B. Formulation of Dynamic Differential Equations Representing Causal Interactions
Building upon the variables defined in Section IV.A, the Transactional Degradation of Democracy (TDD) framework can be formalized using dynamic differential equations to capture the recursive interactions between micro-level voter rationalization, legislative behavior, meso-level social norms, and macro-level system outcomes.
1. Voter Rationalization Dynamics (Ar)
Voter rationalization increases with monetary incentives (u) and decreases with perceived justice (). Cognitive dissonance (c) mediates this process. The dynamics can be expressed as:
\frac{dA_r}{dt} = \alpha_1 U - \alpha_2 J + \alpha_3 C
Where:
1,2,3>0 are sensitivity parameters.
Ar[0,1] represents the normalized level of rationalization or transactional compliance.
2. Legislative Behavior Dynamics ()
Legislators' rationalization () is influenced by voter compliance () and the expected return on investment from vote buying ():
\frac{dA_p}{dt} = \beta_1 A_r + \beta_2 ROI - \beta_3 J
