The Regression Discontinuity Design (RDD) offers powerful tools for causal inference in political science. However, traditional electoral RDDs face unique obstacles when studying divided government because institutional changes depend on multiple election outcomes rather than a single outcome.

To overcome this hurdle, we introduce two innovative approaches:

• A measure capturing the electoral distance to divided government, easily analyzed with standard sharp RDD methods

• The Probability Restricted Design (PRD) simulating "as if random" assignment for complex political phenomena

Both techniques preserve causal identification while accommodating messy reality.

Applying these, we reexamine how divided government affects budget deficits. Our findings suggest that the how rather than just the likelihood of divided government significantly shapes fiscal policy outcomes.

This approach advances research by demonstrating nuanced applications of RDDs to thorny political questions.