Following a long-standing philosophical tradition, impartiality is a distinctive and determining feature of moral judgments, especially in matters of distributive justice. This broad ethical tradition was revived in welfare economics by Vickrey, and above all, Harsanyi, under the form of the so-called Impartial Observer Theorem. The paper offers an analytical reconstruction of this argument and a step-wise philosophical critique of its premisses. It eventually provides a new formal version of the theorem based on subjective probability.

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)

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 chapter briefly reviews the present state of judgment aggregation theory and tentatively suggests a future direction for that theory. In the review, we start by emphasizing the difference between the doctrinal paradox and the discursive dilemma, two idealized examples which classically serve to motivate the theory, and then proceed to reconstruct it as a brand of logical theory, unlike in some other interpretations, using a single impossibility theorem as a key to its technical development. In the prospective part, (...) having mentioned existing applications to social choice theory and computer science, which we do not discuss here, we consider a potential application to law and economics. This would be based on a deeper exploration of the doctrinal paradox and its relevance to the functioning of collegiate courts. On this topic, legal theorists have provided empirical observations and theoretical hints that judgment aggregation theorists would be in a position to clarify and further elaborate. As a general message, the chapter means to suggest that the future of judgment aggregation theory lies with its applications rather than its internal theoretical development. (shrink)

The aim of this article is to introduce the theory of judgment aggregation, a growing interdisciplinary research area. The theory addresses the following question: How can a group of individuals make consistent collective judgments on a given set of propositions on the basis of the group members' individual judgments on them? I begin by explaining the observation that initially sparked the interest in judgment aggregation, the so-called "doctinal" and "discursive paradoxes". I then introduce the basic formal model of (...) judgment aggregation, which allows me to present some illustrative variants of a generic impossibility result. I subsequently turn to the question of how this impossibility result can be avoided, going through several possible escape routes. Finally, I relate the theory of judgment aggregation to other branches of aggregation theory. Rather than offering a comprehensive survey of the theory of judgment aggregation, I hope to introduce the theory in a succinct and pedagogical way, providing an illustrative rather than exhaustive coverage of some of its key ideas and results. (shrink)

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)

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)

Antimicrobial resistance (AMR) is a global public health disaster driven largely by antibiotic use in human health care. Doctors considering whether to prescribe antibiotics face an ethical conflict between upholding individual patient health and advancing public health aims. Existing literature mainly examines whether patients awaiting consultations desire or expect to receive antibiotic prescriptions, but does not report views of the wider public regarding conditions under which doctors should prescribe antibiotics. It also does not explore the ethical significance of public views (...) or their sensitivity to awareness of AMR risks or the standpoint (self-interested or impartial) taken by participants. Methods: An online survey was conducted with a sample of the U.S. public (n = 158). Participants were asked to indicate what relative priority should be given to individual patients and society-at-large from various standpoints and in various contexts, including antibiotic prescription. Results: Of the participants, 50.3% thought that doctors should generally prioritize individual patients over society, whereas 32.0% prioritized society over individual patients. When asked in the context of AMR, 39.2% prioritized individuals whereas 45.5% prioritized society. Participants were significantly less willing to prioritize society over individuals when they themselves were the patient, both in general (p = .001) and in relation to AMR specifically (p = .006). Conclusions: Participants’ attitudes were more oriented to society and sensitive to collective responsibility when informed about the social costs of antibiotic use and when considered from a third-person rather than first-person perspective. That is, as participants came closer to taking the perspective of an informed and impartial “ideal observer,” their support for prioritizing society increased. Our findings suggest that, insofar as antibiotic policies and practices should be informed by attitudes that are impartial and well-informed, there is significant support for prioritizing society. (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)

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation.

[First published in Italian as: “L’irreligione e lo spettatore imparziale nel sistema morale di Adam Smith”, in Rivista di Filosofia 3 (3):375-403 (2005). -/- Translated by E. Lecaldano.] -/- A number of commentators on Smith’s philosophy have observed that the relationship between his moral theory and his theological beliefs is “exceedingly difficult to unravel.” The available evidence, as generally presented, suggests that although Smith was not entirely orthodox by contemporary standards, he has no obvious or significant irreligious commitments or orientation. (...) Contrary to this view of things, this essay argues that behind the veneer of orthodoxy that covers Smith’s discussion in The Theory of the Moral Sentiments there are significant irreligious themes present in his work. -/- . (shrink)

How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove (...) two new theorems. Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete, arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping profiles of consistent individual judgment sets to consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation function that is "neutral" between the acceptance and rejection of each proposition is dictatorial. We relate this theorem to (...) the literature. (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)

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)

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)

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to (...) give the latter its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. (shrink)

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)

Garrett Cullity contends that fairness is appropriate impartiality (See Cullity (2004) Chapters 8 and 10 and Cullity (2008)). Cullity deploys his account of fairness as a means of limiting the extreme moral demand to make sacrifices in order to aid others that was posed by Peter Singer in his seminal article ‘Famine, Affluence and Morality’. My paper is founded upon the combination of (1) the observation that the idea that fairness consists in appropriate impartiality is very vague and (2) the (...) fact that psychological studies show the self-serving bias is especially likely to infect one’s judgements when the ideas involved are vague. I argue that Cullity’s solution to extreme moral demandingness is threatened by these findings. I then comment on whether some other theories of fairness are vulnerable to the same objection. (shrink)

I build on Adam Smith’s account of the impartial spectator in The Theory of Moral Sentiments in order to offer a modest ideal observer theory of moral judgment that is adequate in the following sense: the account specifies the hypothetical conditions that guarantee the authoritativeness of an agent’s (or agents’) responses in constituting the standard in question, and, if an actual agent or an actual community of agents are not under those conditions, their responses are not authoritative in (...) setting this standard. However, in the account that I provide, the hypothetical conditions can themselves be constructed from the psychology and interactions of actual human beings. In other words, facts about the morally appropriate and inappropriate are determined from hypothetical conditions that––while agents in a given society might have yet to attain them––can be constructed from those agents’ shared experiences. Thus, the account offers both an attainable standard of moral judgment and a standard that can transcend the biases of the society which gave rise to it. I also defend the account against three challenges: (a) ideal observer theories do not offer the right kind of motivation to act on the verdicts of the ideal observer; (b) ideal observer theories cannot explain why the idealization in question is well-motivated and not objectionably ad hoc; (c) the standard used in ideal observer theories cannot be defended upon further reflection, because we would need a non-arbitrary, second-order standard to govern our reflection on the first-order standard of moral judgment. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than (...) “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

This paper applies ideas and tools from social choice theory (such as Arrow's theorem and related results) to linguistics. Specifically, the paper investigates the problem of constraint aggregation in optimality theory from a social-choice-theoretic perspective.

The motivating question of this paper is: ‘How are our beliefs in the theorems of mathematics justified?’ This is distinguished from the question ‘How are our mathematical beliefs reliably true?’ We examine an influential answer, outlined by Russell, championed by Gödel, and developed by those searching for new axioms to settle undecidables, that our mathematical beliefs are justified by ‘intuitions’, as our scientific beliefs are justified by observations. On this view, axioms are analogous to laws of nature. They are (...) postulated to best systematize the data to be explained. We argue that there is a decisive difference between the cases. There is agreement on the data to be systematized in the scientific case that has no analog in the mathematical one. There is virtual consensus over observations, but conspicuous dispute over intuitions. In this respect, mathematics more closely resembles stereotypical philosophy. We conclude by distinguishing two ideas that have long been associated -- realism (the idea that there is an independent reality) and objectivity (the idea that in a disagreement, only one of us can be right). We argue that, while realism is true of mathematics and philosophy, these domains fail to be objective. One upshot of the discussion is that even questions of fundamental physics may fail to be objective in roughly the sense that the question, ‘Is the Parallel Postulate is true?’, understood as one of pure mathematics, fails to be. Another is a kind of pragmatism. Factual questions in mathematics, modality, logic, and evaluative areas go proxy for non-factual practical ones. -/- . (shrink)

Dutch book and accuracy arguments are used to justify certain rationality constraints on credence functions. Underlying these Dutch book and accuracy arguments are associated theorems, and I show that the interpretation of these theorems can vary along a range of dimensions. Given that the theorems can be interpreted in a variety of different ways, what is the status of the associated arguments? I consider three possibilities: we could aggregate the results of the differently interpreted theorems in (...) some way, and motivate rationality constraints based on this aggregation; we could be permissive, and accept the conclusions of the Dutch book and accuracy arguments under all interpretations of the associated theorems; or we could select one uniquely correct interpretation of the Dutch book or accuracy theorem, and use that to justify certain rationality constraints. I show that each possibility faces problems, and conclude that Dutch book and accuracy theorems cannot be used to justify any principle of rationality. (shrink)

The problem of multiple-computations discovered by Hilary Putnam presents a deep difficulty for functionalism (of all sorts, computational and causal). We describe in out- line why Putnam’s result, and likewise the more restricted result we call the Multiple- Computations Theorem, are in fact theorems of statistical mechanics. We show why the mere interaction of a computing system with its environment cannot single out a computation as the preferred one amongst the many computations implemented by the system. We explain why (...) nonreductive approaches to solving the multiple- computations problem, and in particular why computational externalism, are dualistic in the sense that they imply that nonphysical facts in the environment of a computing system single out the computation. We discuss certain attempts to dissolve Putnam’s unrestricted result by appealing to systems with certain kinds of input and output states as a special case of computational externalism, and show why this approach is not workable without collapsing to behaviorism. We conclude with some remarks about the nonphysical nature of mainstream approaches to both statistical mechanics and the quantum theory of measurement with respect to the singling out of partitions and observables. (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 has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments (...) in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (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)

The new …eld of judgment aggregation aims to …nd collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which (...) decide propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic. (shrink)

We propose a formal framework to examine the relationship between models and observations. To make our analysis precise,models are reduced to first-order theories that represent both terminological knowledge – e.g., the laws that are supposed to regulate the domain under analysis and that allow for explanations, predictions, and simulations – and assertional knowledge – e.g., information about specific entities in the domain of interest. Observations are introduced into the domain of quantification of a distinct first-order theory that describes their nature (...) and their organization and takes track of the way they are experimentally acquired or intentionally elaborated. A model mainly represents the theoretical knowledge or hypotheses on a domain, while the theory of observations mainly represents the empirical knowledge and the given experimental practices. We propose a precise identity criterion for observations and we explore different links between models and observations by assuming a degree of independence between them. By exploiting some techniques developed in the field of social choice theory and judgment aggregation, we sketch some strategies to solve inconsistencies between a given set of observations and the assumed theoretical hypotheses. The solutions of these inconsistencies can impact both the observations – e.g., the theoretical knowledge and the analysis of the way observations are collected or produced may highlight some unreliable sources – and the models – e.g. empirical evidences may invalidate some theoretical laws. (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)

Suppose we can save either a larger group of persons or a distinct, smaller group from some harm. Many people think that, all else equal, we ought to save the greater number. This article defends this view (with qualifications). But unlike earlier theories, it does not rely on the idea that several people's interests or claims receive greater aggregate weight. The argument starts from the idea that due to their stakes, the affected people have claims to have a say in (...) the rescue decision. As rescuers, our primary duty is to respect these procedural claims, which we must do by doing what these people would decide, in a process where each is given an equal vote on the matter. So in cases where each votes in their own self-interest, respect for their equal right to decide, or their autonomy, will lead us to save the greater number. The argument is explained in detail, with special attention to the questions of how, exactly, it avoids aggregation, and of why majority rule is superior to lottery procedures. The view has further advantages. Especially, it explains the “partial” relevance of numbers in cases involving unequal harms, and it does so in a way that dissolves the appearance of paradox that besets theories of “partial aggregation.”. (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)

Bell’s theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell’s theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant entangled system. Einstein was repulsed by such “spooky action at a distance” (...) and was led to question whether quantum mechanics could provide a complete description of physical reality. In this paper I argue that quantum mechanics does not require spooky action at a distance of any kind and yet it is entirely reasonable to question the assumption that quantum mechanics can provide a complete description of physical reality. The magic of entangled quantum states has little to do with entanglement and everything to do with superposition, a property of all quantum systems and a foundational tenet of quantum mechanics. (shrink)

Buddhism originated and developed in an Indian cultural context that featured many first-person practices for producing and exploring states of consciousness through the systematic training of attention. In contrast, the dominant methods of investigating the mind in Western cognitive science have emphasized third-person observation of the brain and behavior. In this chapter, we explore how these two different projects might prove mutually beneficial. We lay the groundwork for a cross-cultural cognitive science by using one traditional Buddhist model of the mind (...) – that of the five aggregates – as a lens for examining contemporary cognitive science conceptions of consciousness. (shrink)

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which (...) there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a). (shrink)

The Buddhist denial of the world seems hard to defend if it is confronted with empirical data. Surveys on subjective life satisfaction consistently report that the majority is satisfied with their lives. Is the desire to escape from the cycle of rebirth a sign of risk-aversion or even irrationality? How would an impartial observer evaluate the world? -/- An impartial view is achieved by interpreting the surveys on life satisfaction as probability distributions for life’s risks and chances. (...) It turns out that there is no indisputable metric for measuring risks and no reliable forecast. Given this uncertainty the denial of the world cannot easily be dismissed as being irrational. (shrink)

A probability aggregation rule assigns to each profile of probability functions across a group of individuals (representing their individual probability assignments to some propositions) a collective probability function (representing the group's probability assignment). The rule is “non-manipulable” if no group member can manipulate the collective probability for any proposition in the direction of his or her own probability by misrepresenting his or her probability function (“strategic voting”). We show that, except in trivial cases, no probability aggregation rule satisfying (...) two mild conditions (non-dictatorship and consensus preservation) is non-manipulable. (shrink)

The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic (...) decision problems can be represented in it. This includes decision problems expressed in languages of classical propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems. (shrink)

In this essay a quantum-dualistic, perspectival and synchronistic interpretation of quantum mechanics is further developed in which the classical world-from-decoherence which is perceived (decoherence) and the perceived world-in-consciousness which is classical (collapse) are not necessarily identified. Thus, Quantum Reality or "{\it unus mundus}" is seen as both i) a physical non-perspectival causal Reality where the quantum-to-classical transition is operated by decoherence, and as ii) a quantum linear superposition of all classical psycho-physical perspectival Realities which are governed by synchronicity as well (...) as causality (corresponding to classical first-person observes who actually populate the world). This interpretation is termed the Nietzsche-Jung-Pauli interpretation and is a re-imagining of the Wigner-von Neumann interpretation which is also consistent with some reading of Bohr's quantum philosophy. (shrink)

According to a theorem recently proved in the theory of logical aggregation, any nonconstant social judgment function that satisfies independence of irrelevant alternatives (IIA) is dictatorial. We show that the strong and not very plausible IIA condition can be replaced with a minimal independence assumption plus a Pareto-like condition. This new version of the impossibility theorem likens it to Arrow’s and arguably enhances its paradoxical value.

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)

The purpose of this paper is to illustrate, formally, an ambiguity in the exercise of political influence. To wit: A voter might exert influence with an eye toward maximizing the probability that the political system (1) obtains the correct (e.g. just) outcome, or (2) obtains the outcome that he judges to be correct (just). And these are two very different things. A variant of Condorcet's Jury Theorem which incorporates the effect of influence on group competence and interdependence is developed. Analytic (...) and numerical results are obtained, the most important of which is that it is never optimal--from the point-of-view of collective accuracy--for a voter to exert influence without limit. He ought to either refrain from influencing other voters or else exert a finite amount of influence, depending on circumstance. Philosophical lessons are drawn from the model, to include a solution to Wollheim's "Paradox in the Theory of Democracy". (shrink)

Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agendas of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without requiring systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or effectively dictatorial if we remove one of the agenda conditions). Our agenda (...) conditions are tight. When applied illustratively to (strict) preference aggregation represented in our model, the result implies that every unbiased social welfare function with universal domain is effectively dictatorial. (shrink)

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by (...) identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, (...) we seek to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

It is not by thinking that we create worlds. It is by understanding the world that we learn to think. Cosmovision is a term that should mean a set of foundations from which emerges a systemic understanding of the Universe, its components as life, the world we live in, nature, human phenomena, and their relationships. It is, therefore, a field of analytical philosophy fed by the sciences, whose objective is this aggregated and epistemologically sustainable knowledge about everything that we are (...) and contain, that surrounds us, and that relates to us in any way. It is something as old as human thought, and, in addition to using elements of scientific cosmology, it encompasses everything in philosophy and science that refers to the universe and life. A cosmovision is not a set of ideas, hypotheses, and assumptions but a system based on observation, analysis, evidence, and demonstration. No cosmovision intends to define, establish, or propose but only to understand, analyse, and interpret. Each of us builds and transports his cosmovision throughout life, without establishing forms, as a background for our thinking and behaviour. Linguistically, the term “cosmovision” would derive from the German, equivalent to the concept of “ Weltanschauung,” as used by several philosophers. However, this linguistic relationship is not applicable because it contradicts what we propose as a cosmovision. This German word refers to a pre-logical or proto- experimental vision of reality, with an intuitive context and far from critical knowledge still non-existent at the time of its formulation. Undoubtedly, cosmovisions, in the sense in which we understand them, house and use these proto-experimental or pre-logical elements that include history, the collective unconscious, and all the archetypes we carry. However, in the concept that we apply here, the cosmovision goes far beyond this content, firstly by constantly submitting it to present critical thinking, and finally by making the analytic experience ( and not the thought itself or intuition) its actual universe. António Lopes expose the breadth of this content: -/- "Cosmovisions are not the product of thought. They do not spring from the simple desire to know. The apprehension of reality is an important moment in its configuration, but, nevertheless, it is only one. It comes from the vital conduct, from the experience of life's evaluation, and from the structure of our psychic totality. The elevation of life to consciousness in the knowledge of reality, in the valuation, and in the volitional reality is the slow and arduous work that humanity has done in the development of the conceptions of life. (W. Dilthey, 1992 [1911]: 120)”(1) -/- In this work, we seek to outline a cosmovision based on the realities that science offers today. We do not propose, at any time, to do science; or theorise philosophy, but we will always seek to be supported by them or, at least, protected by them from the cognitive distortions that we usually carry. ________________________________________________ (1) Lopes , Antonio – “ Weltanschauung (Cosmovision)” (2009 ) in Carlos Ceia's E-Dictionary of Literary Terms. -/- . (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.

Suppose the members of a group (e.g., committee, jury, expert panel) each form a judgment on which worlds in a given set are possible, subject to the constraint that at least one world is possible but not all are. The group seeks to aggregate these individual judgments into a collective judgment, subject to the same constraint. I show that no judgment aggregation rule can solve this problem in accordance with three conditions: “unanimity,” “independence” and “non-dictatorship,” Although the result is (...) a variant of an existing theorem on “group identification” (Kasher and Rubinstein, Logique et Analyse 160:385–395, 1997), the aggregation of judgments on which worlds are possible (or permissible, desirable, etc.) appears not to have been studied yet. The result challenges us to take a stance on which of its conditions to relax. (shrink)