In this paper I investigate the possibility of a dictatorship in the context of Harsanyi's Social Aggregation Theorem. Preliminarily, some propositions about Harsanyi's Theorem are presented using an alternative principle that I name Quasi-strong Pareto, which is the latter part of Strong Pareto. Then I define dictatorship as a requirement that social preference agrees with a dictator's preference or those of members of dictatorial group even if their preferences strictly contradict those of all other people (...) in the society. Conclusively, although in each version of Harsanyi's Theorem with Pareto Indifference, Weak Preference Pareto or Weak Pareto the social utility function may have a form of dictatorship, however if individuals' vNM utility functions are all 'individualistic' and Quasi-strong Pareto is satisfied, then the dictatorship is excluded. (shrink)

This is a chapter of a collective volume of Rawls's and Harsanyi's theories of distributive justice. It focuses on Harsanyi's important Social Aggregation Theorem and technically reconstructs it as a theorem in welfarist social choice.

Often, when one faces a choice between alternative actions, there are reasons both for and against each alternative. On one way of understanding these words, what one “ought to do all things considered (ATC)” is determined by the totality of these reasons. So, these reasons can somehow be “combined” or “aggregated” to yield an ATC verdict on these alternatives. First, various assumptions about this sort of aggregation of reasons are articulated. Then it is shown that these assumptions allow for (...) the proof of a “Reasons Aggregation Theorem” – parallel to John Harsanyi’s 1955 “Social Aggregation Theorem”. All reasons for action are grounded in reason-providing values; and, for every such reason-providing value, there is in principle a way of measuring how strongly this value counts against each alternative. The theorem tells us that the appropriate measure of how much reason ATC there is against each alternative is simply a weighted sum of the strengths with which these values count against that alternative; the agent ought not ATC to perform an action iff there is ATC more reason against it than against some available alternative. (shrink)

This paper is about the role of interpersonal comparisons in Harsanyi's aggregation theorem. Harsanyi interpreted his theorem to show that a broadly utilitarian theory of distribution must be true even if there are no interpersonal comparisons of well-being. How is this possible? The orthodox view is that it is not. Some argue that the interpersonal comparability of well-being is hidden in Harsanyi's premises. Others argue that it is a surprising conclusion of Harsanyi's theorem, (...) which is not presupposed by any one of the premises. I argue instead that Harsanyi was right: his theorem and its weighted-utilitarian conclusion do not require interpersonal comparisons of well-being. The key to making sense of this possibility is to treat Harsanyi's weights as dimensional constants rather than dimensionless numbers. (shrink)

The purpose of this paper is to show how some of the controversial questions concerning utilitarianism can be clarified by the modelling techniques and the other analytical tools of decision theory (and, sometimes, of game theory). It is suggested that the moral rules of utilitarian ethics have a logical status similar to that of the normative rules (theorems) of such formal normative disciplines as decision theory and game theory.The paper argues that social utility should be defined, not in hedonistic or (...) in ideal-utilitarian terms, but rather in terms of individual preferences, in accordance with the author's equiprobability model of moral value judgments. (shrink)

1.1 In 1955, John Harsanyi proved a remarkable theorem:1 Suppose n agents satisfy the assumptions of von Neumann/Morgenstern (1947) expected utility theory, and so does the group as a whole (or an observer). Suppose that, if each member of the group prefers option a to b, then so does the group, or the observer (Pareto condition). Then the group’s utility function is a weighted sum of the individual utility functions. Despite Harsanyi’s insistence that what he calls the Utilitarian (...) class='Hi'>Theorem embeds utilitarianism into a theory of rationality, the theorem has fallen short of having the kind of impact on the discussion of utilitarianism for which Harsanyi hoped. Yet how could the theorem influence this discussion? Utilitarianism is as attractive to some as it is appalling to others. The prospects for this dispute to be affected by a theorem seem dim. Yet a closer look shows how the theorem could make a contribution. To fix ideas, I understand by utilitarianism the following claims: (1) Consequentialism: Actions are evaluated in terms of their consequences only. (2) Bayesianism: An agent's beliefs about possible outcomes are captured probabilistically. (3) Welfarism: The judgement of the relative goodness of states of affairs is based.. (shrink)

A necessary and sufficient condition for linear aggregation of SSB utility functionals is presented. Harsanyi's social aggregation theorem for von Neumann–Morgenstern utility functions is shown to be a corollary to this result. Two generalizations of Fishburn and Gehrlein's conditional linear aggregation theorem for SSB utility functionals are also established.

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then (...) shown to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (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)

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but (...) achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs. (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)

The article is a plea for ethicists to regard probability as one of their most important concerns. It outlines a series of topics of central importance in ethical theory in which probability is implicated, often in a surprisingly deep way, and lists a number of open problems. Topics covered include: interpretations of probability in ethical contexts; the evaluative and normative significance of risk or uncertainty; uses and abuses of expected utility theory; veils of ignorance; Harsanyi’s aggregation theorem; population (...) size problems; equality; fairness; giving priority to the worse off; continuity; incommensurability; nonexpected utility theory; evaluative measurement; aggregation; causal and evidential decision theory; act consequentialism; rule consequentialism; and deontology. (shrink)

This paper proves two theorems for homogeneous juries that arise from different solutions to the problem of aggregation of dichotomous choice. In the first theorem, negative correlation increases the competence of the jury, while positive correlation has the opposite effect. An enlargement of the jury with positive correlation can be detrimental up to a certain size, beyond which it becomes beneficial. The second theorem finds a family of distributions for which correlation has no effect on a jury’s (...) competence. The approach allows us to compute the bounds on a jury’s competence as the maximum and minimum probability of it being correct for a given individual competence and dependence structure. (shrink)

The book-making argument was introduced by de Finetti as a principle to prove the existence and uniqueness of subjective probabilities. It has subsequently been accepted as a principle of rationality for decisions under uncertainty. This note shows that the book-making argument has relevant applications to welfare: it gives a new foundation for utilitarianism that is alternative to Harsanyi’s, it generalizes foundations based on the theorem of the alternative, and it avoids arguments based on expected utility.

This chapter of the Handbook of Utility Theory aims at covering the connections between utility theory and social ethics. The chapter first discusses the philosophical interpretations of utility functions, then explains how social choice theory uses them to represent interpersonal comparisons of welfare in either utilitarian or non-utilitarian representations of social preferences. The chapter also contains an extensive account of John Harsanyi's formal reconstruction of utilitarianism and its developments in the later literature, especially when society faces uncertainty rather than (...) probabilistic risk. (shrink)

This paper re-examines the welfare economics of risk. It singles out a class of criteria, the “expected equally-distributed equivalent”, as the unique class which avoids serious drawbacks of existing approaches. Such criteria behave like ex-post criteria when the final statistical distribution of wellbeing is known ex ante, and like ex-ante criteria when risk generates no inequality. The paper also provides a new result on the tension between inequality aversion and respect of individual ex ante preferences, in the vein of Harsanyi’s (...) aggregation theorem. (shrink)

Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory. We do this in two frameworks: an Arrovian framework with a fixed population and no interpersonal comparisons, and a generalized framework with variable populations and full interpersonal comparability. In each framework we use extensive measurement to introduce novel domain restrictions, independence (...) conditions, and constraints on social evaluation. We prove a welfarism theorem for these domains and characterize the social welfare functions that satisfy the axioms of extensive measurement at both the individual and social levels. The main results are simple axiomatizations of strong dictatorship in the Arrovian framework and classical utilitarianism in the generalized framework. (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)

Risky prospects represent policies that impose different types of risks on multiple people. I present an example from food safety. A utilitarian following Harsanyi's Aggregation Theorem ranks such prospects according to their mean expected utility or the expectation of the social utility. Such a ranking is not sensitive to any of four types of distributional concerns. I develop a model that lets the policy analyst rank prospects relative to the distributional concerns that she considers fitting in the (...) context at hand. I name this model ‘the Distribution View’ posing an alternative to Parfit's Priority View for risky prospects. (shrink)

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems (...) are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity. (shrink)

The publication in English of Karl R. Popper's The Logic of Scientific Discovery twenty-five years after the appearance of the German original, is an important event. At the time when many philosophers questioned the cognitive value of scientific hypotheses , Popper has shown how to reconcile the free use of bold explanatory hypotheses with an insistence on empirical testing. Many of Popper's views have now been accepted even by most of his earlier opponents, which is no small tribute to a (...) philosopher who had challenged an important current of opinion. But, though the basic aspects of Popper's theory have attracted considerable attention in recent years, some of his finer points have received insufficient discussion. It is hoped that the publication of this important book in English translation will now help to remedy this situation. (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)

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)

The paper first summarizes the author's decision-theoretical model of moral behavior, in order to compare the moral implications of the act-utilitarian and of the rule-utilitarian versions of utilitarian theory. This model is then applied to three voting examples. It is argued that the moral behavior of act-utilitarian individuals will have the nature of a noncooperative game, played in the extensive mode, and involving action-by-action maximization of social utility by each player. In contrast, the moral behavior of rule-utilitarian individuals will have (...) the nature of a cooperative game, played in the normal mode, and involving a firm commitment by each player to a specific moral strategy (viz. to the strategy selected by the rule-utilitarian choice criterion) — even if some individual actions prescribed by this strategy, when considered in isolation, should fail to maximize social utility. The most important advantage that rule utilitarianism as an ethical theory has over act utilitarianism lies in its ability to give full recognition to the moral and social importance of individual rights and personal obligations. It is easy to verify that action-by-action maximization of social utility, as required by act utilitarianism, would destroy these rights and obligations. In contrast, rule utilitarianism can fully recognize the moral validity of these rights and obligations precisely because of its commitment to an overall moral strategy, independent of action-by-action social-utility maximization. The paper ends with a discussion of the voter's paradox problem. The conventional theory of rational behavior cannot avoid the paradoxical conclusion that, in any large electorate, voting is always an irrational activity because one's own individual vote is extremely unlikely to make any difference to the outcome of any election. But it can be shown that, by using the principles of rule-utilitarian theory, this paradox can easily be resolved and that, in actual fact, voting, even in large electorates, may be perfectly rational action. More generally, the example of rule utilitarianism shows what an important role the concept of a rational commitment can play in the analysis of rational behavior. (shrink)

When von Neumann's and Morgenstern's Theory of Games and Economic Behavior appeared in 1944, one thought that a complete theory of strategic social behavior had appeared out of nowhere. However, game theory has, to this very day, remained a fast-growing assemblage of models which have gradually been united in a new social theory - a theory that is far from being completed even after recent advances in game theory, as evidenced by the work of the three Nobel Prize winners, John (...) F. Nash, John C. Harsanyi, and Reinhard Selten. Two of them, Harsanyi and Selten, have contributed important articles to the present volume. This book leaves no doubt that the game-theoretical models are on the right track to becoming a respectable new theory, just like the great theories of the twentieth century originated from formerly separate models which merged in the course of decades. For social scientists, the age of great discover ies is not over. The recent advances of today's game theory surpass by far the results of traditional game theory. For example, modem game theory has a new empirical and social foundation, namely, societal experiences; this has changed its methods, its "rationality. " Morgenstern (I worked together with him for four years) dreamed of an encompassing theory of social behavior. With the inclusion of the concept of evolution in mathematical form, this dream will become true. Perhaps the new foundation will even lead to a new name, "conflict theory" instead of "game theory. (shrink)

Drawing on the so-called “doctrinal paradox”, List and Pettit (2002) have shown that, given an unrestricted domain condition, there exists no procedure for aggregating individual sets of judgments over multiple interconnected propositions into corresponding collective ones, where the procedure satisfies some minimal conditions similar to the conditions of Arrow’s theorem. I prove that we can avoid the paradox and the associated impossibility result by introducing an appropriate domain restriction: a structure condition, called unidimensional alignment, is shown to open up (...) a possibility result, similar in spirit to Black’s median voter theorem. Specifically, I prove that, given unidimensional alignment, propositionwise majority voting is the unique procedure for aggregating individual sets of judgments into collective ones in accordance with the above mentioned minimal conditions. (shrink)

We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (2)uncertain social (...) prospects, (3)uncertain individual prospects. Concerning(1), we propose a finite horizon variant of Koopmans’s (1960) axiomatization of infinite discounted utility sums. The main results concern(2). We push the classic comparison between the exanteand expostsocial welfare criteria one step further by avoiding any expected utility assumptions, and as a consequence obtain what appears to be the strongest existing form of Harsanyi’s (1955) Aggregation Theorem. Concerning(3), we derive a subjective probability for Anscombe and Aumann’s (1963) finite case by merely assuming that there are two epistemically independent sources of uncertainty. (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.

Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann-Morgenstern utilities, he has done nothing to establish any con- nection between the notion of von Neumann-Morgenstern utility and that of well-being, and hence that utilitarianism does not follow. The present article defends Harsanyi against the Sen-Weymark (...) cri- tique. I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann-Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked. (shrink)

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

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)

Limited Aggregation is the view that when there are competing moral claims that demand our attention, we should sometimes satisfy the largest aggregate of claims, depending on the strength of the claims in question. In recent years, philosophers such as Patrick Tomlin and Alastair Norcross have argued that Limited Aggregation violates a number of rational choice principles such as Transitivity, Separability, and Contraction Consistency. Current versions of Limited Aggregation are what may be called Comparative Approaches because they (...) involve assessing the relative strengths of various claims. In this paper, we offer a non-comparative version of Limited Aggregation, what we call the Threshold Approach. It states that there is a non-relative threshold that separates various claims. We demonstrate that the Threshold Approach does not violate rational choice principles such as Transitivity, Separability, and Contraction Consistency, and we show that potential concerns regarding such a view are surmountable. (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)

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)

Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann–Morgenstern utilities, he has done nothing to establish any connection between the notion of von Neumann–Morgenstern utility and that of well-being, and hence that utilitarianism does not follow. -/- The present article defends Harsanyi against the Sen–Weymark (...) critique. I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann–Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked. (shrink)

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)

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)

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow’s Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (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)

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)