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This is the last of four papers devoted to the 2021 German federal elections continuing our analysis of the 2009, 2013 and 2017 Bundestag elections. It is shown that the policy representation by the Bundestag could be improved using the alternative Third Vote election method. Under the Third Vote, electors cast no votes for parties by name. The electoral ballot consists of questions on topical policy issues ('General speed limit on motorways?'—Yes/No, 'Germany should increase its defense spending?'—Yes/No, etc.), and the parties answer to these questions before the elections — as required by the Wahl-O-Mat, the German voting advice applications. However, the Third Vote is not concerned with individual advices or individual voting intermediation. The electoral ballots are processed to construct the electorate's policy profile with balances of public opinion on all the issues. Then the matching of the parties' profiles with the electorate's profile is measured using the parties' indices of popularity (average percentage of electors represented on all the issues) and universality (percentage of questions when a majority is represented). These indices of representativeness are used instead of the conventional index 'number of votes received' to define the party quotas in the Bundestag. This method is hypothetically applied to reallocate the Bundestag seats to the eligible parties, resulting in a considerable gain in the Bundestag's representativeness. Finally, we discuss mixed election procedures combining the Third Vote with the conventional voting by party name and analyze possible ...

This is the first out of four papers devoted to the 2021 German federal elections continuing our analysis of the 2009, 2013 and 2017 Bundestag elections by the methods of the mathematical theory of democracy. This one estimates the policy representation ability of the 39 parties that participated in the 2021 elections and the Bundestag. For this purpose, the positions of the parties on 38 topical issues are compared with the results of recent public opinion polls. Then the parties' indices of popularity (the average percentage of the population represented) and universality (frequency in representing a majority) are constructed. Assuming that the Bundestag's position on the 38 issues is determined by the Bundestag majority, the Bundestag's indices of popularity and universality are estimated as well. The main conclusion is that the representativeness of the Bundestag parties and the Bundestag (before coalition-formation) has sig-nificantly increased since 2017. In particular, the election winner, the SPD, is now ranked 4 instead of 22 in 2017, having the mean index (popularity + universality) / 2 = 65% instead of 52 % in 2017. The Bundestag's mean index is now equal to 61% instead of former 40%. As for the ruling 'Traffic light coalition', SPD+GRÜNE+FDP, its compatibility is as low as 45% and the representativeness is not the best ...

This is the second out of four papers devoted to the 2021 German federal elections continuing our anal-ysis of the 2009, 2013 and 2017 Bundestag elections. This paper arranges the contesting parties into a 'spectrum' that reflects the spatial proximity of their policy profiles. The latter are 38-dimensional vectors of the parties' answers to 38 policy questions from the 2021 Wahl-O-Mat, the German voting advice application (VAA). Applying Principal component analysis (PCA), we construct a contiguous party ordering where the neighboring parties have close policy profiles. The ordering fits to the left-right ideological axis rolled up in a circumference, which can be unfolded by splitting it at one of its largest gaps. Rigorously speaking, we obtain a horseshoe-shaped left-right axis with the far-left and far-right ends approaching each other. For comparisons, alternative party orderings are constructed using four other models. Finally, the 2013, 2017 and 2021 German political spectra are ...

This is the third of four papers devoted to the 2021 German federal elections continuing our analysis of the 2009, 2013 and 2017 Bundestag elections. Currently, only China has a parliament larger than the German Bundestag, which still grows due to the increasing number of overhang mandates. The unfettered growth of the Bundestag — caused by allotting too many direct mandates to parties that received too few second votes — can be prevented by relaxing the principle of 'one man—one vote' and introducing adjustable vote weights of Bundestag members. Such a practice could make numerous adjustment (leveling) seats unnecessary and the basic 598 Bundestag seats sufficient under most circumstances. For this purpose, the members of the overrepresented parties (because they receive too many direct mandates) should have vote power = 1 and the members of other parties should have adjustment vote weights > 1. We explain the adjustment vote weights using the example of the 2021 Bundestag. The second point discussed is the incomplete compliance of the Sainte-Lague/Schepers method, which dates back to 1832 and is used to apportion the Bundestag, with the mathematical standards of the 21st century. This method results in apportionments that are often not the best ones found by discrete ...

Currently, only China has a parliament larger than the German Bundestag, which continues to grow due to the increasing number of overhang mandates. In 2016, Norbert Lammert, then president of the Bundestag, proposed to restrict it to 630 members by allocating mandates according to quotas for each of the German states (Länder), which should be proportional to their population. This idea found no approval among the German parties, neither large nor small [Finthammer 2018]. Only in October 2019, after predictions that the next Bundestag could exceed 800 seats, did some 100 German experts in constitutional law write an open letter suggesting to constrain its size by reducing the number of effective constituencies, and the Bundestag vice-president, Thomas Oppermann, called for such a reform without delay. These and other proposals require a profound change in the existing election system. But a mathematical solution to the problem does not require such changes and is much simpler. We can prevent unfettered growth of the Bundestag — caused by allotting too many direct mandates to parties that received too few second votes — by replacing the principle of 'one man, one vote' with a new concept: fraction-valued votes for Bundestag members. Such a practice could make overhang mandates unnecessary and the basic 598 Bundestag seats sufficient under all circumstances. For this purpose, the members of the overrepresented parties (because they receive too many direct mandates) should have vote power 1. We explain the vote power adjustments using the example of the 2017 ...

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 ...

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.

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 current trends in the capital/labor split and the impacts thereof on the growth of inequality are one of the main concerns of national governments, European Commission and international organizations like UN, ILO, IMF, OECD and WB. These trends are usually studied at the macro level of functional distribution of income, that is, among capital and labor, and less with regard to productivity, remuneration policies or some other particular factors. In this paper, we contribute to the studies of the second type, explaining the decreasing labor income share in terms of unpaid working time and underpaid hourly earnings. For this purpose, we refer to the decreasing labor-labor exchange rate, i.e. devaluation of one's labor in exchange for other's labor embodied in the commodities affordable for one's earnings. We show that the productivity growth allows employers to compensate workers with always a lower labor equivalent, i.e. increasingly underpay works, maintaining however an impression of fair pay due to an increasing purchasing power of earnings. This conclusion is based on the OECD 1990-2014 data for G7 countries (Canada, France, Germany, Italy, Japan, United Kingdom and United States) and Denmark (known for the world least inequality). Then statistically significant implications for the growth of inequality are derived and some policy suggestions are formulated like taxing the enterprises with the inner Gini that surpasses the national level.

The paper estimates the policy representation of 34 German parties that have participated in the 2017 Bundestag (federal) election. For this purpose, the party positions on 31 topical issues are compared with the results of recent public opinion polls. Then we construct the party indices of popularity (the average percentage of the population represented) and universality (frequency in representing a majority). Regarding policy representation, the election winner, the conservative union CDU/CSU is ranked only 27th. The most representative among six Bundestag parties is the GRÜNE, constituting the smallest faction. In turn, the Bundestag indices of representativeness are about 40%, meaning that it is non-representative rather than representative. However, if the Bundestag were elected using 'the third vote', i.e. if the size of the Bundestag factions were made proportional to the indices of representativeness, it could significantly gain in policy representation.

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.

The voting method described in [Tangian 2017b] has been experimentally approbated during the 2016 election to the Karlsruhe Institute of Technology (KIT) Student Parliament [Tangian 2017c]. Under this election method, the voters cast no votes but are asked about their preferences on the policy issues which are declared in the party manifestos (like in voting advice applications, e.g. German Wahl-O-Mat). Then the degree to which the parties match with the electorate's policy profile is expressed by the parties' indices of popularity (the average percentage of the voters represented on all the issues) and universality (frequency in representing a majority), and the parliament seats are distributed among the parties in proportion to their indices. This way it is hoped to bridge direct and representative democracies and to make the latter 'more representative' and, respectively, 'more democratic'. The voters are no longer swayed by politicians' charisma and communication skills but are directed to subject matters behind personal images, ideological symbols and populist declarations. It is supposed that a method that focuses on properties of decisions proposed (e.g., political and economic implications of Brexit) can make vote more profound and responsible. Indeed, the 2016 experiment proved that the method can increase the parliament's representativeness. At the same time, it revealed that the critical point is the selection of questions by the electoral committee: 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). In the given paper, we describe a similar experiment during the election to the KIT Student Parliament in July 2017, where the problems mentioned are tackled. The parties are asked to formulate the questions themselves and to answer all of them, including the questions by other parties. The collected 94 questions are then reduced to 25 using an optimization model aimed at contrasting as much as possible between the parties by maximizing the total distance between the vectors which characterize their policy profiles. The 2017 experiment confirms that the alternative election method significantly increases the parliament representativeness while avoiding the accusation of partiality in the question selection. However, the equalization of parliament factions is still persisting. Analyzing this effect, we find that the student parties' positions are insufficiently diverse to reflect voters' policy preferences, meaning that the student parties fail to consistently represent electorate groups, representing different sets of voters on each issue. In mathematical terms, the question selection based on maximizing the distance between the party vectors reduces their space location almost to a two-dimensional plane, which is inadequate to represent the multi-dimensional space of voters' policy profiles. To surmount this effect it is suggested to replace the actual question selection criterion by the one which enhances the multi-dimensional space location of the party policy profiles.

The paper estimates the policy representation of 34 German parties that participate in the 2017 Bundestag (federal) election. For this purpose, the party positions on 31 topical issues are compared with the results of recent public opinion polls. Then we construct the party indices of popularity (the average percentage of the population represented) and universality (frequency in representing a majority). We find that the currently governing conservative union CDU/CSU and the social-democratic SPD are ranked only 27th and 22nd, respectively, being least representative among the four parties in the 2013 Bundestag. The most representative Bundestag faction is the GRÜNE - the smallest one. The current Bundestag representativeness is about 50%, as if the correspondence with the electorate's preference on every policy issue is being decided by tossing a coin, meaning that the 2013 Bundestag is practically unrelated to public opinion.