Changes

The model examines a policy space <math>x\in[-0.5,0.5]</math>and a lobbyist's efforts to bribe legislators to adopt a policy near his ideal point. The lobbyist's utility function is <math>u(x,B)=-(x-L)^{2}</math>, where x is the policy chosen, L is the lobbyist's ideal point and B is the total number of bribes paid to legislators. An The lobbyist is assumed to have an infinite budget.  The legislature is infinitely sized legislature and consists of individual legislators whose ideal points <math>z</math> are distributed uniformly over [-0.5,0.5] (<math>z~U[-0.5,0.5]</math>. Legislators preferences preferences are also negative quadratic. A legislator will choose policy x over policy y iff <math>b_{x}-\alpha(x-z)^{2}>b_{y}-\alpha(y-z)^{2}</math>, where <math>b_{x},b_{y}</math> refer to the amount of bribes offered for voting for position x or y, and z is the legislator's ideal point. The parameter <math>\alpha</math> represents the "intensity" of the legislator's preferences -- ie, how much he cares. One might alternatively think of <math>\alpha</math> as how much his constituents care.