Direct democracy allows citizens to reverse decisions made by legislatures and even initiate new laws that legislatures are unwilling to pass, thereby supposedly leading to more representative policies. Yet, turnout in referendums is lower than in parliamentary elections: 40% between 1981 and 1999 as compared to 45% in national elections in Switzerland. Given that turnout tends to be skewed towards citizens of high socio-economic status, critics argue that if participation is that low, referendum outcomes are not representative of the preferences of the population at large. We test this assertion using post-referendum surveys encompassing 148 national referendums held in Switzerland between 1981 and 1999. Comparing opinion majorities in the representative surveys against actual referendum outcomes, we find that on average only 7% of referendums did not match the majority opinion among all citizens and 14% did not match the majority opinion among non-voters. We then use parametric bootstrap to take into account sampling error and provide estimates of the uncertainty around the counts of unrepresentative referendums. This also enables us to address the question whether some groups are significantly less well represented than others.
