In the previous chapter, I presented an intuitive and example-based framework for understanding how uncertainty and vote buying shape statutory policy making. This theme is developed further in this chapter with the introduction of a relatively simple mathematical model. Its main goal is to shed light on how party loyalty, conflicting influences, and vote buying affect chief executives' legislative performance.
There is obviously no such thing as the right degree of abstraction for all analytic purposes. In the mathematical representation of the lawmaking process that I present in this chapter, I ignore many details and make a series of simplifications. The model is thus tractable, yet rich enough to generate interesting testable propositions.
Throughout the chapter, I attempt to keep the exposition of the main ideas as simple as possible, without losing mathematical precision and generality. In some passages, I rely on figures and numerical examples to convey intuition about the results. Technical details are left to the footnotes, and formal proofs can be found in Appendix A. For expositional purposes, I adopt the following convention: Legislators are identified as female and chief executives as male.
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