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)

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 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)

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)

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)

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.

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)

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.

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)

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)

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)

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)

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)

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)

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)

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)

Despite a consensus across the political spectrum that the problem of the chronically uninsured is in dire need of solution, little progress has been made. Public spending goes to topping up coverage for the elderly, already heavily subsidized under Medicare, or helping people temporarily without insurance because of international trade dislocations, so that it is clear that something is lacking in the case for significantly reducing the number of uninsured persons. In this paper I suggest that there have been two (...) missing ingredients: a strategy for breaking the political deadlock around this issue, and information about the benefits of coverage sufficient to persuade kindly but skeptical taxpayers that they should be willing to pay to help solve this problem. (shrink)

Despite a consensus across the political spectrum that the problem of the chronically uninsured is in dire need of solution, little progress has heen made. Public spending goes to topping up coverage for the elderly, already heavily subsidized under Medicare, or helping people temporarily without insurance because of international trade dislocations, so that it is clear that something is lacking in the case for significantly reducing the number of uninsured persons. In this paper I suggest that there have been two (...) missing ingredients: a strategy for breaking the political deadlock around this issue, and information about the benefits of coverage sufficient to persuade kindly but skeptical taxpayers that they should be willing to pay to help solve this problem.This article begins with a discussion of these two problems. It then outlines a strategy based on income-related or conditioned refundable tax credits for private and public insurance, coupled with a plan to assemble persuasive information that may move things forward. (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)

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)

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)

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.

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)

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)

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.

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)

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)

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)

In voting theory, monotonicity is the axiom that an improvement in the ranking of a candidate by voters cannot cause a candidate who would otherwise win to lose. The participation axiom states that the sincere report of a voter’s preferences cannot cause an outcome that the voter regards as less attractive than the one that would result from the voter’s non-participation. This article identifies three binary distinctions in the types of circumstances in which failures of monotonicity or participation can occur. (...) Two of the three distinctions apply to monotonicity, while one of those and the third apply to participation. The distinction that is unique to monotonicity is whether the voters whose changed rankings demonstrate non-monotonicity are better off or worse off. The distinction that is unique to participation is whether the marginally participating voter causes his first choice to lose or his last choice to win. The overlapping distinction is whether the profile of voters’ rankings has a Condorcet winner or a cycle at the top. This article traces the occurrence of all of the resulting combination of characteristics in the voting methods that can exhibit failures of monotonicity. (shrink)