An algorithmic approach to detect non-injectivity of the Partial Borda Count

Voting is how we elect today’s voices, faces, and leaders in our country. It is argued to be a very essential right we have as a people. A voter votes, by listing their preferences. Their preferences are relating the candidates to one each other (i.e. whether they prefer candidate A to candidate B or if they are indifferent between the two). There are many different social choice functions that can be used to calculate the results of an election. This project glances over the theory of Condorcet, Borda, Arrow, and Young, all of whom had a great impact on voting theory and social choice theory. I experiment with partially-ordered preferences using the Partial Borda Count. The Partial Borda Count switches from being injective (one-to-one) to non-injective (multiple posets going to the same score vector) for all elections with 5-elements or higher. I created an algorithm that determines certain posets that go to the same score vectors for n-candidate elections (if n \u3e 5). My algorithm was able to detect all of the failures of injectivity for a 5-candidate election. I then use this algorithm to see if I can predict which posets go to the same score vector, for a 6-candidate election, without having to construct a 6-element database. It turns out my algorithm proved successful in locating some of the injectivity failures of 6-element elections

Strategic Voting with Almost Perfect Signals

A standard assumption in the literature of strategic voting is the independence of signals. Each juror observes a signal at the interim stage of the game. Then she votes according to her private information in order to maximize her expected utility. This work introduces a dependency between signals, reflecting a more realistic situation, in which evidences can be incontrovertible. We give a full characterization of the symmetric equilibria in non-weakly dominated strategies and we provide a benchmark between the classical approach and this new one

Rational Choice and Categorical Reason

Recently, the positive theory of rational choice has come under attack from experimental psychologists and economists. Their experimental results, gathered together under the banner of behavioral analysis, show that the maximizing model of rational choice often does not provide a very accurate account of how agents actually choose. Moreover, the departures from the model appear systematic rather than random, suggesting that something other than maximization is going on. However, the general tenor of these studies is not to question the normative ideal of maximization. Rather, the departures from the standard account of rational choice are typically characterized, and criticized, as failures to be rational. Agents are only human beings, after all, and human beings are subject to the limitations that must, inevitably and systematically, arise out of personal bias, limits on the salience and availability of important information, and the distorting effects of how a given problem is framed. Thus, real world agents are only, it is said, capable of a bounded rationality, using rules of thumb and various heuristics (sometimes helpful, sometimes not) rather than the fully fledged maximizing rationality that is still largely accepted as the ideal for rational choice. This paper argues that, for many decision-making problems, the normative account of rationality that animates rational choice theory, and not just the positive account that is criticized by the behaviorists, is deficient, even as a theory of ideally rational behavior, and that an alternative account of rational choice is required. Rationality, it is suggested, provides for an ordered particularity, including particular decisions, but the notion of an ordering that informs this alternative account of ideally rational behavior, and which is more appropriate in some decision-making contexts, including many legal ones, is very different from the idea of an ordering that informs the standard account within rational choice theory. The latter, which is closely allied to the idea of maximization, remains largely quantitative and single-minded in its orientation, this despite the pluralism of motivations that it appears to be willing and able to accommodate within its seemingly minimalist structure. The alternative account is more qualitative, or categorical (although not absolute), offering a conception of a rational ordering of particularity that is more allied to the idea of an understanding or interpretation (under rules or principles) than it is to maximization. In this paper this alternative conception of rationality is referred to as categorical reason. The real challenge for the paper, however, is not so much to articulate two alternative accounts of rationality, but to begin to make each accessible to the other within some common intellectual framework. While rational choice theory provides a useful and precise set of tools for beginning this process of achieving mutual understanding, the paper argues that some quite fundamental postulates of rational choice theory (including the most basic choice consistency axiom and the strong independence assumption) will have to be relaxed if the contributions of categorical reason are properly to be accommodated within it. However, the paper shows that there is much advantage in this, even for what the rational choice theorist hopes to achieve, and illustrates the point by reference to some systematic difficulties that the rational choice theorist faces in the theory of social choice and game theory

Choosing How to Choose: Self Stable Majority Rules

We consider the endogenous choice of a voting rule, characterized by the majority size needed to elect change over the status quo, by a society who will use the rule to make future decisions. Under simple assumptions on the uncertainty concerning the future alternatives that will be voted upon, voters' have induced preferences over voting rules that are single-peaked and intermediate. We explore the existence of self-stable voting rules, i.e., voting rules such that there is no alternative rule that would beat the given voting rule if the given voting rule is used to choose between the rules. There are situations where self-stable voting rules do not exist. We explore conditions that guarantee existence, as well as issues relating to efficiency and constitutional design.

Democracy and the Common Good: A Study of the Weighted Majority Rule

In this study I analyse the performance of a democratic decision-making rule: the weighted majority rule. It assigns to each voter a number of votes that is proportional to her stakes in the decision. It has been shown that, for collective decisions with two options, the weighted majority rule in combination with self-interested voters maximises the common good when the latter is understood in terms of either the sum-total or prioritarian sum of the voters’ well-being. The main result of my study is that this argument for the weighted majority rule — that it maximises the common good — can be improved along the following three main lines. (1) The argument can be adapted to other criteria of the common good, such as sufficientarian, maximin, leximin or non-welfarist criteria. I propose a generic argument for the collective optimality of the weighted majority rule that works for all of these criteria. (2) The assumption of self-interested voters can be relaxed. First, common-interest voters can be accommodated. Second, even if voters are less than fully competent in judging their self-interest or the common interest, the weighted majority rule is weakly collectively optimal, that is, it almost certainly maximises the common good given large numbers of voters. Third, even for smaller groups of voters, the weighted majority rule still has some attractive features. (3) The scope of the argument can be extended to decisions with more than two options. I state the conditions under which the weighted majority rule maximises the common good even in multi-option contexts. I also analyse the possibility and the detrimental effects of strategic voting. Furthermore, I argue that self-interested voters have reason to accept the weighted majority rule

Choosing How to Choose: Self-Stable Majority Rules

We consider the endogenous choice of a voting rule, characterized by the majority size needed to elect change over the status quo, by a society who will use the rule to make future decisions. Under simple assumptions on the uncertainty concerning the future alternatives that will be voted upon, voters' have induced preferences over voting rules that are single-peaked and intermediate. We explore the existence of self-stable voting rules, i.e., voting rules such that there is no alternative rule that would beat the given voting rule if the given voting rule is used to choose between the rules. There are situations where self-stable voting rules do not exist. We explore conditions that guarantee existence, as well as issues relating to efficiency and constitutional design

Theories of referendum and the analysis of agenda-setting.

The referendum is often considered to be a form of direct democracy, and is often justified in terms of results representing the will of the majority. This view is disputable for three reasons: i) based on the results of social choice theory, it may be argued that the outcomes of referendums may be arbitrary and open to various interpretations; ii) it is debatable what the role of popular majorities should be in decision-making; many theorists of democracy think that unchecked majority rule should not prevail; iii) because of the differences in agenda-setting, there is considerable functional variation between referendums. Different forms of referendums have also been justified by different theoretical arguments: popular initiatives have been promoted by radical democrats, whereas referendums used as a check on legislature have been supported by 'Madisonian' democrats. In the analysis of agenda-setting it is important to distinguish i) how and by whom the referendum is initiated and ii) on what kind of issues they may be held. The influence of the referendum on the political agenda depends on whether the referendum is initiated by representatives (ad hoc or optional referendum); or by a certain number of citizens (popular initiative); or whether it is a check on laws passed by the parliament (mandatory, suspensive and abrogative referendums). Furthermore, these distinctions are important for understanding the strategic character of referendums, i.e. the strategic use of optional referendums by the representatives (parliamentary parties, president etc.), or the representatives' anticipation and reaction to the possibility of the other forms of referendums. Referendum in 22 democracies are classified, and their 'functional properties' (Smith 1976) are analysed. In order to get a more precise picture on how referendums function as a part of political systems and how political actors use the referendum, three cases, Sweden, Denmark and Switzerland, are analysed. Although the idea of giving the people a say is the common element of all forms of referendums, the differences between agenda-setting institutions explain why, how and under whose control 'the people's voice' is heard

Vers des modes de scrutin moins manipulables

We study coalitional manipulation of voting systems: can a subset of voters, by voting strategically, elect a candidate they all prefer to the candidate who would have won if all voters had voted truthfully? From a theoretical point of view, we develop a formalism which makes it possible to study all voting systems, whether the ballots are orders of preference on the candidates (ordinal systems), ratings or approval values (cardinal systems), or even more general objects. We show that for almost all classical voting systems, their manipulability can be strictly reduced by adding a preliminary test aiming to elect the Condorcet winner if there is one. For the other voting systems, we define the generalized Condorcification which leads to similar results. Then we define the notion of decomposable culture, an assumption of which the probabilistic independence of voters is a special case. Under this assumption, we prove that, for each voting system, there exists a voting system which is ordinal, shares certain properties with the original voting system, and is at most as manipulable. Thus, the search for a voting system of minimal manipulability (in a class of reasonable systems) can be restricted to those which are ordinal and satisfy the Condorcet criterion. In order to allow everyone to examine these phenomena in practice, we present SVVAMP, a Python package of our own dedicated to the study of voting systems and their manipulability. Then we use it to compare the coalitional manipulability of various voting systems in several types of cultures, i.e. probabilistic models that generate populations of voters equipped with random preferences. We then complete the analysis with elections from real experiments. Finally, we determine the voting systems with minimal manipulability for very low values of the number of voters and of the number of candidates, and we compare them with the classical voting systems of the literature. In general, we establish that Borda's method, Range voting, and Approval voting are particularly manipulable. Conversely, we show the excellent resistance to manipulation of the system called IRV, also known as STV, and of its variant Condorcet-IRV.Nous étudions la manipulation par coalition des modes de scrutin: est-ce qu'un sous-ensemble des électeurs, en votant de façon stratégique, peut faire élire un candidat qu'ils préfèrent tous au candidat qui aurait été vainqueur si tous les électeurs avaient voté sincèrement? D'un point de vue théorique, nous développons un formalisme qui permet d'étudier tous les modes de scrutin, que les bulletins soient des ordres de préférences sur les candidats (systèmes ordinaux), des notes ou des valeurs d'approbation (systèmes cardinaux) ou des objets encore plus généraux. Nous montrons que pour la quasi-totalité des modes de scrutin classiques, on peut réduire strictement leur manipulabilité en ajoutant un test préliminaire visant à élire le vainqueur de Condorcet s'il en existe un. Pour les autres modes de scrutin, nous définissons la condorcification généralisée qui permet d'obtenir des résultats similaires. Puis nous définissons la notion de culture décomposable, une hypothèse dont l'indépendance probabiliste des électeurs est un cas particulier. Sous cette hypothèse, nous prouvons que, pour tout mode de scrutin, il existe un mode de scrutin qui est ordinal, qui partage certaines propriétés avec le mode de scrutin original et qui est au plus aussi manipulable. Ainsi, la recherche d'un mode de scrutin de manipulabilité minimale (dans une classe de systèmes raisonnables) peut être restreinte à ceux qui sont ordinaux et vérifient le critère de Condorcet. Afin de permettre à tous d'examiner ces phénomènes en pratique, nous présentons SVVAMP, un package Python de notre cru dédié à l'étude des modes de scrutin et de leur manipulabilité. Puis nous l'utilisons pour comparer la manipulabilité par coalition de divers modes de scrutin dans plusieurs types de cultures, c'est-à-dire des modèles probabilistes permettant de générer des populations d'électeurs munis de préférences aléatoires. Nous complétons ensuite l'analyse avec des élections issues d'expériences réelles. Enfin, nous déterminons les modes de scrutin de manipulabilité minimale pour de très faibles valeurs du nombre d'électeurs et du nombre de candidats et nous les comparons avec les modes de scrutin classiques. De manière générale, nous établissons que la méthode de Borda, le vote par notation et le vote par assentiment sont particulièrement manipulables. À l'inverse, nous montrons l'excellente résistance à la manipulation du système appelé VTI, également connu par son acronyme anglophone STV ou IRV, et de sa variante Condorcet-VTI

Political information, elections and public policy

This thesis contributes to the study of the role of information in elections and public policy formation. Its main focus is on information acquisition and voting behaviour. Chapter 1 discusses the motivation of this research and presents a survey of related literature. Chapter 2 focuses on electoral turnout, Chapter 3 on public policy, and Chapter 4 on mass media. Chapter 2 studies the impact of information on electoral turnout. Since incentives to be informed are correlated with other incentives to participate in public life, a model of information acquisition and turnout is introduced to isolate potential instrumental variables and try to establish a causal relation. Results are tested on the 1997 General Election in Britain. It is shown that information, as well as ideology, matters for turnout. It also contributes to explain the systematic correlation of turnout with variables like education and income. Voters' knowledge of candidates and of other political issues is also substantially influenced by mass media. Chapter 3 presents a model that links the distribution of political knowledge with redistributive policies. It argues that voters can have private incentives to be informed about politics and that such incentives are correlated with income. Therefore redistribution will be systematically lower than what the median voter theorem predicts. Moreover, more inequality does not necessarily lead to an increase in redistribution and constitutional restrictions might have unintended consequences. In Chapter 4 it is argued that instrumentally motivated voters should increase their demand for information when elections are close. In supplying news, mass media should take into account information demand, as well as the value of customers to advertisers and the cost of reaching marginal readers. Information supply should therefore be larger in electoral constituencies where the contest is expected to be closer, the population is on average more valuable for advertisers, and the population density is higher. These conclusions are then tested with good results on data from the 1997 General Election in Britain