Strategic political environments : gerrymandering and campaign expenditures

My dissertation contains three chapters studying the strategic allocation of resources in political environments.

Chapter 2 asks if redistricting is the result of partisan gerrymandering or apolitical considerations. I develop a statistical test for partisan gerrymandering and apply it to the U.S. Congressional districting plan chosen by the Republican legislature in Pennsylvania in 2001. First, I formally model the optimization problem faced by a strategic Republican redistricter and characterize the theoretically optimal solution. I then estimate the likelihood a district is represented by a Republican, conditional on district demographics. This estimate allows me to determine the value of the gerrymanderer's objective function under any districting plan. Next, I use a geographic representation of the state to randomly generate a sample of legally valid plans. Finally, I calculate the estimated value of a strategic Republican redistricter's objective function under each of the sample plans and under the actual plan chosen by Republicans. When controlling for incumbency the formal test shows that the Republicans' plan was a partisan gerrymander.

In Chapter 3 I introduce a new and novel electoral reform that continues to allow redistricting but changes the incentives to do so. This reform ensures that parties earn seats proportional to their performance at the polls without substantially changing the electoral system in the U.S. In order to evaluate the reform's impacts, I model and solve a game that incorporates the redistricting decision, candidate choice, state legislative elections, and policy choice. Unsurprisingly, strategic redistricting biases policy in favor of the redistricting party. In the environments studied, the new reform never increases policy bias, and often reduces it.

Political campaigns often require the strategic allocation of resources across multiple contests. In Chapter 4 I analyze these environments in terms of the canonical Colonel Blotto game, beginning with the most basic of Blotto games: Two officers simultaneously allocate their forces across two fields of battle. The larger force on each front wins that battle, and the payoff is the sum of the values of the battles won. I completely characterize the set of Nash equilibria to any such game and provide the unique equilibrium payoffs. This characterization comes from an intuitive graphical algorithm which I then apply to several generalizations of the game. I completely characterize the set of equilibria and provide the unique equilibrium payoffs to Blotto games with battlefield values that vary across players and games with general resource constraints. I also use my approach to solve the Blotto games on more than two battlefields with asymmetric battlefields and force endowments.