This paper critically engages Philip Mirowki's essay, "The scientific dimensions of social knowledge and their distant echoes in 20th-century American philosophy of science." It argues that although the cold war context of anti-democratic elitism best suited for making decisions about engaging in nuclear war may seem to be politically and ideologically motivated, in fact we need to carefully consider the arguments underlying the new rational choice based political philosophies of the post-WWII era typified by Arrow's impossibility theorem. (...) A distrust of democratic decision-making principles may be developed by social scientists whose leanings may be toward the left or right side of the spectrum of political practices. (shrink)

This book develops John Dewey's broad conception of social conflict as a natural process of discovery and preference adjustment, resolving Kenneth Arrow's famous theorem of the impossibility of ordering diverse preferences through voting. It addresses the nature and resolution of today's urgent problems and political polarization.

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...) basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

Arrow’s impossibility result not only had a profound influence on welfare economics, but was, as this paper shows, also widely discussed in philosophy of science and in the engineering design literature.

In 1951, Kenneth Arrow published his now celebrated book Social Choice and Individual Values. Although not the first book to be written on social choice, Arrow's work ushered in a voluminous literature mostly produced by economists but by philosophers and political scientists as well. Arrow's chief result was a proof of the impossibility of a social welfare function . He showed that there could be no decision procedure for aggregating individual preference orderings into a grand, overall social (...) preference ordering. The result has been hailed by some as a sort of Godel Theorem of economics. It has seemed to many to have, if not the complexity of the Godel Theorem, at least the same astonishing counter-intuitiveness. On the other hand, some social choice theorists, while conceding the validity of the Arrow Theorem, have challenged its soundness by quarreling with one or more of its presuppositions. (shrink)

This paper is concerned with social choice without completeness of social preference. Completeness requires that pairs of alternatives are perfectly comparable. We introduce the concept of minimal comparability, which requires that for any profile, there is some comparable pair of distinct alternatives. Complete silence should be avoided according to this condition. We show that there exists no normatively desirable aggregation rule satisfying minimal comparability.

Riker (1982) famously argued that Arrow’s impossibility theorem undermined the logical foundations of “populism”, the view that in a democracy, laws and policies ought to express “the will of the people”. In response, his critics have questioned the use of Arrow’s theorem on the grounds that not all configurations of preferences are likely to occur in practice; the critics allege, in particular, that majority preference cycles, whose possibility the theorem exploits, rarely happen. In this essay, I (...) argue that the critics’ rejoinder to Riker misses the mark even if its factual claim about preferences is correct: Arrow’s theorem and related results threaten the populist’s principle of democratic legitimacy even if majority preference cycles never occur. In this particular context, the assumption of an unrestricted domain is justified irrespective of the preferences citizens are likely to have. (shrink)

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although (...) we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

Kenneth Arrow’s “impossibility” theorem—or “general possibility” theorem, as he called it—answers a very basic question in the theory of collective decision-making. Say there are some alternatives to choose among. They could be policies, public projects, candidates in an election, distributions of income and labour requirements among the members of a society, or just about anything else. There are some people whose preferences will inform this choice, and the question is: which procedures are there for deriving, from what (...) is known or can be found out about their preferences, a collective or “social” ordering of the alternatives from better to worse? The answer is startling. Arrow’s theorem says there are no such procedures whatsoever—none, anyway, that satisfy certain apparently quite reasonable assumptions concerning the autonomy of the people and the rationality of their preferences. The technical framework in which Arrow gave the question of social orderings a precise sense and its rigorous answer is now widely used for studying problems in welfare economics. The impossibility theorem itself set much of the agenda for contemporary social choice theory. Arrow accomplished this while still a graduate student. In 1972, he received the Nobel Prize in economics for his contributions. (shrink)

There is an extensive literature in social choice theory studying the consequences of weakening the assumptions of Arrow's Impossibility Theorem. Much of this literature suggests that there is no escape from Arrow-style impossibility theorems unless one drastically violates the Independence of Irrelevant Alternatives (IIA). In this paper, we present a more positive outlook. We propose a model of comparing candidates in elections, which we call the Advantage-Standard (AS) model. The requirement that a collective choice rule (CCR) (...) be rationalizable by the AS model is in the spirit of but weaker than IIA; yet it is stronger than what is known in the literature as weak IIA (two profiles alike on x, y cannot have opposite strict social preferences on x and y). In addition to motivating violations of IIA, the AS model makes intelligible violations of another Arrovian assumption: the negative transitivity of the strict social preference relation P. While previous literature shows that only weakening IIA to weak IIA or only weakening negative transitivity of P to acyclicity still leads to impossibility theorems, we show that jointly weakening IIA to AS rationalizability and weakening negative transitivity of P leads to no such impossibility theorems. Indeed, we show that several appealing CCRs are AS rationalizable, including even transitive CCRs. (shrink)

This book discusses how rational choice theory grew out of RAND's work for the US Air Force. It concentrates on the work of William J. Riker, Kenneth J. Arrow, James M. Buchanan, Russel Hardin, and John Rawls. It argues that within the context of the US Cold War with its intensive anti-communist and anti-collectivist sentiment, the foundations of capitalist democracy were grounded in the hyper individualist theory of non-cooperative games.

Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if the collection of feasible sets consists of all subsets of alternatives containing a prespecified (...) list of alternatives and if there are at least three additional alternatives not on this list, replacing nondictatorship by anonymity results in an impossibility theorem. (shrink)

In his classic monograph, Social Choice and Individual Values, Arrow introduced the notion of a decisive coalition of voters as part of his mathematical framework for social choice theory. The subsequent literature on Arrow’s Impossibility Theorem has shown the importance for social choice theory of reasoning about coalitions of voters with different grades of decisiveness. The goal of this paper is a fine-grained analysis of reasoning about decisive coalitions, formalizing how the concept of a decisive coalition gives rise (...) to a social choice theoretic language and logic all of its own. We show that given Arrow’s axioms of the Independence of Irrelevant Alternatives and Universal Domain, rationality postulates for social preference correspond to strong axioms about decisive coalitions. We demonstrate this correspondence with results of a kind familiar in economics—representation theorems—as well as results of a kind coming from mathematical logic—completeness theorems. We present a complete logic for reasoning about decisive coalitions, along with formal proofs of Arrow’s and Wilson’s theorems. In addition, we prove the correctness of an algorithm for calculating, given any social rationality postulate of a certain form in the language of binary preference, the corresponding axiom in the language of decisive coalitions. These results suggest for social choice theory new perspectives and tools from logic. (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 (...) class='Hi'>theorem. (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 (...) class='Hi'>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)

In this paper, we show that Arrow’s well-known impossibility theorem is instrumental in bringing the ongoing discussion about verisimilitude to a more general level of abstraction. After some preparatory technical steps, we show that Arrow’s requirements for voting procedures in social choice are also natural desiderata for a general verisimilitude definition that places content and likeness considerations on the same footing. Our main result states that no qualitative unifying procedure of a functional form can simultaneously satisfy the requirements (...) of Unanimity, Independence of irrelevant alternatives and Non-dictatorship at the level of sentence variables. By giving a formal account of the incompatibility of the considerations of content and likeness, our impossibility result makes it possible to systematize the discussion about verisimilitude, and to understand it in more general terms. (shrink)

Shows how, as a consequence of the Arrow Impossibility Theorem, objectivity in grading is chimerical, given a sufficiently knowledgeable teacher (of his students, not his subject) in a sufficiently small class. -/- PDF available from JStor only; permission to post full version previously granted by journal editors and publisher expired. -/- Unpublished reply posted gratis.

According to conciliatory views about the epistemology of disagreement, when epistemic peers have conflicting doxastic attitudes toward a proposition and fully disclose to one another the reasons for their attitudes toward that proposition (and neither has independent reason to believe the other to be mistaken), each peer should always change his attitude toward that proposition to one that is closer to the attitudes of those peers with which there is disagreement. According to pure higher-order evidence views, higher-order evidence for a (...) proposition always suffices to determine the proper rational response to disagreement about that proposition within a group of epistemic peers. Using an analogue of Arrow's Impossibility Theorem, I shall argue that no conciliatory and pure higher-order evidence view about the epistemology of disagreement can provide a true and general answer to the question of what disagreeing epistemic peers should do after fully disclosing to each other the (first-order) reasons for their conflicting doxastic attitudes. (shrink)

Separates the purely combinatorial component of Arrow's impossibility theorem in the theory of collective preference from its decision-theoretic part, and likewise for the closely related Blair/Bordes/Kelly/Suzumura theorem. Such a separation provides a particularly elegant proof of Arrow's result, via a new 'splitting theorem'.

Since Kenneth Arrow showed the general possibility theorem, a number of social choice theorists have provided alternative proofs of it. In a recent article, Geanakoplos (Econ Theory 26:211–215, 2005) has constructed a new proof of the theorem. The present article provides alternative proofs of various Arrovian impossibility results from the 1960s to the 1970s by utilizing Geanakoplos’s method. We prove semi-order impossibility theorems, the quasi-transitive veto theorem, the quasi-transitive dictatorship theorem, the triple acyclic veto (...) theorem, and the impossibility theorem without the Pareto principle. (shrink)

In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit. Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments and Arrow’s theorem. I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit to the (...) conditions on the aggregation procedure. (shrink)

We argue that a semantics for counterfactual conditionals in terms of comparative overall similarity faces a formal limitation due to Arrow’s impossibility theorem from social choice theory. According to Lewis’s account, the truth-conditions for counterfactual conditionals are given in terms of the comparative overall similarity between possible worlds, which is in turn determined by various aspects of similarity between possible worlds. We argue that a function from aspects of similarity to overall similarity should satisfy certain plausible constraints while (...) Arrow’s impossibility theorem rules out that such a function satisfies all the constraints simultaneously. We argue that a way out of this impasse is to represent aspectual similarity in terms of ranking functions instead of representing it in a purely ordinal fashion. Further, we argue against the claim that the determination of overall similarity by aspects of similarity faces a difficulty in addition to the Arrovian limitation, namely the incommensurability of different aspects of similarity. The phenomena that have been cited as evidence for such incommensurability are best explained by ordinary vagueness. (shrink)

In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete axiomatisation for (...) this class, without having the number of individuals or alternatives specified in the language. We are able to express classical axiomatic requirements in our first-order language, giving formal axioms for three classical theorems of preference aggregation by Arrow, by Sen, and by Kirman and Sondermann. We explore to what extent such theorems can be formally derived from our axiomatisations, obtaining positive results for Sen’s Theorem and the Kirman-Sondermann Theorem. For the case of Arrow’s Theorem, which does not apply in the case of infinite societies, we have to resort to fixing the number of individuals with an additional axiom. In the long run, we hope that our approach to formalisation can serve as the basis for a fully automated proof of classical and new theorems in social choice theory. (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.

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result (...) to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts , content-aspects and likeness-aspects of verisimilitude are not in conflict with each (...) other, but in agreement . We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6). (shrink)

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts, content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, (...) but in agreement. We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic versus semantic formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence. (shrink)

John Barrow is increasingly recognized as one of our most elegant and accomplished science writers, a brilliant commentator on cosmology, mathematics, and modern physics. Barrow now tackles the heady topic of impossibility, in perhaps his strongest book yet. Writing with grace and insight, Barrow argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. He first examines the limits on scientific inquiry imposed by the deficiencies of the human mind: (...) our brain evolved to meet the demands of our immediate environment, Barrow notes, and much that lies outside this small circle may also lie outside our understanding. Barrow investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines the deeper theoretical restrictions on our ability to know, including Godel's theorem--which proved that there were things that could not be proved--and Arrow's Impossibility theorem about democratic voting systems. Finally, having explored the limits imposed on us from without, Barrow considers whether there are limits we should impose upon ourselves. For instance, if the secrets of the atom are to be found only by recreating extreme environments at great financial cost, just how much should we devote to that quest? Weaving together this intriguing tapestry, he illuminates some of the most profound questions of science, from the possibility of time travel to the very structure of the universe. (shrink)

We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow's famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a method of determining defeats studied in our recent work: Split Cycle. In particular, (...) Split Cycle provides the most resolute definition of defeat among any satisfying the six axioms for democratic defeat. In addition, we analyze how Split Cycle escapes Arrow's Impossibility Theorem and related impossibility results. (shrink)

It is argued in this paper that amalgamating confirmation from various sources is relevantly different from social-choice contexts, and that proving an impossibility theorem for aggregating confirmation measures directs attention to irrelevant issues.

By applying Arrow’s impossibility theorem for social choice to scientific theory choice, Okasha concludes that there is no acceptable theory choice rule. Okasha identifies the only way out of the impossibility in enriching the input for the theory choice rule, following Sen’s work for social choice. However, such a route seems not to be available for ‘large scale’ theory choices—i.e. choices among ‘key theories’ which imply a change of paradigm—based on Kuhn’s criteria, since these criteria cannot provide (...) a richer input. The aim of the paper is to explore two lines of response to this conclusion. The first response proposes an example suggesting that Kuhn’s criteria may, indeed, provide sufficiently rich inputs. The second one proposes to use Kuhn’s criteria to evaluate prior probability and likelihood of the theories, and then take these as elements of the ‘Bayesian theory choice rule’ that avoids the impossibility. I will then argue against an objection to the second response, derived from Stegenga’s observation that a rule that translates the information provided by Kuhn’s criteria into prior probabilities suffers from Arrovian impossibility. Finally, I will answer a separate interesting question suggested by Stegenga’s observation. (shrink)

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the (...) Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations. (shrink)

Kuhn’s famous thesis that there is ‘no unique algorithm’ for choosing between rival scientific theories is analysed using the machinery of social choice theory. It is shown that the problem of theory choice as posed by Kuhn is formally identical to a standard social choice problem. This suggests that analogues of well-known results from the social choice literature, such as Arrow’s impossibility theorem, may apply to theory choice. If an analogue of Arrow’s theorem does hold for theory (...) choice this would refute Kuhn’s thesis, but it would also pose a threat to the rationality of science, a threat that is if anything more worrying than that posed by Kuhn. Various possible ‘escape routes’ from Arrow’s impossibility result are examined, in particular Amartya Sen’s idea of ‘enriching the informational basis’. It is shown that Sen’s idea can be applied to the problem of theory choice in science. This in turn sheds light on two well-known approaches to inductive inference in philosophy of science: Bayesianism and statistical model selection. (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)

Arrow's account (1951/1963) of the problem of social choice is based upon the assumption that the preferences of each individual in the relevant group are expressible by a single ordering. This paper lifts that assumption and develops a multidimensional generalization of Arrow's framework. I show that, like Arrow's original framework, the multidimensional generalization is affected by an impossibility theorem, highlighting not only the threat of dictatorship of a single individual, but also the threat of dominance (...) of a single dimension. In particular, even if preferences are single-peaked across individuals within each dimension – a situation called intradimensional single-peakedness – any aggregation procedure satisfying Arrow-type conditions will make one dimension dominant. I introduce lexicographic hierarchies of dimensions as a class of possible aggregation procedures under intradimensional single-peakedness. The interpretation of the results is discussed. (shrink)

Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself 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 its members' judgments; the second presents the discursive paradox; the third gives an informal statement of the more general impossibility result; the formal proof is presented in an appendix. The fourth section, finally, discusses some escape routes from that impossibility. (shrink)

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set (...) of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem. (Published Online July 11 2006) Footnotes1 Much of this article was written while the author was a fellow at the Swedish Collegium for Advanced Study in the Social Sciences (SCASSS) in Uppsala. I want to thank the Collegium for providing me with excellent working conditions. Wlodek Rabinowicz and other fellows gave me valuable comments at a seminar at SCASSS when an early version of the paper was presented. I also want to thank Luc Bovens, Franz Dietrich, Christian List and an anonymous referee for their excellent comments on a later version. The final version was prepared during a stay at Oxford University for which I am grateful to the British Academy. (shrink)

In a recent article I compared the problem of theory choice, in which scientists must choose between competing theories, with the problem of social choice, in which society must choose between competing social alternatives. I argued that the formal machinery of social choice theory can be used to shed light on the problem of theory choice in science, an argument that has been criticized by Michael Morreau and Jacob Stegenga. This article replies to Morreau’s and Stegenga’s criticisms.

In a recent paper Samir Okasha has suggested an application of Arrow’s impossibility theorem to theory choice. When epistemic virtues are interpreted as ‘voters’ in charge of ranking competing theories, and there are more than two theories at stake, the final ordering is bound to coincide with the one proposed by one of the voters, provided a number of seemingly reasonable conditions are in place. In a similar spirit, Jacob Stegenga has shown that Arrow’s theorem applies to (...) the amalgamation of evidence; the ‘voters’ here are the different sources of evidence. As with Okasha’s proposal, it is not clear how to avoid Arrow’s pessimistic conclusion.In this paper we develop a novel argument that purports to show that, in typical examples, Arrow’s result does not obtain when dealing with evidence amalgamation. The reason is that we cannot escape the well-known Duhem problem: the evidence actually confirms complex conjunctions that include various auxiliary hypotheses. We argue that confirmational holism induces us to restrict the domain of a reasonable amalgamation function, thus violating one of Arrow’s conditions. The upshot is that we are now able to see the Duhem problem under a different, positive light – namely, as a phenomenon that makes the aggregation of the evidence possible in the first place, when there are at least three options on the table. (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)

Applying Weglorz' mode s of set theory without the axiom of choice, we investigate Arrow-type social we fare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying “finite discrimination”, if and only if in Weglorz' mode there is a free ultrafilter on a set representing the individuals.