Classical debates, recently rejoined, rage over the question of whether we want our political outcomes to be right or whether we want them to be fair. Democracy can be (and has been) justified in either way, or both at once. For epistemic democrats, the aim of democracy is to "track the truth."1 For them, democracy is more desirable than alternative forms of decision-making because, and insofar as, it does that. One democratic decision rule is more desirable than another according to (...) that same standard, so far as epistemic democrats are concerned.2 For procedural democrats, the aim of democracy is instead to embody certain procedural virtues.3 Procedural democrats are divided among themselves over what those virtues might be, as well as over which procedures best embody them. But all procedural democrats agree on the one central point.. (shrink)
Suppose that the members of a certain group each hold a rational set of judgments on some interconnected questions. And imagine that the group itself now has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem (...) that that difficulty illustrates. Our paper describes this impossibility result and provides an exploration of its significance. The result naturally invites comparison with Kenneth Arrow's famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002). The paper is in four sections. The first section documents the need for various groups to aggregate the sets of judgments held by members on certain issues; the second presents the discursive paradox that arises.. (shrink)
Are companies, churches, and states genuine agents? Or are they just collections of individuals that give a misleading impression of unity? This question is important, since the answer dictates how we should explain the behaviour of these entities and whether we should treat them as responsible and accountable on the model of individual agents. Group Agency offers a new approach to that question and is relevant, therefore, to a range of fields from philosophy to law, politics, and the social sciences. (...) Christian List and Philip Pettit argue that there really are group or corporate agents, over and above the individual agents who compose them, and that a proper approach to the social sciences, law, morality, and politics must take account of this fact. Unlike some earlier defences of group agency, their account is entirely unmysterious in character and, despite not being technically difficult, is grounded in cutting-edge work in social choice theory, economics, and philosophy. (shrink)
The ``doctrinal paradox'' or ``discursive dilemma'' shows that propositionwise majority voting over the judgments held by multiple individuals on some interconnected propositions can lead to inconsistent collective judgments on these propositions. List and Pettit (2002) have proved that this paradox illustrates a more general impossibility theorem showing that there exists no aggregation procedure that generally produces consistent collective judgments and satisfies certain minimal conditions. Although the paradox and the theorem concern the aggregation of judgments rather than preferences, they invite (...) comparison with two established results on the aggregation of preferences: the Condorcet paradox and Arrow's impossibility theorem. We may ask whether the new impossibility theorem is a special case of Arrow's theorem, or whether there are interesting disanalogies between the two results. In this paper, we compare the two theorems, and show that they are not straightforward corollaries of each other. We further suggest that, while the framework of preference aggregation can be mapped into the framework of judgment aggregation, there exists no obvious reverse mapping. Finally, we address one particular minimal condition that is used in both theorems – an independence condition – and suggest that this condition points towards a unifying property underlying both impossibility results. (shrink)
In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, nondictatorship and propositionwise independence. But it is only partially known for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the (...) most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006) and Dietrich and List (2007a). (shrink)
In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, nondictatorship and propositionwise independence. But it is only partially known for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the (...) most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006) and Dietrich and List (2007a). (shrink)
Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It offers few resources to describe some prior beliefs as rational or well-justified, and others as irrational or unreasonable. A different strand of epistemology takes the central epistemological question to be not how to change one’s beliefs in light of new evidence, but what reasons justify a given (...) set of beliefs in the first place. We offer an account of rational belief formation that closes some of the gap between Bayesianism and its reason-based alternative, formalizing the idea that an agent can have reasons for his or her (prior) beliefs, in addition to evidence or information in the ordinary Bayesian sense. Our analysis of reasons for belief is part of a larger programme of research on the role of reasons in rational agency (Dietrich and List, Nous, 2012a, in press; Int J Game Theory, 2012b, in press). (shrink)
This item was published as 'Appendix 3: An Implication of the k-option Condorcet jury mechanism for the probability of cycles' in List and Goodin (2001) http://eprints.lse.ac.uk/705/. Standard results suggest that the probability of cycles should increase as the number of options increases and also as the number of individuals increases. These results are, however, premised on a so-called "impartial culture" assumption: any logically possible preference ordering is assumed to be as likely to be held by an individual as any (...) other. The present chapter shows, in the three-option case, that given suitably systematic, however slight, deviations from an impartial culture situation, the probability of a cycle converges either to zero (more typically) or to one (less typically) as the number of individuals increases. (shrink)
In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which there (...) are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a). (shrink)
In this note, I correct an error in List (2003). I warmly thank Ron Holzman for drawing my attention to this error, and Franz Dietrich for giving me some key insights that have led to the present correction, particularly the formulation of assumption (a*) below. Theorem 2 (speci…cally, the claim that (i) implies (ii) and the associated Proposition 2) in List (2003) requires an additional assumption on the set X of propositions under consideration (the agenda). Let me use (...) the de…nitions and notation from List (2003). Also, de…ne a set of propositions to be satis…able if some truth-value assignment makes all its members true, and, for each Y X, de…ne Y : := f: : 2Yg. In List (2003), I assumed that (a) X contains at least two distinct atomic propositions P; Q and their conjunction (P ^ Q), and (b) X contains proposition-negation pairs (i.e. if 2 X, then : 2 X, where :: is identi…ed with ). While assumption (b) is correct as stated, Theorem 2 requires assumption (a*) instead of (a). (shrink)
It is often argued that higher-level special-science properties cannot be causally efficacious since the lower-level physical properties on which they supervene are doing all the causal work. This claim is usually derived from an exclusion principle stating that if a higher-level property F supervenes on a physical property F* that is causally sufficient for a property G, then F cannot cause G. We employ an account of causation as difference-making to show that the truth or falsity of this principle is (...) a contingent matter and derive necessary and sufficient conditions under which a version of it holds. We argue that one important instance of the principle, far from undermining non-reductive physicalism, actually supports the causal autonomy of certain higher-level properties. (shrink)
Can groups be rational agents over and above their individual members? We argue that group agents are distinguished by their capacity to mimic the way in which individual agents act and that this capacity must 'supervene' on the group members' contributions. But what is the nature of this supervenience relation? Focusing on group judgments, we argue that, for a group to be rational, its judgment on a particular proposition cannot generally be a function of the members' individual judgments on that (...) proposition. Rather, it must be a function of their individual sets of judgments across many propositions. So, knowing what the group members individually think about some proposition does not generally tell us how the group collectively adjudicates that proposition: the supervenience relation must be 'set-wise', not 'proposition-wise'. Our account preserves the individualistic view that group agency is nothing mysterious, but also suggests that a group agent may hold judgments that are not directly continuous with its members' corresponding individual judgments. (shrink)
On one very simple formulation, the exclusion argument against dualism starts from the assertion that the following theses are inconsistent:
(1) Being in pain causes me to wince. (2) Being in phys1 causes me to wince. (3) Being in pain is distinct from being in phys. (4) If being in pain causes me to wince, nothing distinct from being in pain
The systems studied in the special sciences are often said to be causally autonomous, in the sense that their higher-level properties have causal powers that are independent of those of their more basic physical properties. This view was espoused by the British emergentists, who claimed that systems achieving a certain level of organizational complexity have distinctive causal powers that emerge from their constituent elements but do not derive from them.2 More recently, non-reductive physicalists have espoused a similar view about the (...) causal autonomy of specialscience properties. They argue that since these properties can typically have multiple physical realizations, they are not identical to physical properties, and further they possess causal powers that differ from those of their physical realizers.3 Despite the orthodoxy of this view, it is hard to find a clear exposition of its meaning or a defence of it in terms of a well-motivated account of causation. In this paper, we aim to address this gap in the literature by clarifying what is implied by the doctrine of the causal autonomy of special-science properties and by defending the doctrine using a prominent theory of causation from the philosophy of science. The theory of causation we employ is a simplified version of an “interventionist” theory advanced by James Woodward (2003, forthcoming a, b), according to which a cause makes a counterfactual difference to its effects. In terms of this theory, it is possible to show that a special-science property can make a difference to some effect while the physical property that realizes it does not. Although other philosophers have also used counterfactual analyses of causation to argue for the causal autonomy of special-science properties,4 the theory of causation we employ is able to establish this with an unprecedented level of precision.. (shrink)
There is a surprising disconnect between formal rational choice theory and philosophical work on reasons. The one is silent on the role of reasons in rational choices, the other rarely engages with the formal models of decision problems used by social scientists. To bridge this gap, we propose a new, reason-based theory of rational choice. At its core is an account of preference formation, according to which an agent's preferences are determined by his or her motivating reasons, together with a (...) 'weighing relation' between different combinations of reasons. By explaining how someone's preferences may vary with changes in his or her motivating reasons, our theory illuminates the relationship between deliberation about reasons and rational choices. Although primarily positive, the theory can also help us think about how those preferences and choices ought to respond to normative reasons. (shrink)
Distributed cognition refers to processes which are (i) cognitive and (ii) distributed across multiple agents or devices rather than performed by a single agent. Distributed cognition has attracted interest in several fields ranging from sociology and law to computer science and the philosophy of science. In this paper, I discuss distributed cognition from a social-choice-theoretic perspective. Drawing on models of judgment aggregation, I address two questions. First, how can we model a group of individuals as a distributed cognitive system? Second, (...) can a group acting as a distributed cognitive system be ‘rational’ and ‘track the truth’ in the outputs it produces? I argue that a group’s performance as a distributed cognitive system depends on its ‘aggregation procedure’ – its mechanism for aggregating the group members’ inputs into collective outputs – and I investigate the properties of an aggregation procedure that matter. (shrink)
The aim of this article is to introduce the theory of judgment aggregation, a growing interdisciplinary research area. The theory addresses the following question: How can a group of individuals make consistent collective judgments on a given set of propositions on the basis of the group members' individual judgments on them? I begin by explaining the observation that initially sparked the interest in judgment aggregation, the so-called "doctinal" and "discursive paradoxes". I then introduce the basic formal model of judgment aggregation, (...) which allows me to present some illustrative variants of a generic impossibility result. I subsequently turn to the question of how this impossibility result can be avoided, going through several possible escape routes. Finally, I relate the theory of judgment aggregation to other branches of aggregation theory. Rather than offering a comprehensive survey of the theory of judgment aggregation, I hope to introduce the theory in a succinct and pedagogical way, providing an illustrative rather than exhaustive coverage of some of its key ideas and results. (shrink)
At the core of republican thought, on Philip Pettit’s account, lies the conception of freedom as non-domination, as opposed to freedom as noninterference in the liberal sense. I revisit the distinction between liberal and republican freedom and argue that republican freedom incorporates a particular rule-of-law requirement, whereas liberal freedom does not. Liberals may also endorse such a requirement, but not as part of their conception of freedom itself. I offer a formal analysis of this rule-of-law requirement and compare liberal and (...) republican freedom on its basis. While I agree with Pettit that republican freedom has broader implications than liberal freedom, I conclude that we face a trade-off between two dimensions of freedom (scope and robustness) and that it is harder for republicans to solve that trade-off than it is for liberals. Key Words: freedom • republicanism • liberalism • noninterference • non-domination • rule of law • robustness • liberal paradox. (shrink)
How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...) Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)
In this paper, we present a simple axiomatic justification for indifference before opening, avoiding any expectation reasoning, which is often considered problematic in infinite cases. Although the two-envelope paradox assumes an expectation-maximizing agent, we show that analogous paradoxes arise for agents using difierent decision principles such as maximin and maximax, and that our justification for indifierence before opening applies here too.
Political theorists have offered many accounts of collective decision-making under pluralism. I discuss a key dimension on which such accounts differ: the importance assigned not only to the choices made but also to the reasons underlying those choices. On that dimension, different accounts lie in between two extremes. The ‘minimal liberal account’ holds that collective decisions should be made only on practical actions or policies and that underlying reasons should be kept private. The ‘comprehensive deliberative account’ stresses the importance of (...) giving reasons for collective decisions, where such reasons should also be collectively decided. I compare these two accounts on the basis of a formal model developed in the growing literature on the ‘discursive dilemma’ and ‘judgment aggregation’ and address several questions: What is the trade-off between the (minimal liberal) demand for reaching agreement on outcomes and the (comprehensive deliberative) demand for reason-giving? How large should the ‘sphere of public reason’ be? When do the decision procedures suggested by the two accounts agree and when not? How good are these procedures at truthtracking on factual matters? What strategic incentives do they generate for decision-makers? My discussion identifies what is at stake in the choice between minimal liberal and comprehensive deliberative accounts of collective decisionmaking, and sheds light not only on these two ideal-typical accounts themselves, but also on many characteristics that intermediate accounts share with them. (shrink)
Pettit (2006) argues that deferring to majority testimony is not generally rational: it may lead to inconsistent beliefs. He suggests that “another ... approach will do better”: deferring to supermajority testimony. But this approach may also lead to inconsistencies. Here I identify the conditions under which deference to supermajority testimony ensures consistency, and those under which it does not. I also introduce the new concept of ‘consistency of degree k’, which is weaker than full consistency by ruling out only ‘blatant’ (...) inconsistencies in an agent’s beliefs while permitting less blatant ones, and show that, while supermajoritarian deference often fails to ensure full consistency, it is a route to consistency in this weaker sense. (shrink)
Although controversy concerning the morality of hunting is generally focused on sport hunting, sport hunting itself is not a morally distinctive kind of hunting. The understanding of hunting in general needs to be supplemented with reference to the goods which hunting seeks. Attempts to draw a moral distinction between sport and subsistence hunting are inadequate and historically suspect. Likewise, trying to establish sport hunting as morally distinctive by emphasizing its similarities to other sports also fails. Nevertheless, there are standards accepted (...) by hunters that support ethical judgments about hunting. Ethical hunting requires reentry into a community of nonhuman beings governed by ecology and evolution, not human constructs, the development of virtues such as tenacity, courage, moderation, and discipline, and the achievement of a heightened respect for the biotic community in which the hunt takes place. By means of such standards, we may yet be able to determine what good hunting is even though we are unable to determine whether sport hunting is good. (shrink)
Philip Pettit (2001) has suggested that there are parallels between his republican account of freedom and Amartya Sen's (1970) account of freedom as decisive preference. In this paper, I discuss these parallels from a social-choice-theoretic perspective. I sketch a formalization of republican freedom and argue that republican freedom is formally very similar to freedom as defined in Sen's “minimal liberalism” condition. In consequence, the republican account of freedom is vulnerable to a version of Sen's liberal paradox, an inconsistency between universal (...) domain, freedom, and the weak Pareto principle. I argue that some standard escape routes from the liberal paradox – those via domain restriction – are not easily available to the republican. I suggest that republicans need to take seriously the challenge of the impossibility of a Paretian republican. Footnotes1 I am grateful to Luc Bovens, Geoffrey Brennan, Keith Dowding, Philip Pettit, and Wlodek Rabinowicz for very helpful comments and discussion. (shrink)
Suppose the members of a group (e.g., committee, jury, expert panel) each form a judgment on which worlds in a given set are possible, subject to the constraint that at least one world is possible but not all are. The group seeks to aggregate these individual judgments into a collective judgment, subject to the same constraint. I show that no judgment aggregation rule can solve this problem in accordance with three conditions: “unanimity,” “independence” and “non-dictatorship,” Although the result is a (...) variant of an existing theorem on “group identification” (Kasher and Rubinstein, Logique et Analyse 160:385–395, 1997), the aggregation of judgments on which worlds are possible (or permissible, desirable, etc.) appears not to have been studied yet. The result challenges us to take a stance on which of its conditions to relax. (shrink)
In a recent paper on ‘The Many as One’, Lewis A. Kornhauser and Lawrence G. Sager look at an issue that we take to be of great importance in political theory. How far should groups in public life try to speak with one voice, and act with one mind? How far should public groups try to display what Ronald Dworkin calls integrity? We do not expect the many on the market to be integrated in this sense. But should we expect (...) integration among the many in the legislature, for example, or among the many on the courts? We agree with Kornhauser and Sager about a number of their claims but think that they miss out on important detail and do not achieve a fully general perspective on the issues raised. Our own contribution is in three sections. We address, first, the nature of the integrity challenge; second, the range of cases in which the challenge arises; and third, the question of whether public groups should be designed and required to meet that challenge. (shrink)
While a large social-choice-theoretic literature discusses the aggregation of individual judgments into collective ones, there is relatively little formal work on the transformation of individual judgments in group deliberation. I develop a model of judgment transformation and prove a baseline impossibility result: Any judgment transformation function satisfying some initially plausible condition is the identity function, under which no opinion change occurs. I identify escape routes from this impossibility result and argue that successful group deliberation must be ‘holistic’: individuals cannot generally (...) revise their judgments on a proposition based on judgments on that proposition alone but must take other propositions into account too. I discuss the significance of these findings for democratic theory. (shrink)
On the orthodox view in economics, interpersonal comparisons of utilityare not empirically meaningful, and ``hence'' impossible. To reassess this view, this paper draws onthe parallels between the problem of interpersonal comparisons of utility and the problem of translation of linguisticmeaning, as explored by Quine. I discuss several cases of what the empirical evidence for interpersonal comparisonsof utility might be and show that, even on the strongest of these, interpersonal comparisons are empiricallyunderdetermined and, if we also deny any appropriate truth of (...) the matter, indeterminate. However, the underdeterminationcan be broken non-arbitrarily (though not purely empirically) if (i) we assign normative significance to certainstates of affairs or (ii) we posit a fixed connection between certain empirically observable proxies and utility.I conclude that, even if interpersonal comparisons are not empirically meaningful, they are not in principle impossible. (shrink)
I argue that sport hunting is a right thing according to Leopold’s land ethic. First, I argue that what Leopold means by a “thing” (“A thing is right . . .”) is not a human action, as is generally assumed, but rather a practice of conservation that is an activity connecting humans to the land. Such an “outdoor” activity emphasizes internal rewards and the achievement of excellence according to standards which at least partially define the activity. To say that hunting (...) is a right thing is to say that the practice of sport hunting tends in the direction of the land ethic. The actions of individual hunters are judged to be ethical or not by the standards of the practice; these standards are in turn evaluated by the precepts of the land ethic. Second, I discuss how the practical standards are evaluated. I argue that the concepts of integrity, stability, and beauty, contrary to some interpretations, are not inherent values of the biotic community, but rather labels carefully chosen by Leopold as three conduits for the ecological conscience necessary for the land ethic: the ethical, the ecological, and the aesthetic. I show that Leopold uses this model for his own evaluation of the practice of hunting as well as his evaluation of other practices of conservation. Thus, to ask about whether sport hunting is a right thing is to ask about the historical evolution of the standards of this practice and, of equal importance, about the future direction of these standards with regard to the land ethic. (shrink)
How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to …lling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...) Our …rst theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the speci…c kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)
Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a (...) shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)
A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits a framing effect if (...) and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. Footnotes1 We are grateful to Luc Bovens, Robin Cubitt and three anonymous reviewers for Economics and Philosophy for very helpful comments and suggestions. (shrink)
While a large social-choice-theoretic literature discusses the aggregation of individual judgments into collective ones, there is much less formal work on the transformation of judgments in group communication. I develop a model of judgment transformation and prove a baseline impossibility theorem: Any judgment transformation function satisfying some initially plausible conditions is the identity function, under which no opinion change occurs. I identify escape routes from this impossibility and argue that the kind of group communication envisaged by deliberative democats must be (...) "holistic": It must focus on webs of connected propositions, not on one proposition at a time, which echoes the Duhem-Quine "holism thesis" on scientific theory testing. My approach provides a map of the logical space in which different possible group communication processes are located. (shrink)
that a defendant is guilty (a patient has condition C), and the evidence E that a majority of h out of n independent jurors (diagnostic tests) have voted for H, and a minority of k n – h against H. How likely is the majority verdict to be correct? By Condorcet's formula, the probability that H is true given E depends only on each juror's competence and on the absolute margin between the majority and the minority h – k, but (...) neither on the number n, nor on the proportion h/n. This paper reassesses that result and explores its implications. First, using the classical Condorcet jury model, I derive a more general version of Condorcet's formula, confirming the significance of the absolute margin, but showing that the probability that H is true given E depends also on an additional parameter: the prior probability that H is true. Second, I show that a related result holds when we consider not the degree of belief we attach to H given E, but the degree of support E gives to H. Third, I address the implications for the definition of special majority voting, a procedure used to capture the asymmetry between false positive and false negative decisions. I argue that the standard definition of special majority voting in terms of a required proportion of the jury is epistemically questionable, and that the classical Condorcet jury model leads to an alternative definition in terms of a required absolute margin between the majority and the minority. Finally, I show that the results on the significance of the absolute margin can be resisted if the so-called assumption of symmetrical juror competence is relaxed. Introduction The classical Condorcet jury model and the Condorcet jury theorem The significance of the absolute margin for the degree of belief we attach to the hypothesis given the evidence The significance of the absolute margin for the degree of support the evidence gives to the hypothesis An implication for the definition of special majority voting 5.1 Making positive decisions if and only if the truth of the hypothesis is beyond any reasonable doubt 5.2 Tracking the truth in the limit 5.3 Summary The jury model without the assumption of symmetrical competence Concluding remarks. (shrink)
How can di¤erent individuals’probability assignments to some events be aggregated into a collective probability assignment? Although there are several classic results on this problem, they all assume that the ‘agenda’ of relevant events forms a -algebra, an overly demanding assumption for many practical applications. We drop this assumption and explore probabilistic opinion pooling on general agendas. Our main theorems characterize linear pooling and neutral pooling for large classes of agendas, with standard results as special cases.
One of the hallmark themes of Karl Popper’s approach to the social sciences was the insistence that when social scientists are members of the society they study, then they are liable to affect that society. In particular, they are liable to affect it in such a way that the claims they make lose their validity. “The interaction between the scientist’s pronouncements and social life almost invariably creates situations in which we have not only to consider the truth of such pronouncements, (...) but also their actual influence on future developments. The social scientist may be striving to find the truth; but, at the same time, he must always be exerting a definite influence upon society. The very fact that his pronouncements do exert an influence destroys their objectivity.” (Popper 1963. (shrink)
The land ethic of Aldo Leopold has increasingly received attention as an example of an environmental virtue ethic. However, an important remaining question is how to cultivate and transmit environmental virtues. The answer to this question can be found in the pursuit of wild leisure. The classical view of leisure primarily as articulated in Aristotle’s Politics provides a good starting point for an examination of wild leisure. Leopold thought wild leisure was important and associated it with his land ethic. Leopold’s (...) view of wild leisure focused on the role of perception in ecological education and the habituation of virtue. The classical virtue of moderation when habituated by wild leisure becomes the central virtue required by an ecological conscience. Wild leisure educates just those intellectual and scientific virtues necessary for refined perception and prudence. These virtues provide connections between good citizenship and land citizenship. (shrink)
Free speech, its many definitions, and efforts by special interest groups to assure their message is distributed have led to sharp conflict and rising tensions, particularly in universities. For over 10 years, tactics at the University of Massachusetts to assure newspaper content acceptable to special interest groups serve as an example in this article. Women editors seeking guaranteed pages in the university newspaper for women with content unreviewed by regular editors illustrates the rocky path of protest, negotiation, and examination and (...) a resulting confusion and dissatisfaction among all parties. (shrink)
We show that, when a group takes independent majority votes on interconnected propositions, the outcome is consistent once the pro…le of individual judgment sets respects appropriate structural conditions. We introduce several such conditions on pro…les, based on ordering the propositions or ordering the individuals, and we clarify the relations between these conditions. By restricting the conditions to appropriate subagendas, we obtain local conditions that are less demanding but still guarantee consistent majority judgments. By applying the conditions to agendas representing preference (...) aggregation problems, we show parallels of some conditions to existing social-choice-theoretic conditions, speci…cally to order restriction and intermediateness, restricted to triples of alternatives in the case of our local conditions. (shrink)
I argue that free will and determinism are compatible, even when we take free will to require the ability to do otherwise and even when we interpret that ability modally, as the possibility of doing otherwise, and not just conditionally or dispositionally. My argument draws on a distinction between physical and agential possibility. Although in a deterministic world only one future sequence of events is physically possible for each state of the world, the more coarsely defined state of an agent (...) and his or her environment can be consistent with more than one such sequence, and thus different actions can be “agentially possible”. The agential perspective is supported by our best theories of human behaviour, and so we should take it at face value when we refer to what an agent can and cannot do. On the picture I defend, free will is not a physical phenomenon, but a higher-level one on a par with other higher-level phenomena such as agency and intentionality. (shrink)
An agent’s action counts as free only if the action is endorsed by the agent in an appropriate way, as opposed to having been merely indeterministically picked from some set of alternative possibilities, for instance by randomization or some contingency outside the agent’s control.
April 2011 Can we design a perfect democratic decision procedure? Condorcet famously observed that majority rule, our paradigmatic democratic procedure, has some desirable properties, but sometimes produces inconsistent outcomes. Revisiting Condorcet’s insights in light of recent work on the aggregation of judgments, I show that there is a conflict between three initially plausible requirements of democracy: “robustness to pluralism”, “basic majoritarianism”, and “collective rationality”. For all but the simplest collective decision problems, no decision procedure meets these three requirements at once; (...) at most two can be met together. This “democratic trilemma” raises the question of which requirement to give up. Since different answers correspond to different views about what matters most in a democracy, the trilemma suggests a map of the “logical space” in which different conceptions of democracy are located. It also sharpens our thinking about other impossibility problems of social choice and how to avoid them, by capturing a core structure many of these problems have in common. More broadly, it raises the idea of “cartography of logical space” in relation to contested political concepts. (shrink)
On Hume’s account of motivation, beliefs and desires are very di¤erent kinds of propositional attitudes. Beliefs are cognitive attitudes, desires emotive ones. An agent’s belief in a proposition captures the weight he or she assigns to this proposition in his or her cognitive representation of the world. An agent’s desire for a proposition captures the degree to which he or she prefers its truth, motivating him or her to act accordingly. Although beliefs and desires are sometimes entangled, they play very (...) di¤erent roles in rational agency.1 In two classic papers (Lewis 1988, 1996), David Lewis discusses several challenges to this Humean picture, but ultimately rejects them. We think that his discussion of a central anti-Humean alternative – the desire-as-belief thesis – is in need of re…nement. On this thesis, the desire for proposition p is given by the belief that p is desirable. Lewis claims that ‘[e]xcept in trivial cases, [this thesis] collapses into contradiction’(Lewis 1996, p. 308). The problem, he argues, is that the thesis is inconsistent with the purportedly plausible requirement that one’s desire for a proposition should not change upon learning that the proposition is true; call this the invariance requirement. In this paper, we revisit Lewis’s argument. We show that, if one carefully distinguishes between non-evaluative and evaluative propositions, the desire-asbelief thesis can be rendered consistent with the invariance requirement. Lewis’s conclusion holds only under certain conditions: the desire-as-belief thesis con- ‡icts with the invariance requirement if and only if there are certain correlations between non-evaluative and evaluative propositions. But when there are such correlations, we suggest, the invariance requirement loses its plausibility. Thus Lewis’s argument against the desire-as-belief thesis appears to be valid only in cases in which it is unsound. (shrink)
There is a surprising disconnect between formal rational choice theory and philosophical work on reasons. The one is silent on the role of reasons in rational choices, the other rarely engages with the formal models of decision problems used by social scientists. To bridge this gap, we propose a new, reason-based theory of rational choice. At its core is an account of preference formation, according to which an agent’s preferences are determined by his or her motivating reasons, together with a (...) ‘weighing relation’ between different combinations of reasons. By explaining how someone’s preferences may vary with changes in his or her motivating reasons, our theory illuminates the relationship between deliberation about reasons and rational choices. Although primarily positive, the theory can also help us think about how those preferences and choices ought to respond to normative reasons. (shrink)
The world is increasingly characterized by transnational interdependence, cross-border policy externalities and the widely perceived need to provide certain global collective goods and to avoid global collective bads. Consider, for example, the problem of climate change and the need to limit greenhouse gas emissions; the problem of global refugee flows and the commitment to protect the human rights of forced migrants; and the problem of controlling and eradicating infectious diseases that can spread very fast, such as new forms of influenza. (...) In all these cases, the need for “global governance”, that is, the challenge to make good collective decisions and to coordinate actions transnationally, is more pressing than ever. There are at least two dimensions of this challenge. First, global public goods are typically underprovided, and global public bads over-occur, in part because there are too few mechanisms to prevent free-riding at the global level (the “efficiency dimension”).1 And second, where global public goods are provided, and global public bads avoided, this is often the result of bargaining based on differential.. (shrink)
The two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote (...) these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect. (shrink)
This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than exhaustive review is intended to give readers (...) who are new to the field of judgment aggregation a sense of this rapidly growing research area. (shrink)
On one very simple formulation, the exclusion argument against dualism starts from the assertion that the following theses are inconsistent: (1) Being in pain causes me to wince. (2) Being in phys1 causes me to wince. (3) Being in pain is distinct from being in phys. (4) If being in pain causes me to wince, nothing distinct from being in pain causes me to wince. The dualist is then invited to agree that (1) and (2) are empirical claims that are (...) (in the context) non-negotiable; and that (4) is a principle of causation or an instance of a principle we must accept, often called ‘the exclusion principle’. The conclusion of the argument is that (3)—a thesis distinctive of traditional dualism—has to go.2 This argument is widely thought to put considerable pressure on dualism if not to refute it outright. In this paper we argue to the contrary that, whether or not their position is ultimately true, dualists have a simple response. Whether there is an inconsistency in (1)-(4) depends on how ‘distinctness’ is interpreted in claims (3) and (4). (Of course the same thing applies, mutatis mutandis to the other terms in (1)-(4); we concentrate here on ‘distinctness’.) As one of us has argued elsewhere, there are a number of different but still legitimate interpretations of ‘distinctness’ (see Stoljar 2006; see also Sandford 2005). Usually the term.. (shrink)
Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Instead, preferences are usually assumed to be …xed and exogenously given. We introduce a framework for conceptualizing preference formation and preference change. In our model, an agent’s preferences are based on certain ‘motivationally salient’properties of the alternatives over which the preferences are held. Preferences may change as new properties of the alternatives become salient or previously salient (...) ones cease to be so. We suggest that our approach captures endogenous preferences in various contexts, and helps to illuminate the distinction between formal and substantive concepts of rationality, as well as the role of perception in rational choice. (shrink)
The Ostrogorski paradox and the discursive dilemma are seemingly unrelated paradoxes of aggregation. The former is discussed in traditional social choice theory, while the latter is at the core of the new literature on judgment aggregation. Both paradoxes arise when, in a group, each individual consistently makes a judgment, or expresses a preference, (in the form of yes or no) over specific propositions, and the collective outcome is in some respect inconsistent. While the result is logically inconsistent in the case (...) of the discursive paradox, it is not stable with respect to the level of aggregation in the case of the Ostrogorski paradox. In the following I argue that, despite these differences, the two problems have a similar structure. My conclusion will be twofold: on the one hand, the similarities between the paradoxes support the claim that these problems should be tackled using the same aggregation procedure; on the other hand, applying the same procedure to these paradoxes will help clarify the strengths and weaknesses of the aggregation method itself. More specifically, I will show that an operator defined in artificial intelligence to merge belief bases can deal with both paradoxes. (shrink)
Jonathan Aldred shares our desire to promote a reconciliation between social choice theory and deliberative democracy in the interests of a more comprehensive and compelling account of democracy.1 His comments on some details of our analysis – specifically, our use of Arrow’s conditions of universal domain and independence of irrelevant alternatives – give us an opportunity to clarify our position. His discussion of the independence condition in particular identifies some ambiguity in our exposition, and as such is useful. We are (...) less impressed by the way Aldred characterizes the overall terms of the reconciliation we propose. We believe that his argument on this matter should be resisted because it provides deliberative democrats with a bad excuse to dismiss social choice theory altogether, which is surely not what he intends. (shrink)
In a recent paper on ‘The Many as One’, Lewis A. Kornhauser and Lawrence G. Sager look at an issue that we take to be of great importance in political theory.i How far should groups in public life try to speak with one voice, and act with one mind? How far should public groups try to display what Ronald Dworkin calls integrity?ii We do not expect the many on the market to be integrated in this sense. But should we expect (...) integration among the many in the legislature, for example, or among the many on the courts? We agree with Kornhauser and Sager about a number of their claims but think that they miss out on important detail and do not achieve a fully general perspective on the issues raised. Our own contribution is in three sections. We address, first, the nature of the integrity challenge; second, the range of cases in which the challenge arises; and third, the question of whether public groups should be designed and required to meet that challenge. (shrink)
According to standard rational choice theory, as commonly used in political science and economics, an agent’s fundamental preferences are exogenously …xed, and any preference change over decision options is due to Bayesian information learning. Although elegant and parsimonious, this model fails to account for preference change driven by experiences or psychological changes distinct from information learning. We develop a model of non-informational preference change. Alternatives are modelled as points in some multidimensional space, only some of whose dimensions play a role (...) in shaping the agent’s preferences. Any change in these ‘motivationally salient’ dimensions can change the agent’s preferences. How it does so is described by a new representation theorem. Our model not only captures a wide range of frequently observed phenomena, but also generalizes some standard representations of preferences in political science and economics. (shrink)
This introduces the symposium on judgment aggregation. The theory of judgment aggregation asks how several individuals' judgments on some logically connected propositions can be aggregated into consistent collective judgments. The aim of this introduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's impossibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous (...) impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium. (shrink)
Complaints are common about the arbitrary and conservative bias of special-majority rules. Such complaints, however, apply to asymmetrical versions of those rules alone. Symmetrical special-majority rules remedy that defect, albeit at the cost of often rendering no determinate verdict. Here what is formally at stake, both procedurally and epistemically, is explored in the choice between those two forms of special-majority rule and simple-majority rule; and practical ways are suggested of resolving matters left open by symmetrical special-majority rules – such as (...) ‘judicial extrapolation’ or ‘subsidiarity’ in a federal system. (shrink)
Using data from a randomized field experiment within a Deliberative Poll, we examine deliberation’s effects on both policy attitudes and the extent to which ordinal rankings of policy options approach single-peakedness (a help in avoiding cyclical majorities). The issues were airport expansion and revenue-sharing in New Haven, Connecticut and its surrounding towns. Half the participants deliberated revenue-sharing, then the airport, the other half the reverse. This split-half design enables us to distinguish the effects of the formal on-site deliberations from those (...) of other aspects of the Deliberative Polling treatment. We find that the formal on-site deliberations accounted for much of the Deliberative Polling effect on one issue, though not the other—thus both confirming deliberation’s capacity to shape attitudes and preferences and raising the question of how its effects may depend on the kind of issue being deliberated. We suggest that deliberation’s effects are larger for less salient issues. (shrink)
Majority cycling and related social choice paradoxes are often thought to threaten the meaningfulness of democracy. But deliberation can prevent majority cycles – not by inducing unanimity, which is unrealistic, but by bringing preferences closer to single-peakedness. We present the first empirical test of this hypothesis, using data from Deliberative Polls. Comparing preferences before and after deliberation, we find increases in proximity to single-peakedness. The increases are greater for lower versus higher salience issues and for individuals who seem to have (...) deliberated more versus less effectively. They are not merely a byproduct of increased substantive agreement (which in fact does not generally increase). Our results both refine and support the idea that deliberation, by increasing proximity to single-peakedness, provides an escape from the problem of majority cycling. (shrink)
May's theorem famously shows that, in social decisions between two options, simple majority rule uniquely satisfies four appealing conditions. Although this result is often cited in support of majority rule, it has never been extended beyond decisions based on pairwise comparisons of options. We generalize May's theorem to many-option decisions where voters each cast one vote. Surprisingly, plurality rule uniquely satisfies May's conditions. This suggests a conditional defense of plurality rule: If a society's balloting procedure collects only a single vote (...) from each voter, then plurality rule is the uniquely compelling electoral procedure. To illustrate the conditional nature of this claim, we also identify a richer informational environment in which approval voting, not plurality rule, is supported by a May-style argument. (shrink)
Since Sen's insightful analysis of Arrow's Impossibility Theorem (Sen, 1970/1979), Arrow's theorem is often interpreted as a consequence of the exclusion of interpersonal information from Arrow's framework. Interpersonal comparability of either welfare levels or welfare units is known to be sufficient for circumventing Arrow's impossibility result (e.g. Sen, 1970/1979, 1982; Roberts, 1980; d'Aspremont, 1985). But it is less well known whether one of these types of comparability is also necessary or whether Arrow's conditions can already be satisfied in much narrower (...) informational frameworks. This note explores such a framework: the assumption of (ONC+0), ordinal measurability of welfare with the additional measurability of a 'zero-line', is shown to point towards new, albeit limited, escape-routes from Arrow's theorem. Some existence and classification results are established, using the condition that social orderings be transitive as well as the condition that social orderings be quasi-transitive. (shrink)
How can collective decisions be made among individuals with conflicting preferences or judgments? Arrow’s impossibility theorem and other social-choice-theoretic results suggest that, for many collective decision problems, there are no attractive democratic solutions. In response, deliberative democrats argue that group deliberation makes collective decisions more tractable. How can deliberation accomplish this? In this chapter, I explore the distinction between two different types of agreement and discuss how they can facilitate collective decision making. Deliberative democrats have traditionally defended the hypothesis that (...) group deliberation generates consensus on what decision option should be chosen: substantive agreement. But substantive agreement is not only empirically unrealistic, but also logically unnecessary for meaningful collective decision making. An alternative, less demanding hypothesis is that, under certain conditions, group deliberation generates consensus on how a decision problem should be conceptualized: meta-agreement. I assess the latter hypothesis, explain how it can be empirically tested, and cite some evidence consistent with it. My discussion addresses two contexts of democratic decision making: preference aggregation and judgment aggregation. (shrink)
Decision making typically requires judgements about causal relations: we need to know both the causal e¤ects of our actions and the causal relevance of various environmental factors. Judgements about the nature and strength of causal rela- tions often di¤er, even among experts. How to handle such diversity is the topic of this paper. First we consider the possibility of aggregating causal judgements via the aggregation of probabilistic ones. The broadly negative outcome of this investigation leads us to look at aggregating (...) causal judgements independently of probabilistic ones. We do so by transcribing causal claims into the judgement aggregation framework and applying some recent results in this …eld. Finally we look at the implications for probability aggregation when it is constrained by prior aggregation of causal judgements. (shrink)
The present paper proposes to revive the twenty-year old debate on the question of whether Craig’s theorem poses a challenge to the empirical underdetermination thesis. It will be demonstrated that Quine’s account of this issue in his paper “Empirically Equivalent Systems of the World” (1975) is mathematically flawed and that Quine makes too strong a concession to the Craigian challenge. It will further be pointed out that Craig’s theorem would threaten the empirical underdetermination thesis only if the set of all (...) relevant observation conditionals could be shown to be recursively enumerable — a condition which Quine seems to overlook —, and it will be argued that, at least within the framework of Quine’s philosophy, it is doubtful whether this condition is satisfiable. (shrink)
A central problem of democracy is the aggregation of divergent individual inputs into overall collective decisions. Social-choice-theoretic impossibility results famously demonstrate the intractability of a large class of such aggregation problems. This paper develops a taxonomy of two concepts of agreement, agreement at a substantive level and agreement at a meta-level, and discusses the escape-routes these concepts open up from the impossibility problems of social choice. Specifically, two contexts of democratic aggregation are addressed: first, the familiar context of preferences, and (...) second, the largely unexplored context of sets of judgments over multiple interconnected propositions. Drawing on some recent developments in social choice theory and democratic theory, I will defend the view that, when agreement is conceptualized in democratic theory and when it is sought in democratic practice, more emphasis should be placed on agreement at a meta-level than is commonly done. Finally, I will address the more general question to what extent it is acceptable for the stability of institutions for democratic aggregation to be dependent on specific empirical contingencies. (shrink)
Condorcet’s voting paradox shows that pairwise majority voting may lead to cyclical majority preferences. In a famous paper, Sen (1966) identified a general condition on a profile of individual preference orderings, called triplewise value-restriction, which is sufficient for the avoidance of such cycles. This note aims to make Sen’s result easily accessible. We provide an elementary proof of Sen's possibility theorem and a simple reformulation of Sen’s condition. We discuss how Sen’s condition is logically related to a number of precursors. (...) Finally, we state a necessary and sufficient condition for the avoidance of cycles, and suggest that, although there is still some logical space between that condition and Sen’s sufficient condition, Sen’s condition cannot be further generalized in an appealing way. (shrink)
Condorcet’s voting paradox shows that pairwise majority voting may lead to cyclical majority preferences. In a famous paper, Sen (1966) identified a general condition on a profile of individual preference orderings, called triplewise value-restriction, which is sufficient for the avoidance of such cycles. This note aims to make Sen’s result easily accessible. We provide an elementary proof of Sen's possibility theorem and a simple reformulation of Sen’s condition. We discuss how Sen’s condition is logically related to a number (...) of precursors. Finally, we state a necessary and sufficient condition for the avoidance of cycles, and suggest that, although there is still some logical space between that condition and Sen’s sufficient condition, Sen’s condition cannot be further generalized in an appealing way. (shrink)
One fundamental thesis within the rapidly growing literature on deliberative democracy is that the stability and quality of a democracy depend not only on formal institutions such as the electoral system or the structure of parliamentary representation. They depend also on certain democratic competences of the citizens, especially their capacity for democratic communication. According to this thesis, above all the capacity for democratic deliberation, i.e., for argumentation, evaluation and for a balanced decision between policy alternatives, belongs to the central competences (...) relevant to maintaining and developing a democracy. (shrink)
The triumvirate of HIV/AIDS, tuberculosis, and malaria have dominated our public health focus in the developing world. Having claimed millions of lives, these infectious diseases have prompted a large-scale response. Concomitant with these efforts has been a burgeoning bioethics literature examining global health and distributive justice. A scholarly waste-land only a decade ago, there is now a growing and rich literature that aims to unpack our moral obligations when it comes to diseases that affect the majority of the world (many (...) living in absolute poverty). Now, added to the persistent challenges posed by infectious diseases is the growing burden of diseases such as cancer, which disproportionately affect .. (shrink)
Can collectives be wise? The thesis that they can has recently received a lot of attention. It has been argued that, in many judgmental or decision-making tasks, suitably organized groups can outperform their individual members. In particular, it has been suggested that groups are good at meeting what I call the correspondence challenge (as in correspondence with the facts): By pooling information that is dispersed among the individual members, a group can arrive at judgments that accurately track some independent truths (...) or make decisions that maximize an independent objective function (for a popular discussion, see Surowiecki 2004). (shrink)
Two essential intuitions about the concept of multidimensional inequality have been highlighted in the emerging body of literature on this subject: first, multidimensional inequality should be a function of the uniform inequality of a multivariate distribution of goods or attributes across people (Kolm, 1977); and, second, it should also be a function of the cross-correlation between distributions of goods or attributes in different dimensions (Atkinson and Bourguignon, 1982; Walzer, 1983). While the first intuition has played a major role in the (...) design of fully-fledged multidimensional inequality indices, the second one has only recently received attention (Tsui, 1999); and, so far, multidimensional generalized entropy measures are the only inequality measures known to respect both intuitions. The present paper proposes a general method of designing a wider range of multidimensional inequality indices that also respect both intuitions, and illustrates this method by defining two classes of such indices: a generalization of the Gini coefficient, and a generalization of Atkinson's onedimensional measure of inequality. (shrink)
Most accounts of welfare aggregation in the tradition of Arrow's (1951/1963) and Sen's (1970/1979) social-choice-theoretic frameworks represent the welfare of an individual in terms of a single welfare ordering or a single scalar-valued welfare function. I develop a multidimensional generalization of Arrow's and Sen's frameworks, representing individual welfare in terms of multiple personal welfare functions, corresponding to multiple 'dimensions' of welfare. I show that, as in the one-dimensional case, the existence of attractive aggregation procedures depends on certain informational assumptions, specifically (...) about the measurability of welfare and its comparability not only across individuals but also across dimensions. I state several impossibility and possibility results. Under Arrow-type conditions, insufficient comparability across individuals leads to dictatorship of a single individual, while insufficient comparability across dimensions leads to dominance of a single dimension. Given sufficient comparability both across individuals and across dimensions, a range of possibilities emerges. I discuss the substantive implications of the results. (shrink)
For centuries, homo sapiens has learned tricks of design from other species, including both non-human animals and plants. In applied sciences such as engineering and aerodynamics, “biomimicry” exploits designs that arise from natural selection. The inventor of Velcro hook-and-loop fasteners, used in everyday clothes as well as high-tech products, copied the hooks by which cockleburs snag the fur of passing animals; the shape of the Mercedes Benz bionic car mimics the boxfish to maximize aerodynamic efficiency; and Speedo’s Fastskin body-hugging (...) swimsuit, recently adopted by most Olympic swimmers, mimics the micro-features of sharkskin to minimize drag (Bushan.. (shrink)
Condorcet's classic jury theorem shows that when the members of a group have noisy but independent information about what is best for the group as a whole, majority decisions tend to outperform dictatorial ones. When voting is supplemented by communication, however, the resulting interdependencies between decision-makers can strengthen or undermine this effect: they can facilitate information pooling, but also amplify errors. We consider an intriguing non-human case of independent information pooling combined with communication: the case of nest-site choice by honey (...) bee swarms. It is empirically well-documented that when there are different nest sites that vary in quality, the bees usually choose the best one. We develop a new agent-based model of the bees’ decision process and show that its remarkable reliability stems from a particular interplay of independence and interdependence between the bees. (shrink)
Although the pairwise Condorcet winner criterion may seem an attractive democratic decision procedure, it is famously threatened by Condorcet's paradox: pairwise majority voting may lead to cyclical collective preferences. But how probable is the occurrence of cycles?
Group decisions must often obey exogenous constraints. While in a preference aggregation problem constraints are modelled by restricting the set of feasible alternatives, this paper discusses the modelling of constraints when aggregating individual yes/no judgments on interconnected propositions. For example, court judgments in breach-of-contract cases should respect the constraint that action and obligation are necessary and sufficient for liability, and judgments on budget items should respect budgetary constraints. In this paper, we make constraints in judgment aggregation explicit by relativizing the (...) rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. This approach of modelling constraints explicitly contrasts with that of building constraints as axioms into the logic, which turns compliance with constraints into a matter of logical consistency and thereby conflates requirements of ordinary logical consistency (such as not to affirm both a proposition and its negation) and requirements dictated by the environment (such as budgetary constraints). We present some general impossibility results on constrained judgment aggregation; they are immediate corollaries of known results on (unconstrained) judgment aggregation. (shrink)
Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the probability of the paradox converges (...) to 1, and when it converges to 0, as the number of individuals increases. Drawing on the Condorcet jury theorem and work by Bovens and Rabinowicz (2001, 2003), I use the model to assess the “truth-tracking” performance of two decision procedures, the premise- and conclusion-based procedures. I compare the present results with existing results on the probability of Condorcet’s paradox. I suggest that the doctrinal paradox is likely to occur under plausible conditions. (shrink)
Max Albert (2003) has recently argued that the theory of power indices “should not ... be considered as part of political science” and that “[v]iewed as a scientific theory, it is a branch of probability theory and can safely be ignored by political scientists”. Albert’s argument rests on a particular claim concerning the theoretical status of power indices, namely that the theory of power indices is not a positive theory, i.e. not one that has falsifiable implications. I re-examine (...) the theoretical status of power indices and argue that it would be unwise for political scientists to ignore such indices. Although I agree with Albert that the theory of power indices is not a positive theory, I suggest that it is a theory of measurement that can usefully supplement other positive and normative socialscientific theories. (shrink)
