A Framework for Understanding Interference Between Units In Geographic Natural Experiments with an Application to All-Mail Voting in Colorado∗

We analyze a geographic natural experiment during the 2010 Colorado primary election, when counties in Colorado had the option to have an all-mail election or could retain traditional in-person voting on election day. We found that the town of Basalt, in the southwestern part of the state, was split in half by two counties that chose different modes of voting, and exploit this natural experiment to understand whether turnout levels were altered by all-mail elections. However, social interactions often give rise to spillover effects in which the exposure of one individual to the treatment affects the outcomes of other units. In our application, treated and control voters lived in very close proximity and treatment spillovers are probable. We use the potential outcomes framework to formalize different causal estimands in the presence of geographic-based spillovers. Using this framework, we develop a test for the presence of interference, an interference-free estimate, and a way to characterize the consequences of mistakenly ignoring interference in the estimation of treatment effects. We also develop an algorithm for identifying subjects that were possibly exposed to spatial spillovers. Our findings suggest that all-mail voting decreased turnout in Colorado, and that spatial interference between voters is very weak and possibly negligible. ∗Authors are in alphabetical order. We thank Jake Bowers, participants at the Causality in Political Networks Conference (University of Chicago, 2013) and the Southeastern Methods Meeting (University of South Carolina 2014) for valuable comments and discussion. Titiunik gratefully acknowledges financial support from the National Science Foundation (SES 1357561). †Associate Professor, Department of Political Science, 211 Pond Lab, Penn State University, University Park, PA 16802 Phone: 814-863-1592, Email: [email protected] ‡Assistant Professor, Department of Political Science, University of Michigan, 5700 Haven Hall, 505 South State St., Ann Arbor, MI 48109 Phone: 734-615-9114, Email: [email protected]