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2020 | Book

Athenian Democracy Read chapter Read first chapter

Analytical Theory of Democracy

History, Mathematics and Applications

Author: Prof. Andranik Tangian

Publisher: Springer International Publishing

Book Series : Studies in Choice and Welfare

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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About this book

This book operationalizes the idea of political representation, which is fundamental to modern democracies. Both individual representatives and representative bodies are evaluated using the indices of popularity (the average percentage of the population whose opinion is represented on topical policy issues) and universality (the percentage of issues for which the prevailing public opinion is represented). Viewed as objective functions, these indices can aid in the search for optimal representatives and representative bodies. By replacing the consistency analysis of the social choice axioms with the calculation of the best compromises, the paradoxes of social choice, such as those of Condorcet and Arrow, can be overcome. These indices also form the core of an alternative election method that is aimed at enhancing policy representation — a recent concept of political representation, which is not supported by the conventional voting systems shaped during the American and French Revolutions. This method is tested in a series of election experiments that focus on implementation details. In addition, non-societal applications such as MCDM, finance or traffic control are considered, where the objects that reflect the properties or behavior of other objects are regarded as their “representatives.” Given its scope, the book will appeal to political scientists, economists and operations researchers, as well as to politicians interested in improving democratic performance and electoral system design.

Table of Contents

Frontmatter

History

Frontmatter
Chapter 1. Athenian Democracy
Abstract
Athenian democracy is generally considered the first reference of classical democracy. Here, we outline its history: from the origins as laid by Draco and Solon in 621 BC– 594 BC, and tyranny of Peisistratos and his sons in the 6th century BC, through to the full institutionalization of democracy by Cleisthenes in 508/507 BC, in the Golden Age under Ephialtes and Pericles in the middle of the 5th century BC, and its subsequent decline in the 4th century BC. This chapter also describes its main features: the active participation of all citizens in legislative, executive, and juridical bodies; the selection of council members, jurors, and civil magistrates by lot (elections were considered an attribute of oligarchy); the procedure of ostracism (banishing); and the administrative reforms to support democratic innovations. The philosophy of Athenian democracy as well as notions about ideal government are illustrated by the views of Thucydides, Pericles, Plato, and Aristotle. Finally, we describe Aristotle’s mathematical model (though textually expressed) that explains the principle of decision making in a democracy, an oligarchy, and a mixed state, which combines elements of them both.
Andranik Tangian
Chapter 2. Echoes of Democracy in Ancient Rome
Abstract
The republican thought dates back to the theory of mixed government, or mixed constitution, founded by Plato and Aristotle who advocated for a power which combines elements of monarchy, oligarchy and democracy. This chapter outlines the development of this theory and illustrates its implementation using an example of the Roman Republic (509 BC– ca. 30 BC). There, participation by the people was assumed to provide political stability and social cohesion, but it was not as multi-sided as in the classical democracy of Athens. It was reduced to the accepting or rejecting of some new laws with no right of initiative, and election of certain officials by the citizenry without, however, giving everybody access to high offices. The chapter concludes with a description of a complex decision situation in the Roman Senate, which, for the first time in history, was rigorously analyzed according to standards of logical reasoning. This analysis, made by Pliny the Younger (62–113?), anticipates the emergence of the mathematics of multi-alternative choice and strategic voting.
Andranik Tangian
Chapter 3. Revival of Democracy in Italian Medieval City-Republics
Abstract
Democracy, abandoned during the early Middle Ages, was revived to a certain extent in the Italian city-republics. The history and political organization of Venetian and Florentine Republics are considered as most exemplary. Although the former had rather aristocratic and the latter oligarchical character, both assumed participation by the people — or a significant part thereof — in the form of assemblies and the election of magistrates. However, elections, in theory aiming at recruiting the most competent, in practice restricted the government to the noble and rich. Democratization also manifested itself in the clergy, in constraining the absolutist power of the Pope and in admittance of civil authorities to certain clerical debates. All of these revitalized interest in the theory of mixed government and forms of people’s participation. The relevant contributions of St. Thomas Aquinas, Marsilius of Padua,William of Ockham, Leonardo Bruni, Francesco Guicciardini, and Niccolo Machiavelli are briefly outlined. Since the wide use of elections required voting procedures, election improvements began to be considered as mathematical problems. In particular, ingenious election methods were invented by two medieval scholars, Ramon Llull and Nicolaus Cusanus, who anticipated the findings of French academicians of the late 18th century.
Andranik Tangian
Chapter 4. Enlightenment and the End of Traditional Democracy
Abstract
The Age of Enlightenment promoted knowledge through science and the organization of the state on rational grounds, having paved the way for the French, American and Polish Revolutions. At the same time, the Enlightenment left a historical puzzle. Although both of its leading political thinkers, Montesquieu and Rousseau, explicitly linked selection of magistrates by lot to democracy and election by vote to aristocracy, the post- Enlightenment democracies adopted ‘aristocratic’ elections as their only instrument of appointment to public offices. This re-identification of the distinctive features of democracy and aristocracy marks the end of the way democracy had been understood for over two millennia. From this turning point on, ‘democracy’ means something different than the classical democracy of Athenian type. This chapter describes the political theories of Montesquieu and Rousseau and their influence on the electoral studies of French mathematicians Borda, Condorcet and Laplace, who attempted to adapt elections to democracy, which, unlike aristocracy, assumes no commonality of values among voters. Extending the voting problem to a heterogeneous electorate resulted in intuitive and logical inconsistencies. Although some new approaches were developed, the principal difficulties remained unsolved.
Andranik Tangian
Chapter 5. Modernity and Schism in Understanding Democracy
Abstract
The two centuries following the American and French Revolutions are marked by a wide propagation of the new republican system, or representative government. Although its founders explicitly contrasted it with democracy, the modern representative governments as practiced in industrialized countries today are commonly interpreted as democracies, primarily due to universal suffrage. This chapter describes the transformations in understanding democracy in real politics as well as responses to these transformations in theoretical works with proposals for how to improve the performance of representative democracy. We argue that the redefinition of democracy perplexed scholars, especially those who have dealt with the voting problem in a general context of universal suffrage by attempting to design a universal voting procedure. It turns out that voting, practiced for centuries in simple situations, is not appropriate as a universal tool of democratic decision making. In 1951, Arrow’s Impossibility Theorem established that egalitarian, majoritybased democracy has its limits; beyond these limits, only a hierarchy headed with a ‘first man’ can operate as its extension, which resembles the structure of representative government. However, its democratic legitimacy depends on the degree of its representativeness, that is, how well the hierarchy represents the public interest. Herewith, we conclude this part of the book and pose the question to be studied next.
Andranik Tangian

Mathematics

Frontmatter
Chapter 6. Direct Democracy
Abstract
Direct democracy is studied with the example of the Athenian Assembly, Council of Five Hundred, Committee of Fifty, president, magistrates, and juries. The democratic institutions are evaluated using indices of popularity (average percentage of the population represented on a number of issues), universality (frequency of cases when the majority opinion is represented) and goodness (average of the group-represented-to-majority ratio). The indices are geometrically interpreted as projections of the institution’s characteristic vectors onto the characteristic (mainstream) vector of the society, which resembles the interaction of force vectors in physics with respect to the direction of motion. We show that the representativeness of democratic institutions selected by lot, as was practiced in Athens, is fairly high. It is also explained why the various democratic institutions with different functions should have different sizes: for instance, legislative bodies like the Athenian Assembly with its quorum of 6000 and executive bodies like magistrates with boards of ten, despite their great difference in size, they have the same degree of representativeness. Finally, it is shown that, in an unstable society, personal power is more efficient than democracy.
Andranik Tangian
Chapter 7. Dictatorship and Democracy
Abstract
The relation between democracy and dictatorship is analyzed using Arrow’s social choice model, where individual preferences are variable, as with an arbitrarily changing social situation. In its original formulation, the model implies the existence of a dictator, or, an individual whose preference always coincides with that of the society. Using the indices of popularity and universality introduced, it is shown that there are always ‘good’ Arrow’s dictators who are more representative than non-representative and should therefore be interpreted rather as political leaders, presidents or the like. Moreover, every Arrow’s dictator or political leader operates in conjunction with a decision-making hierarchy, ‘sharing the responsibility’ for the choices made. All of these correspond to the political design of democracy as practiced today. Since Arrow’s dictators, with their associated decision-making hierarchies, fall into ‘bad’ and ‘good’ types, it is their selection that makes the system dictatorial or democratic. We conclude that the inevitability of a strong ‘first man’ is, per se, not dangerous for democracy. The danger arises when the circumstances change significantly (e.g. if the rulers hold office for too long), resulting in the transformation of democracy into dictatorship.
Andranik Tangian
Chapter 8. Representative Democracy
Abstract
Representative democracy is studied using the example of the 2017 German Bundestag (federal) election. The representative capabilities of 31 German parties that took part in the election are analyzed from the viewpoint of policy representation, or virtual direct democracy. For this purpose, the parties’ positions on 38 topical policy issues are compared with the results of relevant public opinion polls. Then the parties’ indices of popularity (the average percentage of the population represented) and universality (frequency of representing a majority) are computed, as described in the previous chapters. Similar indices are also computed for the Bundestag and the Bundestag coalitions. A special attention is paid to processing cases with missing data. Among other things, it is shown that the election winner is not necessarily the best representative of public opinion, whereas the best representatives may receive too few votes to be allocated Bundestag seats. The same election failure is also observed in the 2009 and 2013 Bundestag elections considered in [Tangian 2014] and the following Chapter 13, respectively. Thereby it is shown that representative democracy, per se, guarantees no adequate representation of public opinion — even in Germany with its multiparty system and strong social-democratic traditions.
Andranik Tangian
Chapter 9. Policy Representation Across the Political Spectrum
Abstract
To trace policy representation across the German political spectrum, we order the 31 German parties that took part in the 2017 federal election so that they are arranged in a ‘spectrum’ according to their policy profiles. The policy profiles are 38-dimensional vectors of the parties’ Yes/No answers to 38 policy questions from the 2017Wahl-O-Mat, the German voting advice application (VAA), and the proximity between the party profiles is described by the matrix of their correlations. Applying principal component analysis (PCA) to this matrix, we construct a contiguous party ordering, where the neighboring parties have close policy profiles. The ordering constructed this way fits nicely to the left–right ideological axis, which is currently considered obsolete by many political scientists. However, this axis is not rectilinear but rolled into a circumference. Now, the far-left and far-right ends of such a political spectrum approach each other, although they remain somewhat distant, resulting in the spectrum’s horseshoe-like (Ω-like) shape. For comparisons, contiguous party orderings are constructed using four other models, and the results are discussed. One takeaway: a serious warning that the electoral success of a party depends neither on its policy representation capability nor on its left–right orientation. This means that the principles of representative democracy are under stress and the current electoral system is failing to meet its objectives.
Andranik Tangian
Chapter 10. Election Method to Enhance Policy Representation
Abstract
Many voters are swayed more by the charisma, personal image and communication skills of the candidates standing for election than by the parties’ manifestos, which causes them to cast votes that are actually in opposition to their policy preferences. Such behavior, known as ‘irrational voting’, results in the election of representatives who do not correspond to the voters’ own views. In this chapter, an alternative election method is proposed, whereby the voters’ policy preferences are taken into account explicitly by means of embedded referenda, testing the degree to which the candidates’ policy profiles match with that of the electorate. Next, the parties are indexed — not with respect to the percentage of votes received but with respect to their representativeness indices of popularity (the average percentage of the population represented) and universality (frequency in representing a majority), as introduced previously. The method is then hypothetically applied to redistribute the Bundestag seats among the party factions in proportion to their indices, producing a considerable gain in the representativeness of the Bundestag. Finally, we discuss mixed election procedures combining the
Andranik Tangian
Chapter 11. Concluding Discussion
Abstract
We discuss the major points that distinguish this study from some others on the same topic. In the domain of collective decision making, the aim is at computable optimal compromises as opposed to axiom consistency analysis in social choice. As for political philosophy, the focus is made on public determination in the sense of the Rousseauvian general will referred to by Borda and Condorcet, as opposed to the individual determination considered in public choice and mathematical economics. To enhance policy representation, we propose the Third Vote election method, which bridges direct and representative democracies. Finally, we explain how the operationalized notion of representativeness can be used in both societal and non-societal applications.
Andranik Tangian

Applications

Frontmatter
Chapter 12. Simple Applications
Abstract
Four simple applications of the formulas derived in the book are considered. The first application illustrates Theorem 4.14 from Section 4.9 about the convergence of the Borda and Condorcet counts as the size of the electorate increases. This application is aimed at planning a public opinion poll for ranking several options (like the candidates for election) with no cyclic majorities. Three other applications are based on formulas from Theorems 6.4 and 6.7 from Sections 6.4 and 6.5. One application deals with planning a public opinion poll with expected and guaranteed levels of representativeness. The other application describes how to plan a TV round table with invitees ‘from the street’, where the public opinion on each of several issues will be represented by at least one invitee. The last application discusses man’s ability to make complex decisions by focusing on seven to ten criteria instead of considering all available information. This is explained by the analogy between selections of criteria and representative bodies that make adequate decisions on behalf of the whole society. In particular, it is concluded that complex problems can often be analyzed with small models, and additional extensions bring much less gain than usually hoped for.
Andranik Tangian
Chapter 13. Analysis of the 2013 German Bundestag Election
Abstract
The 2013 German Bundestag election is analyzed in the same way as the 2017 Bundestag election is analyzed in Chapter 8. The positions of 28 German parties on 38 topical policy issues are compared with the statistics of relevant public opinion polls. The results are summarized in the indices of popularity (the average percentage of the population represented) and universality (frequency of representing a majority) at both the party and the coalition levels. We show that the election winners are not the best representatives of public opinion, whereas the best representatives receive too few votes to be allocated Bundestag seats. Since the same problem is inherent in the 2009, 2013 and 2017 Bundestag elections, we conclude that such an election failure is not occasional but appears to have a systemic character. To overcome it, the Third Vote method introduced in Chapter 10 is applied to hypothetically reallocate the Bundestag seats, resulting, as previously, in a significant gain in the Bundestag’s representativeness.
Andranik Tangian
Chapter 14. Constructing the 2013 German Political Spectrum
Abstract
The 2013 German political spectrum is constructed like the 2017 political spectrum is constructed in Chapter 9. For this purpose, we use the data about the positions of 28 German parties on 38 policy issues shortly before the 2013 Bundestag (federal) election. They are arranged into 28 38-dimensional vectors understood as the parties’ policy profiles, and the correlation between them is regarded as a proximity measure. The political spectrum— a contiguous party ordering where neighboring parties have close profiles — is constructed by applying the principal component analysis (PCA) to the matrix of correlations between the parties’ profiles. As in Chapter 9, the resulting ordering is exactly the left–right axis rolled into a horseshoe-like arc. The far-left and far-right ends approach each other, although they remain somewhat distant. For comparisons, contiguous party orderings are constructed using four other models. Among other things, the highly realistic political spectrum obtained this way demonstrates the flexible applicability of the framework studied.
Andranik Tangian
Chapter 15. The 2016 Third Vote Experiment: Heuristic Test
Abstract
The Third Vote election method considered in Chapters 10 and 13 is experimentally tested during the 2016 student parliament elections at the Karlsruhe Institute of Technology. Under this election method, the voters cast no votes but are asked about their preferences on the policy issues as declared by the parties in their manifestos. 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 allocated to the parties in proportion to their indices. The experiment shows that, while the method can indeed increase the parliament’s representativeness, the crux of the matter lies in selecting the right questions: if the answers to these do not reveal the differences between the parties, the method does not work well. To resolve this problem, we develop an optimization model to select questions that highlight the contrasts between the parties by maximizing the total distance between their policy profiles.
Andranik Tangian
Chapter 16. The 2017 Third Vote Experiment: Choice of Questions
Abstract
The 2016 electoral experiment described in Chapter 15 reveals that the critical point of the Third Vote is the selection of questions for electoral ballots. Since certain questions and their wordings can be favorable for some parties and unfavorable for others, the committee responsible for this task can be always accused of bias in their choices. Furthermore, a heuristic selection of questions may yield insufficient contrast between the parties, causing the equalization of the parliament faction weights. In the 2017 experiment conducted during the elections to the student parliament of the Karlsruhe Institute of Technology (KIT), the parties are therefore asked to formulate the questions themselves and to answer the questions of the other parties. The collected questions are then reduced to a reasonable number by an optimization model aimed at distinguishing the party positions from one another, and only these questions are included on the electoral ballot. The 2017 experiment organized this way confirms that the Third Vote significantly increases the parliament’s representativeness while avoiding the suspicion of partiality. However, the equalization effect still persists.We suppose that this effect could be tackled if the questions magnified the multidimensional salience of the KIT political spectrum determined by the party policy profiles — to better reflect the many-sidedness of the electorate’s preferences.
Andranik Tangian
Chapter 17. The 2018 Third Vote Experiment: Implementation Details
Abstract
This chapter is devoted to the Third Vote experiment conducted during the 2018 elections to the student parliament (StuPa) of the Karlsruhe Institute of Technology (KIT). As in the 2017 experiment, the student parties are asked to formulate questions for the Third Vote electoral ballot themselves and to answer the questions of other parties. The submitted questions are then reduced to a reasonable number by several optimization models in order to highlight the differences between the party positions. The main goal of the actual experiment is a comparative evaluation of the criteria for selecting questions that will expose either an increase or a decrease the representative capability of the StuPa as hypothetically elected using the optimized Third Vote questionnaires. Particular attention is paid to preserving the KIT political spectrum as determined by the residuals of party policy profiles after reducing the list of policy issues. To develop the supporting mathematical tools, we introduce a technique for regularizing the matrices of correlations between party policy profiles, which occasionally degenerate (turn into vectors of equal elements, e.g. consisting of ‘Yes’ answers only) while reducing the number of questions, making the correlations indefinite. After these advances, the Third Vote can be considered an election-ready prototype of a voting method.
Andranik Tangian
Chapter 18. Application to MCDM: Choosing a Library Name
Abstract
From the formal viewpoint, ‘representatives’ do not necessarily have to be individuals. In Chapters 8–10 and 13–17, the representatives are not persons but political parties, and now we go even further, requiring no human nature of representatives but only their capacity to represent the interests of a group of people. More specifically, when choosing among an assortment of alternatives, the group members have various preferences regarding the nature of a solution being sought. Since these choice alternatives reflect collective opinions, they can be considered better or worse representatives of the social/collective will. This idea is applied to the exercise of deciding on a name for the campus library by a supervising committee. Its members have differing opinions, such as whether the library should reflect the national affiliation, be named after a great man, relate to sciences, and so forth. Regarding the balances of opinion on these issues, the alternative library names are evaluated using the indices of popularity and universality, which help to find the optimal compromise and bring the committee to a rational consensus.
Andranik Tangian
Chapter 19. Application to MCDM: Choosing a Place for an Outing
Abstract
As in Chapter 18, ‘representatives’ are understood purely functionally— as objects which reflect certain individual/collective preferences. This approach is applied to several travel alternatives considered by an academic team taking a trip together. The team members have different wishes, such as whether to visit a natural or cultural attraction, whether to spend one or two days on travel, what mode of transportation to take, and so forth. Since various travel alternatives reflect more or less completely these wishes they are considered representatives of the collective preferences and are evaluated using the indices of popularity and universality. Finally, the optimal travel alternative is chosen as well as the plan of future outings that best meets the wishes of the group. The plans consist of several trip alternatives regarded as representative bodies—parliaments or magistrates—which jointly optimally represent the collective wishes.
Andranik Tangian
Chapter 20. Application to Stock Exchange Predictions
Abstract
The model of representation is adapted to predict fluctuations in stock prices. From the formal viewpoint, neither the ‘society’, nor ‘representatives’ are necessarily human, so some objects can represent the behavior of other objects. This idea is applied to the major American and German stocks with which the Dow Jones and DAX indices are computed. For this purpose, the price fluctuations of the Dow Jones stocks are regarded as representatives of those of the DAX stocks a week later. In particular, during the control period of 24 weeks, the fluctuations in American Express stock prices anticipated, on average, the price fluctuations of 2/3 of the DAX stocks. Some selected groups of three to five Dow Jones stocks arranged into ‘parliaments’, whose predictions are made by majority rule, have even better characteristics. Both single Dow Jones stocks and their parliaments are statistically tested on their potential to be used as predictors. For single stocks, the P-values are derived analytically; for the parliaments they are obtained by Monte Carlo simulation with 1000 experiments. The predictive capability of the totality of Dow Jones stocks is also evaluated and statistically tested.
Andranik Tangian
Chapter 21. Application to Traffic Control
Abstract
The model of representatives is applied to find the city street intersections whose traffic situations somehow foreshadow the conditions at other intersections, meaning that some intersections can be considered representatives of others. These representative intersections are forecasters of the jams that could be prevented by switching the ‘green wave’ (coordination of traffic lights to allow continuous traffic flow over several intersections) in the appropriate direction before a slow-down can form. The most representative intersections for forecasting are found using the indices of popularity and universality. Moreover, groups of intersections are arranged into ‘parliaments’, making ‘decisions’ by majority rule. This approach is illustrated by an example of forecasting traffic congestions on the City Ring in Hagen, Germany, based on information from intersections all around the town. The predictive capacity of single forecasters and small groups thereof arranged in parliaments is statistically tested. It is shown that just a few appropriately selected intersections are sufficient to make reliable predictions.
Andranik Tangian
Chapter 22. Statistically Testing the Representative Capability
Abstract
A statistical test of the representative capability of a candidate, party or coalition is developed. As observations, we consider how well the candidate (coalition) positions on several policy issues, such as ‘Domestic deployment of federal armed forces?’—Yes/No; ‘Taxation of passenger diesel cars?’—Yes/No, etc., match up with the prevailing public opinion on these issues. If the issues are few and the candidates are numerous, then even a perfect match says little about the representative capability, because it is always possible that one candidate, or one coalition out of many, will align with public opinion on a couple of topics. To perform the test, the probability of the observed match of the candidate/coalition position with the prevailing public opinion is found under the null hypothesis, assuming no representative capability but coincidence by chance. If this probability is small, then the null hypothesis is rejected and the alternative hypothesis (existence of representative capability) is accepted. The test developed is applied to the five German parties and their coalitions considered in Chapters 8 and 13.
Andranik Tangian
Backmatter
Metadata
Title
Analytical Theory of Democracy
Author
Prof. Andranik Tangian
Copyright Year
2020
Electronic ISBN
978-3-030-39691-6
Print ISBN
978-3-030-39690-9
DOI
https://doi.org/10.1007/978-3-030-39691-6