Selection of questions for VAAs and the VAA-based elections

During the 2016 election to the Student Parliament of the Karlsruhe Institute of Technology (KIT), an experiment on 'The Third Vote' was conducted. The goal was to test an alternative election method based on the idea of internet voting advice applications (VAAs). Under the election method tested, the voters cast no direct votes for candidate parties; rather, they are asked about their preferences on the policy issues as declared in the party manifestos. These embedded referenda measure the degree to which the parties' positions match the policy preferences of the electorate. The parliament seats are then distributed among the parties in proportion to their indices of representativeness: popularity (the average percentage of the population represented on all the issues) and universality (frequency in representing a majority). The Third Vote Experiment reveals that the critical point is the selection of questions: unless they draw sufficient distinctions between the parties, it can cause a malfunction of both the VAA and the VAA-based election method. To solve this problem, this paper develops a model for contrasting as much as possible between the parties by maximizing the total distance between the party policy profiles while simultaneously reducing the number of questions. The guaranteed best solution is obtained by means of an exhaustive search on all the possible combinations of m out of n initial questions. However, since this search is cumbersome, a stepwise removal of questions is proposed. This alternative is shown to offer a good compromise between formal rigor and computational efficiency.