In a three-candidate election, a scoring rule s (s in [0,1]) assigns 1, s, and 0 points (respectively) to each first, second and third place in the individual preference rankings. The Condorcet efficiency of a scoring rule is defined as the conditional probability that this rule selects the winner in accordance with Condorcet criteria (three Condorcet criteria are considered in the paper). We are interested in the following question: What rule s has the greatest (...) class='Hi'>Condorcet efficiency? After recalling the known answer to this question, we investigate the impact of social homogeneity on the optimal value of ?. One of the most salient results we obtain is that the optimality of the Borda rule (s=1/2) holds only if the voters act in an independent way. (shrink)

ABSTRACT John Rawls proposed two criteria for the delimitation of acceptable inequalities. The universal gain principle requires inequalities to be beneficial for all, and the difference principle requires them to be beneficial for the least advantaged. These principles are commonly believed to have originated in Rawls’s work, but they were both clearly expressed in the writings of Nicolas de Condorcet. Contrary to Rawls, Condorcet did not imbed them in the framework of a social contract, but instead sought (...) their foundations in natural rights. Whereas Rawls recommends us to find out what social arrangements rational reasoners would choose in a hypothetical pre-social situation, Condorcet proposes that we ask the underprivileged in our society whether or not they consider themselves to benefit from the prevailing social and economic inequalities. Thus, Condorcet’s original version of the difference principle puts social inequalities to a different test than its latter-day, hypothetical version. (shrink)

We propose a Condorcet-consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying the anti-vote-splitting criterion of independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone-independent methods, Split Cycle mitigates (...) both “spoiler effects” and “strong no show paradoxes.”. (shrink)

In a three-candidate election, a scoring rule λ, λ∈[0,1], assigns 1,λ and 0 points (respectively) to each first, second and third place in the individual preference rankings. The Condorcet efficiency of a scoring rule is defined as the conditional probability that this rule selects the winner in accordance with Condorcet criteria (three Condorcet criteria are considered in the paper). We are interested in the following question: What rule λ has the greatest Condorcet efficiency? After (...) recalling the known answer to this question, we investigate the impact of social homogeneity on the optimal value of λ. One of the most salient results we obtain is that the optimality of the Borda rule (λ=1/2) holds only if the voters act in an independent way. (shrink)

Nicolas de Condorcet (1743-1794), the innovating founder of mathematical thinking in politics, was the last great philosophe of the French Enlightenment and a central figure in the early years of the French Revolution. His political writings give a compelling vision of human progress across world history and express the hopes of that time in the future perfectibility of man. This volume contains a revised translation of 'The Sketch', written while in hiding from the Jacobin Terror, together with lesser-known writings (...) on the emancipation of women, the abolition of slavery, the meanings of freedom and despotism and reflections on revolutionary violence. The introduction by Steven Lukes and Nadia Urbinati sets these works in context and shows why Condorcet is of real interest today as we reinterpret the meaning of Enlightenment, the very idea of progress and the founding ideas of social democracy. (shrink)

Während Condorcets Schriften bislang nur unter dem Gesichtspunkt der Geschichtsphilosophie und mathematischen Entscheidungstheorie rezipiert wurden, präsentiert dieser Band Condorcet als einen zentralen politischen Ordnungsdenker der Französischen Revolution, als einen liberal-republikanischen Autor. Die in der Edition versammelten Quellentexte zeigen, dass er die menschenrechtlichen und demokratischen Leitideen am Ende des 18. Jh.s nachdrücklich artikulierte. Condorcets zentrales Anliegen besteht in der Suche nach einer institutionellen Form demokratischer Ordnung, die ein hohes Maß an bürgerschaftlicher Partizipation mit den liberalen Forderungen individueller Rechte verbindet. Die (...) Schriften zur Emanzipation von Sklaven, zum Bürgerrecht für Frauen, zum Begriff der Revolution sowie sein demokratischer Verfassungsentwurf von 1793 belegen seinen theoretisch komplexen und innovativen Versuch, Antworten auf die Herausforderungen demokratischer Legitimität zu finden. (shrink)

v. 1. Cinq mémoires sur l'instruction publique -- v. 2. Rapport sur l'instruction publique.

Non-compensatory aggregation rules are applied in a variety of problems such as voting theory, multi-criteria analysis, composite indicators, web ranking algorithms and so on. A major open problem is the fact that non-compensability implies the analytical cost of loosing all available information about intensity of preference, i.e. if some variables are measured on interval or ratio scales, they have to be treated as measured on an ordinal scale. Here this problem has been tackled in its most general formulation, that (...) is when mixed measurement scales (interval, ratio and ordinal) are used and both stochastic and fuzzy uncertainties are present. Objectives of this article are first to present a comprehensive review of useful solutions already proposed in the literature and second to advance the state of the art mainly in the theoretical guarantee that weights have the meaning of importance coefficients and they can be summarized in a voting matrix. This is a key result for using non-compensatory Condorcet consistent rules. A proof on the probability of existence of ties in the voting matrix is also developed. (shrink)

In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning to losing. In this note, we prove a new impossibility theorem concerning this axiom: there is no ordinal voting method satisfying positive involvement that also satisfies the Condorcet winner and loser criteria, resolvability, and a common invariance property for Condorcet (...) methods, namely that the choice of winners depends only on the ordering of majority margins by size. (shrink)

This book provides an evaluation of 18 voting procedures in terms of the most important monotonicity-related criteria in fixed and variable electorates. All voting procedures studied aim at electing one out of several candidates given the voters' preferences over the candidates. In addition to (strict) monotonicity failures, the vulnerability of the procedures to variation of the no-show paradoxes is discussed. All vulnerabilities are exemplified and explained. The occurrence of the no-show paradoxes is related to the presence or absence of (...) a Condorcet winner. The primary readership of this book are scholars and students in the area of social choice. (shrink)

In an article from 1973, Rittel and Webber distinguished between “tame” or “benign” problems on the one hand and “wicked” problems on the other. The authors argued that wicked problems occur in nearly all public policy issues. Since different groups adhere to different value-sets, solutions can only be expressed as better or worse. By no means can they be viewed as definitive or objective. In this paper we shall consider, from this very angle, the theory of social choice which is (...) about the aggregation of individual preferences with the aim to derive a consistent social preference. We shall show that collective choice offers wicked problems of various types which differ in their degree of severity. We shall hereby concentrate on welfare functions and voting schemes of different kinds and shall discuss these in the light of various criteria such as Arrow’s independence condition, Condorcet consistency, monotonicity, manipulability, and other properties. (shrink)

Social choice rules are often evaluated and compared by inquiring whether they satisfy certain desirable criteria such as the Condorcet criterion, which states that an alternative should always be chosen when more than half of the voters prefer it over any other alternative. Many of these criteria can be formulated in terms of choice sets that single out reasonable alternatives based on the preferences of the voters. In this paper, we consider choice sets whose definition merely relies (...) on the pairwise majority relation. These sets include the Copeland set, the Smith set, the Schwartz set, von Neumann-Morgenstern stable sets, the Banks set, and the Slater set. We investigate the relationships between these sets and completely characterize their computational complexity, which allows us to obtain hardness results for entire classes of social choice rules. (shrink)

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. (shrink)

Suppose that a majority of jurors decide that a defendant is guilty (or not), and we want to know the likelihood that they reached the correct verdict. The French philosopher Marquis de Condorcet (1743-1794) showed that we can get a mathematically precise answer, a result known as the “Condorcet Jury Theorem.” Condorcet’s theorem isn’t just about juries, though; it’s about collective decision-making in general. As a result, some philosophers have used his theorem to argue for democratic forms (...) of government. This essay explains Condorcet’s theorem and how philosophers have used it as an argument for democracy. (shrink)

The purpose of this thesis is to discuss in depth the issues of civic education and public education in light of Condorcet’s philosophy. Condorcet proposed the revolutionary plan of education reform in the period of the French Revolution. His philosophy is based on republican thought. The republic rests on the sovereignty of the people; people with sovereignty should receive intelligence and be educated for that. Therefore, Condorcet has planned educational programs to enhance people's ability to use reason, (...) that is, “people's reason”, through public education, and to sublimate people and nation into enlightenment rationality. According to Condorcet, there is no true political and social space for citizens without public education, and there are only blind people who are confiscated by dictators. In this case, the citizen falls into anti-enlightenment which is adhered to the limit of immediate utility. Autocracy is always parasitic to the ignorance of citizens. Therefore, the role of public education must be the development of reasoned and free will. The purpose of public education is not to teach the doctrine of civic religion, but to teach all people how to use their reason, teach human rights, and teach people how to judge freely. In this sense, Condorcet's educational philosophy is civic education mediated by people's reason. (shrink)

This paper defends the communitarian account of meaning against Boghossian’s (Wittgensteinian) arguments. Boghossian argues that whilst such an account might be able to accommodate the infinitary characteristic of meaning, it cannot account for its normativity: he claims that, since the dispositions of a group must mirror those of its members, the former cannot be used to evaluate the latter. However, as this paper aims to make clear, this reasoning is fallacious. Modelling the issue with four (justifiable) assumptions, it shows that (...) Condorcet’s ‘Jury Theorem’ can be used to prove that the dispositions of the majority of the members of a group can differ from those of any individual member in a way that makes it possible to use communal dispositions as a standard with which individual dispositions can be assessed. Moreover, the argument of the paper is also shown to have general implications for the use of formal methods in the explanation of the nature of certain fallacious inferences. (shrink)

Despite the importance of the “historiographical revolution” in Kuhn’s work, he did not carry out a specific study about it. Without a systematic investigation into it, he even affirms that the “old” historiography of science (OHS) is unhistorical, suggesting its summary disqualification in the face of his “new historiography” of science (NHS). My wider project, of which this paper is a part, is to better discuss the issue of the justification of the NHS. In this paper, I discuss the justification (...) (and the genesis) of the OHS, focusing on Condorcet and Comte and resorting especially to Koyré. This will allow us to understand that the relation between the OHS and the NHS is a new instance of inter-theoretical incommensurability. And, indeed, that the NHS is not stricto senso a new historiography. It is the same historiography used for other disciplines (art, philosophy), which in the twentieth century begins to be applied to science as well. (shrink)

Condorcet's understanding of the application of the philosophy of natural sceince to social science.

Condorcet's arguments concerning the dependence of unhindered scientific development on the presence of democratic conditions still sounds relevant today, because they are based on specific and complex considerations concerning the character of the social enterprise of science that articulates problems that still continue. The implicit dispute between Condorcet and Rousseau is also the first great historical example of the conflict between the Enlightenment and Romanticism, which accompanies the history of modernity, as an unresolved and indeed irresolvable opposition that (...) belongs to the prehistory of our own confusions and quandaries concerning the relations between culture, science, politics and society. (shrink)

Many studies have considered the probability that a pairwise majority rule (PMR) winner exists for three candidate elections. The absence of a PMR winner indicates an occurrence of Condorcet's Paradox for three candidate elections. This paper summarizes work that has been done in this area with the assumptions of: Impartial Culture, Impartial Anonymous Culture, Maximal Culture, Dual Culture and Uniform Culture. Results are included for the likelihood that there is a strong winner by PMR, a weak winner by PMR, (...) and the probability that a specific candidate is among the winners by PMR. Closed form representations are developed for some of these probabilities for Impartial Anonymous Culture and for Maximal Culture. Consistent results are obtained for all cultures. In particular, very different behaviors are observed for odd and even numbers of voters. The limiting probabilities as the number of voters increases are reached very quickly for odd numbers of voters, and quite slowly for even numbers of voters. The greatest likelihood of observing Condorcet's Paradox typically occurs for small numbers of voters. Results suggest that while examples of Condorcet's Paradox are observed, one should not expect to observe them with great frequency in three candidate elections. (shrink)

This chapter explores the relationship between Goldman's thesis and the classical jury theorem. It identifies the minimal modification needed in order to recover Goldman's thesis in a Condorcetian framework. Goldman's thesis can be recast as a generalization of the classical Condorcet jury theorem. The central move needed to recover Goldman's thesis from a generalized jury theorem is to replace Condorcet's assumption that there is a single truth to be tracked with the assumption of multiple such truths: one for (...) each voter. In Goldman's picture, there is still an indirect, derivative sense in which there exists an 'overall' truth about the correct outcome for the electorate in aggregate. This 'overall' truth is determined, of course, by the profile of voter‐specific truths and therefore depends on the identity of the electorate. The chapter also provides some numerical examples to illustrate the implications of the generalized jury theorem. (shrink)

Overall assessments and balancing of interests -- Multi-criteria analysis -- Intuition -- Legal examples of decision-making with SAW -- Decision-making under uncertainty -- Evidentiary aspects.

Under approval voting, each voter just distinguishes the candidates he approves of from those appearing as unacceptable. The preference approval voting is a hybrid version of the approval voting first introduced by Brams and Sanver The mathematics of preference, choice and order. Springer, Berlin, pp 215–237, 2009). Under PAV, each voter ranks all the candidates and then indicates the ones he approves. In this paper, we provide an analytical representation of the limiting probability that PAV elects the Condorcet winner (...) when she exists in three-candidate elections. We perform our analysis by assuming the assumption of the Extended Impartial Culture. The aim is to measure at which extend PAV performs better than AV both on the propensity of electing the Condorcet winner and on that of the non-election of the Condorcet loser. For this purpose, we also provide an analytical representation of the limiting probability that AV elects the Condorcet winner when she exists in three-candidate elections. Our representation of the limiting probability that AV elects the Condorcet winner is more general than that provided by Diss et al. Handbook on approval voting. Springer, Berlin, pp 255–283, 2010) and it leads to the same figures as the representation provided by Gehrlein and Lepelley. (shrink)

This paper generalises the classical Condorcet jury theorem from majority voting over two options to plurality voting over multiple options. The paper further discusses the debate between epistemic and procedural democracy and situates its formal results in that debate. The paper finally compares a number of different social choice procedures for many-option choices in terms of their epistemic merits. An appendix explores the implications of some of the present mathematical results for the question of how probable majority cycles (as (...) in Condorcet's paradox) are in large electorates. (shrink)

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.

We consider two no-show paradoxes, in which a voter obtains a preferable outcome by abstaining from a vote. One arises when the casting of a ballot that ranks a candidate in first place causes that candidate to lose the election, superseded by a lower-ranked candidate. The other arises when a ballot that ranks a candidate in last place causes that candidate to win, superseding a higher-ranked candidate. We show that when there are at least four candidates and when voters may (...) express indifference, every voting rule satisfying Condorcet’s principle must generate both of these paradoxes. (shrink)

In his 2010 paper “Philosophical Naturalism and Intuitional Methodology”, Alvin I. Goldman invokes the Condorcet Jury Theorem in order to defend the reliability of intuitions. The present note argues that the original conditions of the theorem are all unrealistic when analysed in connection to the case of intuitions. Alternative conditions are discussed.