When voters’ preferences on candidates are mutually coherent, in the sense that they are at all close to being perfectly single-peaked, perfectly single-troughed, or perfectly polarized, there is a large probability that a Condorcet Winner exists in elections with a small number of candidates. Given this fact, the study develops representations for Condorcet Efficiency of plurality rule as a function of the proximity of voters’ preferences on candidates to being perfectly single-peaked, perfectly single-troughed or perfectly polarized. We find (...) that the widely used plurality rule has Condorcet Efficiency values that behave in very different ways under each of these three models of mutual coherence. (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)

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

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)

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)

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)

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)

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

David Williams explores the complex links between Condorcet as visionary ideologist and pragmatic legislator, and between his concept of modernity and the management of change. The Marquis de Condorcet was one of the few Enlightenment thinkers to witness and participate in the French Revolution. Based on an extensive array of printed and original manuscript sources, Williams' analysis of Condorcet's politics will be a major contribution to Enlightenment studies.

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)

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.

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)

The basic theoretical premise of this article is that representation does not necessarily imply a break with democratic principles. Its goal is to challenge the traditional liberal-elitist approach to representative government according to which this system is a mixed regime that is not identifiable with democracy since its main institution, election, is a mechanism that is inherently aristocratic, although it can be implemented in a democratic way. I question this powerful argument by questioning its main assumption: the idea that representative (...) government, since its 18th-century inception, has had a linear and univocal history which was essentially undemocratic.I go back to the age of the French Revolution and analyse Condorcet’s plan of constitution in order to prove my case. Condorcet devised institutional mechanisms and procedures that were able to make representative government democratic by overcoming the polarization between representation and participation and making them related forms of political action constituting the continuum of decision-making and opinion formation in modern democratic society. (shrink)

The Condorcet efficiency of a social choice procedure is usually defined as the probability that this procedure coincides with the majority winner (or majority ordering) in random samples, given a majority winner exists (or given the majority ordering is transitive). Consequently, it is in effect a conditional probability that two sample statistics coincide, given certain side conditions. We raise a different issue of Condorcet efficiencies: What is the probability that a social choice procedure applied to a sample matches (...) with the majority preferences of the population from which the sample was drawn? We investigate the canonical case where the sample statistic is itself also majority rule and the samples are drawn from real world distributions gathered from national election surveys in Germany, France, and the United States. We relate the results to the existing literature on majority cycles and social homogeneity. We find that these samples rarely display majority cycles, whereas the probability that a sample misrepresents the majority preferences of the underlying population varies dramatically and always exceeds the probability that the sample displays cyclic majority preferences. Social homogeneity plays a fundamental role in the type of Condorcet efficiency investigated here. (shrink)

Many political theorists and philosophers use Condorcet's Jury Theorem to defend democracy. This paper illustrates an uncomfortable implication of Condorcet's Jury Theorem. Realistically, when the conditions of Condorcet’s Jury Theorem hold, even in very high stakes elections, having more than 100,000 citizens vote does no significant good in securing good political outcomes. On the Condorcet model, unless voters enjoy voting, or unless they produce some other value by voting, then the cost to most voters of voting (...) exceeds the expected epistemic benefits to the common good of their casting a vote. Anyone who is committed to democracy on the basis of the Jury Theorem ought also to hold that widespread voting is wasteful, at least unless she can provide some further justification of mass democratic participation. (shrink)

In Ruling Majorities and Reasoning Pluralities, Professor Saul Levmore explores the “division of labor” between the various thresholds of agreement required for collective action—supermajority, simple majority, or plurality rule. His particular emphasis is on the choice between the last two options. To improve our understanding of this choice in various settings, Professor Levmore considers the relationship between two well-known contributions to the study of group decisionmaking, namely, the Condorcet Jury Theorem and the Condorcet Criterion, which have not generally (...) been treated together. This essay explores the relationship between these two insights in the context of judicial decisionmaking. Counterintuitively, the essay demonstrates that while the Condorcet Criterion continues to hold great promise as a tool of decision in en banc appellate courts, the Condorcet Jury Theorem is most appealing in judicial contexts that appear less collegial and thus less like a jury. In contexts in which jurists engage in deliberation and in which they anticipate that their outputs will have precedential effect, the Jury Theorem has little if any role to play. In contrast, the Theorem might prove more useful in evaluating low-level judicial outputs or decisions that otherwise are not expected to be treated as precedent. Thus, common law trial court decisions and civil law court decisions are more likely to be useful benchmarks in a Condorcet Jury Theorem analysis. It is because such courts do not anticipate that their decisions will have the force of precedent that they are more likely to be derived from governing legal texts, and thus more prone to characterizations of accuracy, than are judicial outputs that are driven by policy concerns and are generated with the understanding that they will be treated as precedent. (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)

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)

Many voting rules and, in particular, the plurality rule and Condorcet-consistent voting rules satisfy the simple-majority decisiveness property. The problem implied by such decisiveness, namely, the universal disregard of the preferences of the minority, can be ameliorated by applying unbiased scoring rules such as the classical Borda rule, but such amelioration has a price; it implies erosion in the implementation of the widely accepted majority principle . Furthermore, the problems of majority decisiveness and of the erosion in the majority (...) principle are not necessarily severe when one takes into account the likelihood of their occurrence. This paper focuses on the evaluation of the severity of the two problems, comparing simple-majoritarian voting rules that allow the decisiveness of the smallest majority larger than 1/2 and the classical Borda method of counts. Our analysis culminates in the derivation of the conditions that determine, in terms of the number of alternatives k, the number of voters n, and the relative (subjective) weight assigned to the severity of the two problems, which of these rules is superior in light of the dual majoritarian approach. (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)

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)

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)

Nicolas de Condorcet, 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)