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Snyder (1991) - On Buying Legislatures (view source)
Revision as of 17:18, 7 October 2011
, 17:18, 7 October 2011→Proposition 2
===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 hisproposal. Snyder restricts attention to cases where the lobbyist's ideal point <math>L\leq 1/2</math>. Given this, the lobbyist's optimal bribes always satisfy Proposition 1. Note that there are a few boring cases in which the lobbyist's strategy is quite dull. For example, if the status quo is equal to the lobbyist's ideal point (<math>s=L</math> thn the lobbyist does nothing. If <math>s\leq-L</math>, then the the lobbyist can propose <math>x_{D}=L</math>, offer no bribes and win the vote. The more interesting case is when <math>-L<s<L<math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/partial s<0, \partial x_{D}^{\ast}/partial L>0</math> and <math>\partial x_{D}^{\ast}/partial \alpha<0</math>.
==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.
