Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

The paper surveys 17 deterministic electoral procedures for selecting one out of two or more candidates, as well as the susceptibility of each of these procedures to various paradoxes. A detailed appendix exemplifies the paradoxes to which each electoral procedure is susceptible. It is concluded that from the perspective of vulnerability to serious paradoxes, as well as in light of additional technical criteria, Copeland’s or Kemeny’s proposed procedures are the most desirable.

A conception of legitimacy is at the core of normative theories of democracy. Many different conceptions of legitimacy have been put forward, either explicitly or implicitly. In this article, I shall first provide a taxonomy of conceptions of legitimacy that can be identified in contemporary democratic theory. The taxonomy covers both aggregative and deliberative democracy. I then argue for a conception of democratic legitimacy that takes the epistemic dimension of public deliberation seriously. In contrast to standard interpretations of epistemic democracy, (...) however, the conception I put forward avoids procedure-independent standards of correctness. Instead, it relies on a procedural social epistemology and defines legitimacy entirely in terms of the fairness of procedures. I call this conception of democratic legitimacy `Pure Epistemic Proceduralism'. I shall argue that it should be preferred over `Rational Epistemic Proceduralism', the conception of legitimacy that underlies the standard interpretation of epistemic democracy. Key Words: legitimacy • deliberative democracy • epistemic democracy • social epistemology. (shrink)

The paper discusses the sense in which the changes undergone by normative economics in the twentieth century can be said to be progressive. A simple criterion is proposed to decide whether a sequence of normative theories is progressive. This criterion is put to use on the historical transition from the new welfare economics to social choice theory. The paper reconstructs this classic case, and eventually concludes that the latter theory was progressive compared with the former. It also briefly comments on (...) the recent developments in normative economics and their connection with the previous two stages. (Published Online April 18 2006) Footnotes1 This paper suspersedes an earlier one entitled “Is There Progress in Normative Economics?” (Mongin 2002). I thank the organizers of the Fourth ESHET Conference (Graz 2000) for the opportunity they gave me to lecture on this topic. Thanks are also due to J. Alexander, K. Arrow, A. Bird, R. Bradley, M. Dascal, W. Gaertner, N. Gravel, D. Hausman, B. Hill, C. Howson, N. McClennen, A. Trannoy, J. Weymark, J. Worrall, two annonymous referees of this journal, and especially the editor M. Fleurbaey, for helpful comments. The editor's suggestions contributed to determine the final orientation of the paper. The author is grateful to the LSE and the Lachmann Foundation for their support at the time when he was writing the initial version. (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)

Many political philosophers have held that democracy has epistemic benefits. Most commonly, this case is made by arguing that democracies are better able to track the truth than other political arrangements. Truth, however, is not the only epistemic good that is politically valuable. A number of other epistemic goods – goods including evidence, intellectual virtue, epistemic justice, and empathetic understanding – can also have political value, and in ways that go beyond the value of truth. In this paper, I will (...) survey those who have argued that democracy can be valuable because of these other epistemic benefits, considering (1) the ways in which these epistemic goods can be of political value and (2) the challenges that democracies face in producing them. (shrink)

Epistemic democracy aims to show, often by appeal to the Condorcet Jury Theorem, that democracy has a high chance of reaching correct decisions. It has been argued that epistemic democracy is compatible with various metaethical accounts, such as moral realism, conventionalism and majoritarianism. This paper casts doubt on that thesis and reveals the following metaethical dilemma: if we adopt moral realism, it is doubtful that voters are, on average, more than 0.5 likely to track moral facts and identify the correct (...) alternative. By contrast, if we adopt conventionalism or majoritarianism, we cannot expect that voters are both competent and sincere. Either way, the conditions for the application of Condorcet’s theorem are not met. (shrink)

Frente a problemas de decisión colectiva de cierta complejidad, distintos métodos de votación pueden considerarse igualmente democráticos. Ante esta situación, argumento que es posible investigar cuáles de esos métodos producen mejores resultados epistémicos sobre asuntos fácticos. Comienzo ilustrando la relación entre democracia y métodos de votación con un sencillo ejemplo. Muestro cómo el uso de modelos idealizados permite descubrir algunas propiedades de los métodos de votación; varios de estos descubrimientos muestran que, frente a problemas de cierta complejidad, no hay una (...) respuesta clara acerca de cuál es el resultado de una elección democrática. Frente a esto, sugiero que deberíamos tomar en cuenta un rasgo epistémico instrumental de varios métodos de votación: su capacidad para generar respuestas correctas ante varias situaciones. Esta intuición ofrece lecciones importantes para el diseño de instituciones electorales. (shrink)

In this paper we discuss James Buchanan’s contribution in the narrow domain of understanding committee voting under majority rule. We then go on to discuss Charles Plott’s seminal experimental work on the topic that sparked a wave of public choice experimental work. However, given Plott’s claims that Buchanan influenced him significantly, it is puzzling that his work with Morris Fiorina explores a question outside of those which Buchanan and Tullock found interesting. We suggest several ways to resolve this tension. Our (...) chapter concludes by discussing a lacuna in the experimental public choice literature in which Buchanan was particularly interested—logrolling, or vote trading. (shrink)

We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (ii) (...) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (shrink)

Taken as a model for how groups should make collective judgments and decisions, the ideal of deliberative democracy is inherently ambiguous. Consider the idealised case where it is agreed on all sides that a certain conclusion should be endorsed if and only if certain premises are admitted. Does deliberative democracy recommend that members of the group debate the premises and then individually vote, in the light of that debate, on whether or not to support the conclusion? Or does it recommend (...) that members individually vote on the premises, and then let their commitment to the conclusion be settled by whether or not the group endorses the required premises? Deliberative-democratic theory has not addressed this issue, and this is a problem. The discursive dilemma of my title--a generalisation of the doctrinal paradox from analytical jurisprudence--shows that the procedures distinguished can come apart. Thus deliberative democrats must make up their minds on where they stand in relation to the issue; they cannot sit on the fence. This paper is an attempt to address the issue and look at the grounds on which it may be resolved. (shrink)

Property-owning democracies combine the regulative and redistributive functions of the welfare state with the governmental aim of ensuring that wealth and capital are widely dispersed. John Rawls, political philosophy’s most famous property-owning democrat, argued that property-owning democracy was one of two regime types that best realized his two principles of justice, though he was notoriously vague about how a property-owning democracy’s institutions are meant to realize his principles. To compensate for this deficiency, a number of Rawlsian political philosophers have tried (...) to add institutional and policy content to the idea. While their efforts have advanced the discussion, few have criticized the soundness of these attempts. This article attempts to fill the void. I claim that, in comparison to welfare-state capitalism, property-owning democracy is both prohibitively impractical and unjust on Rawlsian grounds. I first argue that property-owning democracy is economically ineffective. Even granting the assumptions of Rawlsian ideal theory, property-owning democracies generate bad incentives and face severe information problems in comparison to more market-friendly welfare states. Further, in nonideal theory the motivations of political officials and citizens will likely be corrupted by the temptation to abuse the awesome state power at their disposal. Second, I argue that property-owning democracy is unjust relative to welfare-state capitalism. The three principles used to defend property-owning democracy—the difference principle, the principle of fair equality of opportunity and the “political liberty” proviso—do not vindicate property-owning democracy and may even prohibit it. Welfare-state capitalism does much better. (shrink)

Most models of the formation of political coalitions use either Euclidean spaces or rely purely on game theory. This limits their applicability. In this article, a single model is presented which is more broadly applicable. In principle any kind of set can be used as a policy space. The model is also able to incorporate different kinds of party motivations: both rent-seeking and idealism. The model uses party preferences and power to identify stable coalitions and predict government policy as well (...) as to indicate which member of the opposition will be able to break up the governing coalition if no stable coalition exists. In the latter case it will also indicate on which issue the government is likely to split. Parties may have preferences over issues such as the composition of cabinet and/or the governing coalition as well as the more traditional issues of government formation. The model also provides a rationale for log-rolling. (shrink)

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This theorem rehabilitates the importance of deliberation (...) and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (shrink)

Public deliberation has been defended as a rational and noncoercive way to overcome paradoxical results from democratic voting, by promoting consensus on the available alternatives on the political agenda. Some critics have argued that full consensus is too demanding and inimical to pluralism and have pointed out that single-peakedness, a much less stringent condition, is sufficient to overcome voting paradoxes. According to these accounts, deliberation can induce single-peakedness through the creation of a ‘meta-agreement’, that is, agreement on the dimension according (...) to which the issues at stake are ‘conceptualized’. We argue here that once all the conditions needed for deliberation to bring about single-peakedness through meta-agreement are unpacked and made explicit, meta-agreement turns out to be a highly demanding condition, and one that is very inhospitable to pluralism. (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)

This paper is a critique of Kenneth Arrow's thesis concerning the logical impossibility of a constitution. I argue that one of the premises of Arrow's proof, that of the transitivity of indifference, is untenable. Several concepts of preference are introduced and counter-instances are offered to the transitivity of indifference defined along the standard lines in terms of these concepts. Alternate analyses of indifference in terms of preference are considered, and it is shown that these do not serve Arrow's purposes either. (...) Finally, it is argued that in the single special case in which indifference could plausibly be held to be transitive, Arrow's thesis is innocuous. (shrink)

It is well-known that different social choice procedures often result in different choice sets. The article focuses on how often this is likely to happen in impartial cultures. The focus is on Borda count, plurality method, max-min method and Copeland's procedure. The probabilities of Condorcet violations of the Borda count and plurality method are also reported. Although blatantly false as a descriptive hypothesis, the impartial culture assumption can be given an interpretation which makes the results obtained in impartial cultures particularly (...) significant, viz. the probabilities of deviations in choice sets indicate how far apart are the intuitions underlying various choice procedures. -/- . (shrink)

This article analyzes the problem of preference imputation in rational choice political science. I argue against the well-established practice in political science of assuming selfish preferences for purely methodological reasons, regardless of its empirical plausibility (this I call a preference for selfish preferences). Real motivations are overlooked due to difficulties of imputing preferences to agents in a non-arbitrary way in the political realm. I compare the problem of preference imputation in economic and political markets, and I show the harmful consequences (...) of the preference for selfish preferences in the field of collective action. Key Words: rational choice theory • preference • functionalism • collective action. (shrink)

In this paper I prove a theorem which is similar to Arrow's famous impossibility theorem. I show that no social welfare function can be both minimally majoritarian and also independent of irrelevant alternatives. My condition of minimal majoritarianism is substantially weaker than simple majority rule.

The main purpose of this paper is to compute the theoretical likelihood of some electoral outcomes under the impartial anonymous culture in four-candidate elections by using the last versions of software like LattE or Normaliz. By comparison with the three-candidate case, our results allow to analyze the impact of the number of candidates on the occurrence of these voting outcomes.

This paper studies the welfare consequences of strategic voting in two commonly used parliamentary agendas by comparing the average utilities obtained in simulated voting under two behavioural assumptions: expected utility maximising behaviour and sincere behaviour. The average utility obtained in simulations is higher with expected utility maximising behaviour than with sincere voting behaviour under a broad range of assumptions. Strategic voting increases welfare particularly if the distribution of preference intensities correlates with voter types.

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 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)

Taken as a model for how groups should make collective judgments and decisions, the ideal of deliberative democracy is inherently ambiguous. Consider the idealised case where it is agreed on all sides that a certain conclusion should be endorsed if and only if certain premises are admitted. Does deliberative democracy recommend that members of the group debate the premises and then individually vote, in the light of that debate, on whether or not to support the conclusion? Or does it recommend (...) that members individually vote on the premises, and then let their commitment to the conclusion be settled by whether or not the group endorses the required premises? Is deliberative democracy to enforce the discipline of reason at the individual level, as in the first possibility, or at the collective level, as in the second? (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)

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 build a multiple hierarchical model of a representative democracy in which citizens elect ward representatives, ward representatives elect county representatives, county representatives elect state representatives, and state representatives elect a prime minister. We use our model to show that the policy determined by the final representative can become more extreme as the number of hierarchical levels increases as a result of increased opportunities for gerrymandering. Thus, a sufficiently large number of voters provide a district maker an advantage, enabling her (...) to implement her favorite policy. (shrink)

The majority rule has caught much attention in recent debate about the aggregation of judgments. But its role in finding the truth is limited. A majority of expert judgments is not necessarily authoritative, even if all experts are equally competent, if they make their judgments independently of each other, and if all the judgments are based on the same source of (good) evidence. In this paper I demonstrate this limitation by presenting a simple counterexample and a related general result. I (...) pave the way for this argument by introducing a Bayesian model of evidence and expert judgment in order to give a precise account of the basic problem. (shrink)

Events in both Eastern Europe and the former USSR illustrate the intimate connection between economic and political processes. Those events also remind us that political and economic institutions are human creations, and that when those institutions are poorly designed, political-economic failure is a direct consequence. It is axiomatic, then, that the transition to stable and prosperous societies in those former Communist states requires careful attention to the design and implementation of democratic institutions.

In certain judgmental situations where a “correct” decision is presumed to exist, optimal decision making requires evaluation of the decision-makers’ capabilities and the selection of the appropriate aggregation rule. The major and so far unresolved difficulty is the former necessity. This article presents the optimal aggregation rule that simultaneously satisfies these two interdependent necessary requirements. In our setting, some record of the voters’ past decisions is available, but the correct decisions are not known. We observe that any arbitrary evaluation of (...) the decision-makers’ capabilities as probabilities yields some optimal aggregation rule that, in turn, yields a maximum-likelihood estimation of decisional skills. Thus, a skill-evaluation equilibrium can be defined as an evaluation of decisional skills that yields itself as a maximum-likelihood estimation of decisional skills. We show that such equilibrium exists and offer a procedure for finding one. The obtained equilibrium is locally optimal and is shown empirically to generally be globally optimal in terms of the correctness of the resulting collective decisions. Interestingly, under minimally competent (almost symmetric) skill distributions that allow unskilled decision makers, the optimal rule considerably outperforms the common simple majority rule (SMR). Furthermore, a sufficient record of past decisions ensures that the collective probability of making a correct decision converges to 1, as opposed to accuracy of about 0.7 under SMR. Our proposed optimal voting procedure relaxes the fundamental (and sometimes unrealistic) assumptions in Condorcet’s celebrated theorem and its extensions, such as sufficiently high decision-making quality, skill homogeneity or existence of a sufficiently large group of decision makers. (shrink)

In a highly influential work, List and Pettit (Group Agency: The Possibility, Design, and Status of Corporate Agents, Oxford University Press, 2011) draw upon the theory of judgement aggregation to offer an argument for the existence of nonreductive group agents; they also suggest that nonreductive group agency is a widespread phenomenon. In this paper, we argue for the following two claims. First, that the axioms they consider cannot naturally be interpreted as either descriptive characterisations or normative constraints upon group judgements, (...) in general. This makes it unclear how the List and Pettit argument is to apply to real world group behaviour. Second, by examining empirical data about how group judgements are made by a powerful international regulatory board, we show how each of the List and Pettit axioms can be violated in ways which are straightforwardly explicable at the level of the individual. This suggests that group agency may best be understood as a pluralistic phenomenon, where close inspection of the dynamics of intragroup deliberation can reveal that what prima facie appears to be a nonreductive group agent is, in fact, reducible. (shrink)

In a recent paper (Okasha, Mind 120:83–115, 2011), Samir Okasha uses Arrow’s theorem to raise a challenge for the rationality of theory choice. He argues that, as soon as one accepts the plausibility of the assumptions leading to Arrow’s theorem, one is compelled to conclude that there are no adequate theory choice algorithms. Okasha offers a partial way out of this predicament by diagnosing the source of Arrow’s theorem and using his diagnosis to deploy an approach that circumvents it. In (...) this paper I explain why, although Okasha is right to emphasise that Arrow’s result is the effect of an informational problem, he is not right to locate this problem at the level of the informational input of a theory choice rule. Once the informational problem is correctly located, Arrow’s theorem may be dismissed as a problem. (shrink)

We identify a new monotonicity condition (called cover monotonicity) for tournament solutions which allows a discrimination among main tournament solutions: The top-cycle, the iterated uncovered set, the minimal covering set, and the bipartisan set are cover monotonic while the uncovered set, Banks set, the Copeland rule, and the Slater rule fail to be so. As cover monotonic tournament solutions induce social choice rules which are Nash implementable in certain non-standard frameworks (such as those set by Bochet and Maniquet (CORE Discussion (...) Paper No. 2006/84, 2006) or Özkal-Sanver and Sanver (Social Choice and Welfare, 26(3), 607–623, 2006), the discrimination generated by cover monotonicity becomes particularly notable when implementability is a concern. (shrink)

Among the many sorts of problems encountered in decision theory, allocation problems occupy a central position. Such problems call for the assignment of a nonnegative real number to each member of a finite set of entities, in such a way that the values so assigned sum to some fixed positive real number s. Familiar cases include the problem of specifying a probability mass function on a countable set of possible states of the world, and the distribution of a certain sum (...) of money, or other resource, among various enterprises. In determining an s-allocation it is common to solicit the opinions of more than one individual, which leads immediately to the question of how to aggregate their typically differing allocations into a single “consensual” allocation. Guided by the traditions of social choice theory decision theorists have taken an axiomatic approach to determining acceptable methods of allocation aggregation. In such approaches so-called “independence” conditions have been ubiquitous. Such conditions dictate that the consensual allocation assigned to each entity should depend only on the allocations assigned by individuals to that entity, taking no account of the allocations that they assign to any other entities. While there are reasons beyond mere simplicity for subjecting allocation aggregation to independence, this radically anti-holistic stricture has frequently proved to severely limit the set of acceptable aggregation methods. As we show in what follows, the limitations are particularly acute in the case of three or more entities which must be assigned nonnegative values summing to some fixed positive number s. For if the set V⊆[0,s] of values that may be assigned to these entities satisfies some simple closure conditions and Vis finite, then independence allows only for dictatorial or imposed aggregation. This theorem builds on and extends a theorem of Bradley and Wagner and, when V={0,1}, yields as a corollary an impossibility theorem of Dietrich on judgment aggregation. (shrink)

The net structure of the spatial theory of elections is investigated and described in the format of structuralism. Three new kinds of intertheoretical relations typical for social theory are identified and defined. The historical development of spatial theory as expressed by specializations and other intertheoretic relations is found to be in a sense 'inverse' to that of theories in the natural sciences. The development begins with a 'most special' case.