Combining the third vote with traditional elections

The German two-vote election system implements two historical conceptions of political representation coined at the end of the 18th century during the American and French Revolutions. The descriptive conception - the parliament portrays the society in miniature - is implemented in the first vote with which local candidates are delegated to the federal parliament. The agent conception - the parliament consists of people's trustees who are not necessarily their countrymen - is implemented in the second vote for a party. The recent conception of representation, policy representation - how well the party system and government represent policy preferences of the electorate, is supported by no election instrument, and the Third Vote election method just aims at filling in this gap. Under the "Third Vote", the voters cast no votes but are asked about their preferences on policy issues as declared in the party manifestos (like in VAAs - voting advice applications, e.g. German Wahl-O-Mat: Abolish Euro -Yes/No; Leave NATO? - Yes/No, etc.). Then the policy profile of the electorate with the balance of public opinion on every issue is determined. The degree to which the parties match with it is expressed by the parties' representativeness indices of popularity (the average percentage of electors represented on all the issues) and universality (the percentage of cases when a majority is represented), and the parliament seats are distributed among the parties in proportion to their indices. The voters are no longer swayed by politicians' charisma and communication skills but are directed to subject matters behind personal images and ideological symbols. The focus on choice properties (political and economic implications of elections, or of single decisions like Bexit or involvement in a new war) is supposed to make vote less emotional and superficial but more rational and responsible, aiming finally at a "more democratic" representative democracy. The Third Vote has been approbated and improved during the 2016, 2017 and 2018 elections to the Student Parliament (StuPa) of the Karlsruhe Institute of Technology (KIT). In the 2016 experiment, the policy questions for the electoral ballots have been taken from the StuPa-OMat - the KIT adaptation of the Wahl-O-Mat to the StuPa elections. However, the questions proposed by the election committee can be favorable for one party and unfavorable for another, making elections manipulable. To avoid impartiality in the 2017 experiment, the competing parties have formulated the questions themselves on their own responsibility - as an element of the electoral campaign, then all the parties have answered all the questions, and finally an optimization model has selected 25 ones to maximally contrast between the party positions. A more sophisticated optimization model in the 2018 experiment has shown even better results. This paper has three subjects. The first one is the Third Vote's equalization effect: an unusually small ratio of the resulting parliament faction sizes, which is surmounted by the Third Vote Plus - a minor modification of the Third Vote. The second subject is combining the Third Vote and Third Vote Plus methods with traditional elections. The third subject is comparative evaluation of three optimization models to select questions. Due to these advances, the Third Vote can be considered an election-ready prototype of a voting method either for use alone or for integration into existing election systems.