Snyder (1991) - On Buying Legislatures
Abstract
This paper analyzes a simple spatial voting model that includes lobbyists who are able to buy votes on bills to change the status q u o . T h e key results a r e : (i) if lobbyists can discriminate across legislators when buying votes, then they will pay the largest bribes to legislators wh o a r e slightly opposed t o the proposed change, rather than t o legislators who strongly support o r strongly oppose the change; (ii) equilibrium policies exist, and with q u a d r a t i c preferences these equilibria always lie between t h e average of t h e lobbyists’ ideal points a n d the median of the legislators’ ideal points; a n d (iii) “moderate” lobbyists, whose positions on a policy issue a r e close t o the median of the legislators’ ideal points, will prefer the issue t o be salient, while more extreme lobbyists will generally prefer the issue t o be obscure.
Model
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. The lobbyist is assumed to have an infinite budget.
The legislature is infinitely sized and consists of individual legislators whose ideal points [math]z[/math] are distributed uniformly over [-0.5,0.5] (z~[math]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}\gt 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.
