For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...) separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (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)

Limited aggregationists argue that when deciding between competing claims to aid we are sometimes required and sometimes forbidden from aggregating weaker claims to outweigh stronger claims. Joe Horton presents a ‘fatal dilemma’ for these views. Views that land on the First Horn of his dilemma suggest that a previously losing group strengthened by fewer and weaker claims can be more choice-worthy than the previously winning group strengthened by more and stronger claims. Views that land on the Second Horn suggest that (...) combining two losing groups together and two winning groups together can turn the losing groups into the winning groups and the winning groups into the losing groups. This paper demonstrates that the ‘fatal dilemma’ is neither fatal nor a dilemma. The First Horn is devastating but avoidable and the Second Horn is unavoidable but not devastating. Nevertheless, Horton’s argument does help to narrow down the acceptable range of views. (shrink)

Aggregative moral theories face a series of devastating problems when we apply them in a physically realistic setting. According to current physics, our universe is likely _infinitely large_, and will contain infinitely many morally valuable events. But standard aggregative theories are ill-equipped to compare outcomes containing infinite total value so, applied in a realistic setting, they cannot compare any outcomes a real-world agent must ever choose between. This problem has been discussed extensively, and non-standard aggregative theories proposed to overcome it. (...) This paper addresses a further problem of similar severity. Physics tells us that, in our universe, how remotely in time an event occurs is _relative_. But our most promising aggregative theories, designed to compare outcomes containing infinitely many valuable events, are sensitive to how remote in time those events are. As I show, the evaluations of those theories are then relative too. But this is absurd; evaluations of outcomes must be absolute. So we must reject such theories. Is this objection fatal for all aggregative theories, at least in a relativistic universe like ours? I demonstrate here that, by further modifying these theories to fit with the physics, we can overcome it. (shrink)

In this article, I firstly discuss why a prioritarian clause can rescue the utilitarian doctrine from the risk of exacerbating inequality in the distribution of resources in those cases in which utility of income does not decline at the margin. Nonetheless, when in the presence of adaptive preferences, classic prioritarianism is more likely than utilitarianism to increase the inequality of resources under all circumstances, independently of the diminishing trend of utility. Hence, I propose to shift the informational focus (...) of prioritarianism from welfare to either social income or capabilities in order to safeguard those who are worse off. Following this, I argue that we may have reasons to limit the aggregative logic of priority-amended utilitarianism through one or more sufficiency thresholds, and that we can partially defuse the negative-thesis objection that is usually levelled against sufficientarianism, provided we interpret the threshold(s) as valid only as long as everyone is led above it. (shrink)

Desire', 'preference', 'utility', '(utility-aggregating) moral desirability' are terms that build on each other in this order. The article follows this definitional structure and presents these terms and their justifications. The aim is to present welfare-ethical criteria of the common good that define 'moral desirability' as an aggregation, e.g. addition, of individual utility: utilitarianism, utility egalitarianism, leximin, prioritarianism.

One of the standard approaches to the metaphysics of personal identity has some counter-intuitive ethical consequences when combined with maximising consequentialism and a plausible doctrine about aggregation of consequences. This metaphysical doctrine is the so-called ‘multiple occupancy’ approach to puzzles about fission and fusion. It gives rise to a new version of the ‘utility monster’ problem, particularly difficult problems about infinite utility, and a new version of a Parfit-style ‘repugnant conclusion’. While the article focuses on maximising consequentialism (...) for simplicity, the problems demonstrated apply more widely to a range of ethical views, especially flavours of consequentialism. This article demonstrates how these problems arise, and discusses a number of options available in the light of these problems for a consequentialist tempted by a multiple occupancy metaphysics. (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)

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)

Mechanisms for QoS provisioning in communication networks range from flow-based resource reservation schemes, providing QoS guarantees, through QoS differentiation based on reservation aggregation techniques to adaptation of applications, compensating for incomplete reservations. Scalable, aggregation-based reservations can also be combined with adaptations for a more flexible and robust overall QoS provisioning. Adaptation is particularly important in wireless networks, where reservations schemes are more difficult to realize. It is widely accepted that usability of Cellular or Mobile IP can be largely (...) improved if adaptation is incorporated. Adaptation, in turn, depends on coding techniques involved and on user requirements. Those impose certain preferences and ordering relations on QoS hierarchies or degradation paths to be followed along when adaptation is performed. With the advent of MPEG4 coding techniques, more sophisticated adaptation schemes are more likely to be supported in the future. (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)

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)

We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising has increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular (...) group in question? According to the credal judgement aggregation principle, linear pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this chapter, I give an argument for linear pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

The social welfare functional approach to social choice theory fails to distinguish a genuine change in individual well-beings from a merely representational change due to the use of different measurement scales. A generalization of the concept of a social welfare functional is introduced that explicitly takes account of the scales that are used to measure well-beings so as to distinguish between these two kinds of changes. This generalization of the standard theoretical framework results in a more satisfactory formulation of welfarism, (...) the doctrine that social alternatives are evaluated and socially ranked solely in terms of the well-beings of the relevant individuals. This scale-dependent form of welfarism is axiomatized using this framework. The implications of this approach for characterizing classes of social welfare orderings are also considered. (shrink)

This paper (first published under the same title in Journal of Mathematical Economics, 29, 1998, p. 331-361) is a sequel to "Consistent Bayesian Aggregation", Journal of Economic Theory, 66, 1995, p. 313-351, by the same author. Both papers examine mathematically whether the the following assumptions are compatible: the individuals and the group both form their preferences according to Subjective Expected Utility (SEU) theory, and the preferences of the group satisfy the Pareto principle with respect to those of the (...) individuals. While the 1995 paper explored these assumptions in the axiomatic context of Savage's (1954-1972) SEU theory, the present paper explores them in the context of Anscombe and Aumann's (1963) alternative SEU theory. We first show that the problematic assumptions become compatible when the Anscombe-Aumann utility functions are state-dependent and no subjective probabilities are elicited. Then we show that the problematic assumptions become incompatible when the Anscombe-Aumann utility functions are state-dependent, like before, but subjective probabilities are elicited using a relevant technical scheme. This last result reinstates the impossibilities proved by the 1995 paper, and thus shows them to be robust with respect to the choice of the SEU axiomatic framework. The technical scheme used for the elicitation of subjective probabilities is that of Karni, Schmeidler and Vind (1983). (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)

Scale-based models of weighing reasons face challenges concerning the context sensitivity of weight, the aggregation of weight, and the methodology for determining what the weights of reasons are. I resolve these challenges.

This paper develops and explores a new framework for theorizing about the measurement and aggregation of well-being. It is a qualitative variation on the framework of social welfare functionals developed by Amartya Sen. In Sen’s framework, a social or overall betterness ordering is assigned to each profile of real-valued utility functions. In the qualitative framework developed here, numerical utilities are replaced by the properties they are supposed to represent. This makes it possible to characterize the measurability and interpersonal (...) comparability of well-being directly, without the use of invariance conditions, and to distinguish between real changes in well-being and merely representational changes in the unit of measurement. The qualitative framework is shown to have important implications for a range of issues in axiology and social choice theory, including the characterization of welfarism, axiomatic derivations of utilitarianism, the meaningfulness of prioritarianism, the informational requirements of variable-population ethics, the impossibility theorems of Arrow and others, and the metaphysics of value. (shrink)

Faced with the choice between saving one person and saving two others, what should we do? It seems intuitively plausible that we ought to save the two, and many forms of consequentialists offer a straightforward rationale for the intuition by appealing to interpersonal aggregation. But still many other philosophers attempt to provide a justification for the duty to save the greater number without combining utilities or claims of separate individuals. I argue against one such attempt proposed by Iwao Hirose. (...) Despite being consequentialist, his argument is aggregation-free since it relies on a non-aggregative value judgement method, instead of interpersonal aggregation, to establish that (other things being equal) a state of affairs is better when more people survive therein. I do not take issue with its consequentialist element; rather, I claim that there is no good reason to adopt the method in question, and thus no good reason to be moved by his argument overall. What we are in search of is not merely a logically possible method that can produce the conclusion that we already want, but one that we have good reason to adopt. Hirose's argument elegantly demonstrates how it could possibly be true that it is right to save the greater number; but it fails to show that we have reason to believe so - even when we do not combine the interests of different individuals. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background (...) uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the (...) Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81. (shrink)

Interactions between an intelligent software agent and a human user are ubiquitous in everyday situations such as access to information, entertainment, and purchases. In such interactions, the ISA mediates the user’s access to the content, or controls some other aspect of the user experience, and is not designed to be neutral about outcomes of user choices. Like human users, ISAs are driven by goals, make autonomous decisions, and can learn from experience. Using ideas from bounded rationality, we frame these interactions (...) as instances of an ISA whose reward depends on actions performed by the user. Such agents benefit by steering the user’s behaviour towards outcomes that maximise the ISA’s utility, which may or may not be aligned with that of the user. Video games, news recommendation aggregation engines, and fitness trackers can all be instances of this general case. Our analysis facilitates distinguishing various subcases of interaction, as well as second-order effects that might include the possibility for adaptive interfaces to induce behavioural addiction, and/or change in user belief. We present these types of interaction within a conceptual framework, and review current examples of persuasive technologies and the issues that arise from their use. We argue that the nature of the feedback commonly used by learning agents to update their models and subsequent decisions could steer the behaviour of human users away from what benefits them, and in a direction that can undermine autonomy and cause further disparity between actions and goals as exemplified by addictive and compulsive behaviour. We discuss some of the ethical, social and legal implications of this technology and argue that it can sometimes exploit and reinforce weaknesses in human beings. (shrink)

Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom (Epistemic Monotonicity) which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not (...) be a vote for an alternative, it may be any type of input, for instance a subjective degree of belief or probability of the correctness of one of the alternatives. The case of a profile of subjective degrees of belief is particularly appealing, since here no parameters such as competence parameters need to be known. (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)

When is it legitimate for a government to ‘nudge’ its citizens, in the sense described by Thaler and Sunstein (2008)? In their original work on the topic, Thaler and Sunstein developed the _‘as judged by themselves’ (or AJBT) test_ to answer this question (Thaler and Sunstein 2008, p. 5). In a recent paper, Paul and Sunstein (2019) raised a concern about this test: it often seems to give the wrong answer in cases in which we are nudged to make a (...) decision that leads to what Paul calls a _personally transformative experience_, that is, one that results in our values changing (Paul 2014). In those cases, the nudgee will judge the nudge to be legitimate after it has taken place, but only because their values have changed as a result of the nudge. In this paper, I take up the challenge of finding an alternative test. I draw on my _aggregate utility account_ of how to choose in the face of what Ullmann-Margalit (2006) calls _big decisions_, that is, decisions that lead to these personally transformative experiences (Pettigrew 2019, Chapters 6 and 7). (shrink)

The Pareto principle states that if the members of society express the same preference judgment between two options, this judgment is compelling for society. A building block of normative economics and social choice theory, and often borrowed by contemporary political philosophy, the principle has rarely been subjected to philosophical criticism. The paper objects to it on the ground that it indifferently applies to those cases in which the individuals agree on both their expressed preferences and their reasons for entertaining them, (...) and those cases in which they agree on their expressed preferences, while differing on their reasons. The latter are cases of "spurious unanimity", and it is normatively inappropriate, or so the paper argues, to defend unanimity preservation at the social level for them, so the Pareto principle is formulated much too broadly. The objection seems especially powerful when the principle is applied in an ex ante context of uncertainty, in which individuals can disagree on both their probabilities and utilities, and nonetheless agree on their preferences over prospects. (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)

In the context of a global pandemic, there is good health-based reason for governments to impose various social distancing measures. However, such measures also cause economic and other harms to people at low risk from the virus. In this paper, I examine how to make such trade-offs in a way that is respectfully justifiable to their losers. I argue that existing proposals like using standard QALY (quality-adjusted life-year) valuations or WELLBYs (wellbeing-adjusted life-years) as the currency for trade-offs do not allow (...) such justification, because they give weight to utilities that are irrelevant in a life-and-death context. Drawing on work on restricted aggregation in ethics, I articulate an alternative framework for balancing claims arising from prospects of different kinds of harm and benefit, and show how it can be applied to reasoning about trade-offs in a pandemic context. (shrink)

This dissertation addresses a debate about the proper relationship between democratic theory and institutions. The debate has been waged between two rival approaches: on the one side is an aggregative and economic theory of democracy, known as constitutional economics, and on the other side is deliberative democracy. The two sides endorse starkly different positions on the issue of what makes a democracy legitimate and stable within an institutional setting. Constitutional economists model political agents in the same way that neoclassical economists (...) model economic agents, that is, as self-regarding, rational maximizers; so that evaluations of democratic legitimacy and stability depend on the extent to which the design of institutional rules and practices maximize individual utility by promoting efficient schemes of collective choice. Deliberative democrats, on the other hand, understand political agents as communicative reason-giving subjects who justify their preferences and positions on issues that jointly affect them in a process of consensus-directed discourse, or deliberation; so that evaluations of democratic legitimacy and order depend on the degree to which institutional norms and practices promote deliberation and draw upon deliberated public judgment. I argue that despite the numerous incompatibilities between constitutional economics and deliberative democracy—which amount to a 'deep divide'—an opportunity to produce a genuine synthesis of the two approaches arises inasmuch as it is possible to overcome several points of opposition in their separate research programmes. The central thesis of the dissertation is that it is possible to construct a bridge spanning the divide between constitutional economists and deliberative democrats, and that Dewey and Bentley's transactional view can facilitate this bridge-building project. Pursuant to this end, the points of opposition between the v research programmes are mediated by way of five concepts which, on balance, favor deliberative democracy and its feasible institutionalization. (shrink)

Since independence, at least 28 African countries have legalized some form of gambling. Yet a range of informal gambling activities have also flourished, often provoking widespread public concern about the negative social and economic impact of unregulated gambling on poor communities. This article addresses an illegal South African numbers game called fahfee. Drawing on interviews with players, operators, and regulatory officials, this article explores two aspects of this game. First, it explores the lives of both players and runners, as well (...) as the clandestine world of the Chinese operators who control the game. Second, the article examines the subjective motivations and aspirations of players, and asks why they continue to play, despite the fact that their aggregate losses easily outstrip their aggregate gains. In contrast with those who reduce its appeal simply to the pursuit of wealth, I conclude that, for the (mostly) black, elderly, working class women who play fahfee several times a week, the associated trade-off—regular, small losses, versus the social enjoyment of playing and the prospect of occasional but realistic windfalls—takes on a whole new meaning, and preferences for relatively lumpy rather than steady consumption streams help explain the continued attraction of fahfee. This reinforces the need to understand players’ own accounts of gambling utility rather than simply to moralistically condemn gambling or to dismiss gamblers behaviour as irrational. (shrink)

How can someone reconcile the desire to eat meat, and a tendency toward vegetarian ideals? How should we reconcile contradictory moral values? How can we aggregate different moral theories? How individual preferences can be fairly aggregated to represent a will, norm, or social decision? Conflict resolution and preference aggregation are tasks that intrigue philosophers, economists, sociologists, decision theorists, and many other scholars, being a rich interdisciplinary area for research. When trying to solve questions about moral uncertainty a meta understanding (...) of the concept of normativity can help us to develop strategies to deal with norms themselves. 2nd-order normativity, or norms about norms, is a hierarchical way to think about how to combine many different normative structures and preferences into a single coherent decision. That is what metanormativity is all about, a way to answer: what should we do when we don’t know what to do? In this study, we will review a decision-making strategy dealing with moral uncertainty, Maximization of Expected Choice-Worthiness. This strategy, proposed by William MacAskill, allows for the aggregation and inter-theoretical comparison of different normative structures, cardinal theories, and ordinal theories. In this study, we will exemplify the metanormative methods proposed by MacAskill, using has an example, a series of vegetarian dilemmas. Given the similarity to this metanormative strategy to expected utility theory, we will also show that it is possible to integrate both models to address decision-making problems in situations of empirical and moral uncertainty. We believe that this kind of ethical-mathematical formalism can be useful to help develop strategies to better aggregate moral preferences and solve conflicts. (shrink)

The Protein Ontology (PRO; http://purl.obolibrary.org/obo/pr) formally defines and describes taxon-specific and taxon-neutral protein-related entities in three major areas: proteins related by evolution; proteins produced from a given gene; and protein-containing complexes. PRO thus serves as a tool for referencing protein entities at any level of specificity. To enhance this ability, and to facilitate the comparison of such entities described in different resources, we developed a standardized representation of proteoforms using UniProtKB as a sequence reference and PSI-MOD as a post-translational modification (...) reference. We illustrate its use in facilitating an alignment between PRO and Reactome protein entities. We also address issues of scalability, describing our first steps into the use of text mining to identify protein-related entities, the large-scale import of proteoform information from expert curated resources, and our ability to dynamically generate PRO terms. Web views for individual terms are now more informative about closely-related terms, including for example an interactive multiple sequence alignment. Finally, we describe recent improvement in semantic utility, with PRO now represented in OWL and as a SPARQL endpoint. These developments will further support the anticipated growth of PRO and facilitate discoverability of and allow aggregation of data relating to protein entities. (shrink)

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment (...) class='Hi'>aggregation. I therefore suggest restricting independence to premises, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent. (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)

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of (...) causal-network aggregation. Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

Advocates of longtermism point out that interventions which focus on improving the prospects of people in the very far future will, in expectation, bring about a significant amount of good. Indeed, in expectation, such long-term interventions bring about far more good than their short-term counterparts. As such, longtermists claim we have compelling moral reason to prefer long-term interventions. In this paper, I show that longtermism is in conflict with plausible deontic scepticism about aggregation. I do so by demonstrating that, (...) from both an ex-ante and ex-post perspective, longtermist interventions – and, in particular, those which aim to mitigate catastrophic risk – typically generate extremely weak claims of assistance from future people. (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)

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)

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, (...) the hallmark of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. (shrink)

Many of us believe (1) Saving a life is more important than averting any number of headaches. But what about risky cases? Surely: (2) In a single choice, if the risk of death is low enough, and the number of headaches at stake high enough, one should avert the headaches rather than avert the risk of death. And yet, if we will face enough iterations of cases like that in (2), in the long run some of those small risks of (...) serious harms will surely eventuate. And yet: (3) Isn't it still permissible for us to run these repeated risks, despite that knowledge? After all, if it were not, then many of the risky activities that we standardly think permissible would in fact be impermissible. Nobody has yet offered a principle that can accommodate all of 1-3. In this paper, I show that we can accommodate all of these judgements, by taking into account both ex ante and ex post perspectives. In doing so, I clear aside an important obstacle to a viable deontological decision theory. (shrink)

Judgment aggregation is naturally applied to the modeling of collective attitudes. In the individual case, we represent agents as having not just beliefs, but also as supporting them with reasons. Can the Judgment Aggregation help model a concept of collective reason? I argue that the resources of the standard judgment aggregation framework are insufficiently general. I develop a generalization of the framework that improves along this dimension. In the new framework, new aggregation rules become available, as (...) well as a natural account of collective reasons. (shrink)

As the ongoing literature on the paradoxes of the Lottery and the Preface reminds us, the nature of the relation between probability and rational acceptability remains far from settled. This article provides a novel perspective on the matter by exploiting a recently noted structural parallel with the problem of judgment aggregation. After offering a number of general desiderata on the relation between finite probability models and sets of accepted sentences in a Boolean sentential language, it is noted that a (...) number of these constraints will be satisfied if and only if acceptable sentences are true under all valuations in a distinguished non-empty set W. Drawing inspiration from distance-based aggregation procedures, various scoring rule based membership conditions for W are discussed and a possible point of contact with ranking theory is considered. The paper closes with various suggestions for further research. (shrink)

This article applies the tools of experimental philosophy to the ongoing debate about both the theoretical viability and the practical import of partially aggregative moral theories in distributive ethics. We conduct a series of three experiments (N=383): First, we document the widespread occurrence of the intuitions that motivate this position. Our study then moves beyond establishing the existence of partially aggregative intuitions in two dimensions: First, we extend experimental work in such a way as to ascertain which amongst existing versions (...) of partial aggregation (localised vs. global) chimes more fully with moral common sense. Specifically, we document how, in tie-breaking cases, ‘irrelevant goods’ judgments (Kamm) are just as robust as the original aggregative/non-aggregative pair of judgments that constitute partial aggregation. Second, by pairing laypeople’s moral judgments in standard cases with their intuitions about the limits of permissible self-prioritisation, we investigate whether one prominent explanation of why irrelevant claims may not be aggregated (Voorhoeve’s ‘personal prerogative’ argument) can be said to underpin people’s intuitions about the (ir)relevance relation of claims in conflict cases. We close with a discussion of our findings’ practical and theoretical import and highlight avenues for future research. (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)

Deferential Monadic Panpsychism is a view that accepts that physical science is capable of discovering the basic structure of reality. However, it denies that reality is fully and exhaustively de- scribed purely in terms of physical science. Consciousness is missing from the physical description and cannot be reduced to it. DMP explores the idea that the physically fundamental features of the world possess some intrinsic mental aspect. It thereby faces a se- vere problem of understanding how more complex mental states (...) emerge from the mental features of the fundamental features. Here I explore the idea that a new form of aggregative emergence, which I call 'combinatorial infusion', could shed light on this problem and bolster the prospects for this form of panpsychism. (shrink)

Matthew Adler's Measuring Social Welfare is an introduction to the social welfare function (SWF) methodology. This essay questions some ideas at the core of the SWF methodology having to do with the relation between the SWF and the measure of well-being. The facts about individual well-being do not single out a particular scale on which well-being must be measured. As with physical quantities, there are multiple scales that can be used to represent the same information about well-being; no one scale (...) is special. Like physical laws, the SWF and its ranking of distributions cannot depend on exactly which of these scales we use. Adler and other theorists in the SWF tradition have used this idea to derive highly restrictive constraints on the shape of the SWF. These constraints rule out seemingly plausible views about distributive justice and population ethics. I argue, however, that these constraints stem from a simple but instructive mistake. The SWF should not be applied to vectors of numbers such as 1 and 2, but rather to vectors of dimensioned quantities such as 1 util and 2 utils. This seemingly pedantic suggestion turns out to have far-reaching consequences. Unlike the orthodox SWF approach, treating welfare levels as dimensioned quantities lets us distinguish between real changes in well-being and mere changes in the unit of measurement. It does this without making the SWF depend on the scale on which welfare is measured, and in a way that avoids the restrictive constraints on the shape of the SWF. (shrink)

There are many reasons we might want to take the opinions of various individuals and pool them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of pooling functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, a little, (...) or not at all. There are far fewer proposals for how to proceed in these cases, and those there are have undesirable features. I begin by considering four proposals and arguing that they don't work. Then I'll describe my own proposal, which is intended to cover the situation in which we want to pool the individual opinions in order to ascribe an opinion to the group considered as an agent in its own right. (shrink)

Consider a subjective expected utility preference relation. It is usually held that the representations which this relation admits differ only in one respect, namely, the possible scales for the measurement of utility. In this paper, I discuss the fact that there are, metaphorically speaking, two additional dimensions along which infinitely many more admissible representations can be found. The first additional dimension is that of state-dependence. The second—and, in this context, much lesser-known—additional dimension is that of act-dependence. The simplest (...) implication of their usually neglected existence is that the standard axiomatizations of subjective expected utility fail to provide the measurement of subjective probability with satisfactory behavioral foundations. (shrink)

This work contributes to the theory of judgement aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgement aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgement aggregation in non-classical logics is that they offer a number of modelling choices to represent agents’ reasoning in aggregation problems. By studying judgement (...) aggregation in logics that are weaker than classical logic, we investigate whether some well-known impossibility results, that were tailored for classical logic, still apply to those weak systems. (shrink)