
<math>z_g^-(x,y)\,</math> is strictly decreasing in <math>\beta\,</math>: With more intense interests there is a smaller centralist set.
 
<math>z_g^-(x,y)\,</math> is strictly increasing in <math>\alpha\,</math>: With more intense legislator preferences there is a larger centralist set.
 
<math>z_g^-(x,y)\,</math> is strictly increasing in <math>x\,</math>: A more extreme alternative leads moderate interests not to try to change the policy.
 
Also as <math>x \uparrow</math> the #votes recruited <math>\downarrow</math>, and as <math>x \uparrow</math> the cost of recruiting a vote increases.
 
It is also possible to calculate when vote recruitment becomes too costly all together for the interest. This is covered in some detail in the paper, but loosely if <math>x > x^*(z_g,0)=\frac{8 \beta z_g}{4 \beta + \alpha}\,</math>, the the cost exceeds the gain.
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