Under the "Third Vote" method, the voters cast no votes but are asked about their preferences on policy issues as declared in the party manifestos (like in voting advice applications, e.g. German Wahl-O-Mat). 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 (e.g., political and economic implications of Brexit) is supposed to make vote more rational and responsible and representative democracy "more representative" and "more democratic". This method has been approbated during the 2016 and 2017 elections of the Karlsruhe Institute of Technology (KIT) Student Parliament (StuPa). The 2016 experiment showed that the method increased the parliament's representativeness but also revealed that the critical point was the selection of questions by the election committee. Indeed, they can be favorable for one party and unfavorable for another, or they can poorly discriminate between the parties, finally causing an equalization of sizes of the party factions in the parliament (regarded by some as the method's malfunction). These problems were tackled in the 2017 experiment. The eligible parties were asked to formulate questions themselves and to answer all of them, including the questions by other parties. The collected 94 questions were reduced to 25 using a model aimed at contrasting as much as possible between the parties by maximizing the total distance between the vectors which characterized their policy profiles. Thereby, the accusation of partiality in the question selection was avoided, the gain in the parliament representativeness was confirmed, but the equalization effect was still persistent. The 2018 experiment has three distinctions. Firstly, we use an advanced model to reduce the list of questions. It enhances the multi-dimensionality of the set of parties' policy profiles aimed at covering the policy space most evenly. For this purpose, the least squares criterion is applied to principal component variances of the correlation or distance matrices for the parties' policy profiles. Then the reduced set of questions results in a ball-shaped "cloud" of parties' policy profiles rather than in a stretched ellipsoid, as in the 2017 experiment. Secondly, we test several variants of the Third Vote, using different optimization models to select questions, and compare their impact on the representativeness of the parliament elected. It turns out that the StuPa is by far most representative if elected by the third votes based on the questions selected using the advanced criterion, and this superiority is observed for all groups of electors considered in the experiment. Thirdly, we tackle the Third Vote's equalization effect. For this purpose, we reduce the party indices, retaining only their part beyond the threshold between representative and nonrepresentative values. The parliament reallocated in proportion to the reduced indices has a similar faction ratio as the one elected by party name, is still more representative than the latter, but less representative than the one allocated in proportion to the complete indices. This means that the optimal proportional representation of public preferences leads to a certain equalization of party factions. Consequently, the equalization effect should not be regarded harmful; it can be tackled, if desired, but at the price of reducing the gain in the parliament representativeness.
