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Snyder (1991) - On Buying Legislatures (view source)
Revision as of 15:15, 7 October 2011
, 15:15, 7 October 2011→Model Solution with Price Discrimination (1)
===Proposition 1===
Suppose s is the status quo and let <math>x>s</math> be an alternative proposal. If <math>0<(x+s)/2\leq 1/2</math>, then the least cost payment function <math>b_{D}(\dot,x,s)</math> which insures that x ties or defeats s is given by the following: If <math>z\in[0,(s+x)/2], b_{D}(z,x,s)=\alpha(x^2-s^2-2(x-s)z)</math>, and <math>b_{D}(z,x,s)=0</math> otherwise. Proof is in the appendix and is not complicated. Note that the above discusses proposals <math>x</math> only when <math>0<(x+s)/2\leq 1/2</math>, because otherwise the proposal passes without any bribes.
Note: Highest bribes paid to legislators whose ideal points are close to the median, but close to his side of the median. The lobbyist does not bribe his close supporters, but rather his marginal supporters. Close supporters will vote for a motion even without bribes.
===Proposition 2===
Now suppose that the lobbyist has some agenda power, and wants to make a proposal <math>x</math> and then bribe the legislators to vote for his
==Model Solution without Price Discrimination (2) ==
The paper continues to solve for equilibrium strategies in which the lobbyist does NOT know the individual legislator's ideal points and must offer all legislators the same bribe.
