Following Lauwers and Van Liedekerke (1995), this paper explores in a model-theoretic framework the relation between Arrovian aggregation rules and ultraproducts, in order to investigate a source of impossibility results for the case of an infinite number of individuals and an aggregation rule based on a free ultrafilter of decisive coalitions.

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)

This paper examines the aggregation of preferences with a finitely additive measure space of agents. We consider three types of non-dictatorship axioms: non-dictatorship, coalitional non-dictatorship, and atomic non-dictatorship. First, we show that the existence of an atom is a necessary and sufficient condition for the existence of a social welfare function that satisfies weak Pareto, independence of irrelevant alternatives, and coalitional non-dictatorship. Second, we simultaneously impose non-dictatorship and coalitional non-dictatorship, and specify a necessary and sufficient condition for the finitely (...) additive measure that guarantees the compatibility among the axioms. Third, we impose all non-dictatorship axioms and show that the corresponding measure is extremely restricted. (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 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)

An important objection to preference-satisfaction theories of well-being is that they cannot make sense of interpersonal comparisons. A tradition dating back to Harsanyi :434, 1953) attempts to solve this problem by appeal to people’s so-called extended preferences. This paper presents a new problem for the extended preferences program, related to Arrow’s celebrated impossibility theorem. We consider three ways in which the extended-preference theorist might avoid this problem, and recommend that she pursue one: developing aggregation rules that (...) violate Arrow’s Independence of Irrelevant Alternatives condition. (shrink)

Cohesion may be based primarily on interpersonal ties or rely instead on the connection between member and group, while groups may cohere temporarily based on the immediate alignment of interests among members or may be tied together more permanently by socio-emotional bonds. Together, these characteristics define four prototypical group types. Cliques and coalitions are based primarily on dyadic ties. Groups of comrades or colleagues rely instead on the connection of members to the group for cohesion, which reduces the marginal cost (...) of increasing group size. The strong glue of socio-emotional cohesion binds cliques and comrades, while coalitions and groups of colleagues are often based on weaker forms of cohesion. The mix of strong and weak adhesives and the greater scalability offered by the member-group bond provide the building blocks for assembling very large societies without overtaxing the social brain. (shrink)

I comment on Amartya Sen's study of the relations between the analysis of freedom and the theory of social choice. Two of his themes are analysed with regard to their contribution to an analytic understanding of the issues. These are: (1) the multiple interpretations of the concept of ‘preferences’ as a foundation for the formal conceptualizations of social choice and freedom; and (2) some issues in the formalization of freedom as a value to be compared with outcomes. Under (2), I (...) mainly point out some difficulties in the existing analyses and mildly support a ‘flexibility’ interpretation of freedom that I have advanced earlier. I conclude with some observations drawn from history and literature which complicate the value bien-pensant thinkers are prone to place on freedom. (Published Online February 16 2006). (shrink)

This volume contains a selection of Professor Uzawa's important contributions to mathematical economics. Subjects covered by these nineteen essays include consumption, production, equilibrium, capital, growth, planning, international trade, and the theory of social overhead capital. Written in the 1960s and early 1970s, the papers form a basis upon which economic theory has developed over the last twenty years. The collection includes some of Uzawa's classic contributions, such as 'Preference and Rational Choice in the Theory of Consumption', 'Time Preference, (...) the Consumption Function, and Optimum Asset Holdings', 'Neutral Inventions and the Stability of Growth Equilibrium', 'On a Two-Sector Model of Economic Growth', 'Time Preference and the Penrose Effect in a Two-Class Model of Economic Growth', and 'On the Economics of Social Overhead Capital'. The collection will be useful not only in understanding the nature of the development in economic theory today, but also in reflecting upon the direction toward which economic theory will be advancing in the future. (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 paper, 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)

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal (...) condition of rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem. (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)

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 new to the field of judgment aggregation a sense of this rapidly growing research area. (shrink)

In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and (...) judgments on budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints. (shrink)

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)

Judgment aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of barely judgments of preference. The theory derives from Kornhauser and Sager’s doctrinal paradox and Pettit’s discursive dilemma, which List and Pettit turned into an impossibility theorem – the first of a long list to come. After mentioning this formative stage, the paper restates what is now regarded as the “canonical theorem” of judgment aggregation theory. The last (...) part of paper discusses how judgment aggregation theory connects with social choice theory and can contribute to it; it singles out two representative applications, one to Arrow’s impossibility theorem and the other to the group identification problem. (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)

Most accounts of welfare aggregation in the tradition of Arrow's and Sen's 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)

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)

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)

A necessary condition for a group being taken as a rational agent is that its choices and judgements are ‘logically contestable’, but this can lead to problems of aggregation, as Arrow impossibility theorem or the discursive dilemma. This paper proposes a contractarian or constitutional approach: the relevant thing is what aggregation mechanisms would be preferred by the members of the group. Two distinctions need to be made: first, judgement aggregation is not aggregation of decisions, and (...) judgement aggregation needs be distinguished from the aggregation of information: we assume that every member of the group has already taken into account the opinions of the other members, by means of a process of public deliberation, but they may end having different opinions; we also assume that the members are rational, so that they have no reasons to accept further changes in their individual opinions. So, from the epistemic point of view, the collective judgment is not a 'better' opinion than those of the individual members. The collective judgement is better seen as a kind of compromise, the outcome of a ‘bargain’, so to say. Basically, we assume that individuals will have an interest in choosing a specific aggregation function by taking into account how are they affected by the collective actions carried out by the group, and grounded on the chosen collective judgement. (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.

My dissertation focuses on problems that arise when a group makes decisions that are in reasonable ways connected to the beliefs and values of the group members. These situations are represented by models of decision-theoretic aggregation: Suppose a model of individual rationality in decision-making applies to each of a group of agents. Suppose this model also applies to the group as a whole, and that this group model is aggregated from the individual models. Two questions arise. First, what sets (...) of reasonable conditions can we consistently impose on the aggregation? Second, what can we learn from insights gained in such models, in particular for ethics and political philosophy? The dissertation has three parts, each using a different model of individual rationality. Each part contains essays addressing questions of either the first or the second kind with regard to its underlying model. Part I uses a social-choice-theoretic model, in which agents are only assumed to rank alternatives. Arrow's "Impossibility Theorem" shows that certain conditions that it would be natural to impose on all aggregation cannot be so imposed, on pain of contradiction. I discuss the impact of this result on the evaluation of majority rule and on democratic theory. I also discuss Sen's "Liberal Paradox", which addresses the possibility of incorporating rights into a social-choice theoretic model. Part II uses the von Neumann/Morgenstern theory of expected utility. A result under this model has been regarded as providing an argument for utilitarianism. I locate a place within utilitarianism where the theorem can do some work. To prepare the ground, I interpret the von Neumann/Morgenstern theory as part of a theory of deliberation. Thereby, this version of expected utility theory can be embedded into the philosophy of practical reasoning. The underlying model in Part III is Bayesian decision theory. Whereas the other two inquiries focus on the philosophical assessment of formal results, the third makes a formal contribution. One essay surveys the area, and a second explores a curious phenomenon that occurs in determining outcomes under one type of Bayesian aggregation. (shrink)

In an article from 1973, Rittel and Webber distinguished between “tame” or “benign” problems on the one hand and “wicked” problems on the other. The authors argued that wicked problems occur in nearly all public policy issues. Since different groups adhere to different value-sets, solutions can only be expressed as better or worse. By no means can they be viewed as definitive or objective. In this paper we shall consider, from this very angle, the theory of social choice which is (...) about the aggregation of individual preferences with the aim to derive a consistent social preference. We shall show that collective choice offers wicked problems of various types which differ in their degree of severity. We shall hereby concentrate on welfare functions and voting schemes of different kinds and shall discuss these in the light of various criteria such as Arrow’s independence condition, Condorcet consistency, monotonicity, manipulability, and other properties. (shrink)

This paper deals with various connections that are found to exist between statistical estimation methods for decision-making and rules of group choice in the social choice area. Initially the aggregation of individual opinions is formulated as a pattern recognition problem; firstly it is shown that individual preferences lead to a natural representation in terms of binary patterns. Then we proceed to show how the search for a group preference pattern can be conducted by classifying the input preference (...) patterns into various ‘pattern classes’ and using the resulting classification boundaries to define the area of mutual agreement over some of the available alternatives. This leads to a decision-theoretic problem which consists in defining a decision rule (for classification) that is least likely to lead to misrecognition of arbitrary preference patterns. A maximum likelihood solution is obtained and compared with some well-known rules of group decision-making. Other solutions are also possible, on the basis of different optimality criteria, and their social choice interpretation is suggested. Finally, a method using Coleman's linear model for attributes is applied to yield group decision rules by feature weighting of election issues. (shrink)

In this paper, we explore the stability of the aggregation procedure of individual preferences. In particular, we propose the stability under the addition of social preference, which is a normative property of democratic collective decision making. We establish impossibility and possibility theorems for non-dictatorial aggregation procedures.

Consider a group of people whose preferences satisfy the axioms of one of the current versions of utility theory, such as von Neumann-Morgenstern (1944), Savage (1954), or Bolker-Jeffrey (1965). There are political and economic contexts in which it is of interest to find ways of aggregating these individual preferences into a group preference ranking. The question then arises of whether methods of aggregation exist in which the group’s preferences also satisfy the axioms of the chosen utility theory, and (...) in which at the same time the aggregation process satisfies certain plausible conditions (e.g., the Pareto conditions below). (shrink)

It is both a moral tragedy and a travesty of social justice that responses to present unacceptable levels of Greenhouse Gases often involve constraining development, and that the burden of t...

Most approaches to iterated belief revision are accompanied by some motivation for the use of the proposed revision operator (or family of operators), and typically encode enough information in the epistemic state of an agent for uniquely determining one-step revision. But in those approaches describing a family of operators there is usually little indication of how to proceed uniquely after the first revision step. In this paper we contribute towards addressing that deficiency by providing a formal framework which goes beyond (...) the first revision step in two ways. First, the framework is obtained by enriching the epistemic state of an agent starting from the following intuitive idea: we associate to each world x two abstract objects x⁺ and x⁻, and we assume that, in addition to preferences over the set of worlds, we are given preferences over this set of objects as well. The latter can be considered as meta-information encoded in the epistemic state which enables us to go beyond the first revision step of the revision operator being applied, and to obtain a unique set of preferences over worlds. We then extend this framework to consider, not only the revision of preferences over worlds, but also the revision of this extended structure itself. We look at some desirable properties for revising the structure and prove the consistency of these properties by giving a concrete operator satisfying all of them. Perhaps more importantly, we show that this framework has strong connections with two other types of constructions in related areas. Firstly, it can be seen as a special case of preference aggregation which opens up the possibility of extending the frame-work presented here into a full-fledged framework for preference aggregation and social choice theory. Secondly, it is related to existing work on the use of interval orderings in a number of different contexts. (shrink)

How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or (...) an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

:Preference-aggregation problems arise in various contexts. One such context, little explored by social choice theorists, is metaethical. ‘Ideal-advisor’ accounts, which have played a major role in metaethics, propose that moral facts are constituted by the idealized preferences of a community of advisors. Such accounts give rise to a preference-aggregation problem: namely, aggregating the advisors’ moral preferences. Do we have reason to believe that the advisors, albeit idealized, can still diverge in their rankings of a given set (...) of alternatives? If so, what are the moral facts when the advisors do diverge? These questions are investigated here using the tools of Arrovian social choice theory. (shrink)

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)

This paper is concerned with the efficiency of information aggregation in a committee whose members have heterogeneous preferences over a binary decision variable. We study a voting game with a pre-vote communication stage and identify conditions under which full information aggregation is possible. In particular, if preferences are common knowledge and each committee member is endowed with information, full information aggregation is possible despite preference heterogeneity.

Patient preference predictors aim to solve the moral problem of making treatment decisions on behalf of incapacitated patients. This commentary on a case of an unrepresented patient at the end of life considers 3 related problems of such predictors: the problem of restricting the scope of inputs to the models (the “scope” problem), the problem of weighing inputs against one another (the “weight” problem), and the problem of multiple reasonable solutions to the scope and weight problems (the “multiple reasonable (...) models” problem). Each of these problems poses challenges to reliably implementing patient preference predictors in important, high-stakes health care decision making. This commentary also suggests a way forward. (shrink)

My focus is on aggregation of individual value rankings of alternatives to a collective value ranking. This is compared with aggregation o individual prefrences to a collective preference. While in an individual preference ranking the alternatives are ordered in accordance with one’s preferences, the order in a value ranking expresses one’s comparative evaluation of the alternatives, from the best to the worst. I suggest that, despite their formal similarity as rankings, this difference in the nature of (...) individual inputs in two aggregation scenarios has important implications: The kind of procedure that looks fine for aggregation of judgments is inappropriate for aggregation of preferences. The procedure I have in mind consists in similarity maximization, or – more precisely – in minimization of the average distance from individual inputs. When applied to judgment aggregation, this procedure can also be approached from the epistemic perspective: the questions are posed concerning its advantages as a truth-tracker. From that perspective, what matters is not only the probability of the outcome of the procedure being true, but also the expected verisimilitude of the outcome: its expected distance from truth. (shrink)

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

My focus is on aggregation of individual value rankings of alternatives to a collective value ranking. This is compared with aggregation o individual prefrences to a collective preference. While in an individual preference ranking the alternatives are ordered in accordance with one’s preferences, the order in a value ranking expresses one’s comparative evaluation of the alternatives, from the best to the worst. I suggest that, despite their formal similarity as rankings, this difference in the nature of (...) individual inputs in two aggregation scenarios has important implications: The kind of procedure that looks fine for aggregation of judgments is inappropriate for aggregation of preferences. The procedure I have in mind consists in similarity maximization, or – more precisely – in minimization of the average distance from individual inputs. When applied to judgment aggregation, this procedure can also be approached from the epistemic perspective: the questions are posed concerning its advantages as a truth-tracker. From that perspective, what matters is not only the probability of the outcome of the procedure being true, but also the expected verisimilitude of the outcome: its expected distance from truth. (shrink)

This paper criticizes non-constructive uses of set theory in formal economics. The main focus is on results on preference aggregation and Arrow’s theorem for infinite electorates, but the present analysis would apply as well, e.g., to analogous results in intergenerational social choice. To separate justified and unjustified uses of infinite populations in social choice, I suggest a principle which may be called the Hildenbrand criterion and argue that results based on unrestricted axiom of choice do not meet (...) this criterion. The technically novel part of this paper is a proposal to use a set-theoretic principle known as the axiom of determinacy ), not as a replacement for Choice, but simply to eliminate applications of set theory violating the Hildenbrand criterion. A particularly appealing aspect of \ from the point of view of the research area in question is its game-theoretic character. (shrink)

The aggregation of individual judgments on logically connected issues often leads to collective inconsistency. This study examines two collective decision-making procedures designed to avoid such inconsistency—one premise-based and the other conclusion-based. While the relative desirability of the two procedures has been studied extensively from a theoretical perspective, the preference of individuals regarding the two procedures has been less studied empirically. In the present study, a scenario-based questionnaire survey of participant preferences for the two procedures was conducted, taking into (...) consideration prevailing social norms in the society to which the participants belong and the heterogeneity of the participants’ past experiences. Results show that a minority opinion not matching a prevailing social norm is more likely to be supported when the conclusion-based procedure is used. This can be explained by a basic property of the conclusion-based procedure: The procedure does not require voters to reveal their reasons for reaching a particular conclusion. This property proves appealing for participants who have a minority opinion. Such a finding is highly relevant to future studies on strategic behaviors in choosing a collective decision-making procedure. (shrink)

Electoral control refers to attempts by an election's organizer to influence the outcome by adding/deleting/partitioning voters or candidates. The important paper of Bartholdi, Tovey, and Trick [1] that introduces control proposes computational complexity as a means of resisting control attempts: Look for election systems where the chair's task in seeking control is itself computationally infeasible.We introduce and study a method of combining two or more candidate-anonymous election schemes in such a way that the combined scheme possesses all the resistances to (...) control possessed by any of its constituents: It combines their strengths. From this and new resistance constructions, we prove for the first time that there exists a neutral, anonymous election scheme that is resistant to all twenty standard types of electoral control. (shrink)