In this appendix, we provide the details of the formal models that provide the foundation for the main theoretical arguments described in Chapter 4.

The Parliamentary Model

The parliamentary model assumes that a Politician, L (for Legislative actor – we introduce P, for President, later), can unilaterally adopt a bill, and a Bureaucratic agent, B, can implement it. The interaction between these two players involves arriving at an outcome on the real line. Without loss of generality, we assume that L's ideal point is xL = 0 and B's ideal point is xB∈ [0,1]. The ideal points are common knowledge, and each player's utility from the final policy outcome is a linear loss function.

In the first stage, the Politician either does nothing, which retains a status quo, Q ∈ ℝ, or adopts a new law, x∈ [0,Ī]. The policy x = Ī is the maximal discretion law, and to simplify the number of parameters in the model, we set Ī = xB + 1 (which, as will become clear, always allows the Bureaucrat to implement the policy that will yield his most preferred outcome). The law, x, defines the upper bound on policies that the Bureaucrat can implement that are in compliance with the statute. We've parameterized the model so that the Politician never has an incentive to set a lower bound that is less than 0. Thus, as x increases, the Bureaucrat's discretion increases.