How influential is ballot design in elections?

We exploit an original dataset from a referendum in Peru to study the influence of voting "arrangements" on electoral outcomes. The relative importance of these arrangements (e.g., ballot design) with respect to the fundamentals (e.g., ideology, candidates' quality) has not been measured. After controlling for a comprehensive set of politicians' characteristics, we estimate unbiased ballot order effects making use of the within party variation in outcomes. We estimate a non-linear probability model and we create counterfactuals to conclude that ballot design not only may have changed the electoral results but also has a greater importance than candidates' ideology, education, experience and party affiliation.