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

Cerreia-Vioglio et al. :341–375, 2011) have proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences—and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory, is employed.

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)

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)

The article shows that a Paretian social welfare function can be history independent and time consistent only if a stringent set of conditions is verified. Individual utilities must be additive. The social welfare function must be a linear combination of these utilities. Social preferences are stationary only if, in addition, all individuals have the same constant discount rate. The results are implemented in two frameworks: deterministic dynamic choice and dynamic choice under uncertainty. The applications highlight that the conditions (...) are unlikely to be met by individual preferences, and that they severely restrict social preferences. (shrink)

Utilitarianism is one of the most famous ethical doctrines, based on the ideal of maximizing pleasure and minimizing pain. But Utilitarians and their opponents lack a clear scientific and philosophical understanding of its foundations, the measurement and aggregation of utility. This is what The Pursuit of Happiness now offers.

The note claims that Rosen's arguments about distribution and aggregation do not support his central claim, either in their own terms or as a reading of Bentham; and suggests a different account of the relation of the objective to the subjective in Bentham.

How many serious mistakes can a brilliant philosopher make in a single paragraph? Many think that Mill answers this question by example—in the third paragraph of Chapter IV of Utilitarianism. Here is the notorious paragraph: The only proof capable of being given that an object is visible, is that people actually see it. The only proof that a sound is audible, is that people hear it: and so of the other sources of our experience. In like manner, I apprehend, the (...) sole evidence it is possible to produce that anything is desirable, is that people do actually desire it. If the end which the utilitarian doctrine proposes to itself were not, in theory and in practice, acknowledged to be an end, nothing could ever convince any person that it was so. No reason can be given why the general happiness is desirable, except that each person, so far as he believes it to be attainable, desires his own happiness. This, however, being a fact, we have not only all the proof which the case admits of, but all which it is possible to require, that happiness is a good: that each person's happiness is a good to that person, and the general happiness, therefore, a good to the aggregate of all persons. Happiness has made out its title as one of the ends of conduct, and consequently one of the criteria of morality. (shrink)

In Chapter 4 of his essay Utilitarianism, “Of what sort of Proof the Principle of Utility is susceptible,” J. S. Mill undertakes to prove, in some sense of that term, the principle of utility. It has very commonly been argued that in the course of this “proof” Mill commits two very obvious fallacies. The first is the naturalistic fallacy which he is held to commit when he argues that since “the only proof capable of being given that an object is (...) visible, is that people actually see it. The only proof that a sound is audible is that people hear it: and so of the other sources of our experience. In like manner … the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it.”1 Here Mill appears to hold that “X is desirable ”—a value judgment—follows deductively from “People desire x”—a factual statement. And the second is the fallacy of composition which seems to be involved in Mill'zs argument that since “each person's happiness is a good to that person … the general happiness, therefore, a good to the aggregate of all persons.”2. (shrink)

In Chapter 4 of his essay Utilitarianism, “Of what sort of Proof the Principle of Utility is susceptible,” J. S. Mill undertakes to prove, in some sense of that term, the principle of utility. It has very commonly been argued that in the course of this “proof” Mill commits two very obvious fallacies. The first is the naturalistic fallacy which he is held to commit when he argues that since “the only proof capable of being given that an object is (...) visible, is that people actually see it. The only proof that a sound is audible is that people hear it: and so of the other sources of our experience. In like manner … the sole evidence it is possible to produce that anything is desirable, is that people do actually desire it.”1 Here Mill appears to hold that “X is desirable ”—a value judgment—follows deductively from “People desire x”—a factual statement. And the second is the fallacy of composition which seems to be involved in Mill'zs argument that since “each person's happiness is a good to that person … the general happiness, therefore, a good to the aggregate of all persons.”2. (shrink)

Background:The management of challenging behaviours in inpatient with intellectual disability and/or autism spectrum disorders can lead to an escalation of control measures. In these complex situations where patients have an intellectual disability/autism spectrum disorder accompanied by a psychiatric comorbidity, the experiences of caregivers related to the crisis management have rarely been studied.Purpose:This study examined the moral experiences of caregivers related to challenging behaviours’ management and alternatives to control measures.Research design:Using Charles Taylor’s hermeneutic framework, a 2-month focused ethnography with a participatory (...) approach was used.Participants and research context:Sixteen caregivers were interviewed in a Canadian mental health setting for adults with intellectual disability/autism spectrum disorder and psychiatric comorbidity.Ethical considerations:The research was conducted in compliance with the Declaration of Helsinki and local Research Ethics Board approval. Written informed consent was collected systematically from participants.Findings:By accounting for caregivers’ moral experiences, this study sheds light on a neglected dimension of the care relationship: the vulnerability of the caregiver. We highlight the main barriers and facilitators to alternatives to control measures. First, a caregiver’s vulnerability was characterised by the overall impact of challenging behaviours and the moral distress associated with the use of control measures and exclusion mechanisms of intellectual disability/autism spectrum disorder patients. Second, a strong ambiguity between care and control measures and a lack of inclusive approaches were identified as the two main barriers to challenging behaviour management. Third, the involvement, both professional and personal, of caregivers was deemed necessary to implement alternatives to control measures.Discussion:A conflict of values opposes two conceptions of autonomy: a rational autonomy, which is counterproductive to the reduction of control measures, versus a relational autonomy based on shared vulnerability.Conclusion:The recognition of caregiver’s vulnerability is a benchmark to create alternative approaches, which defuse the logic of control and promote an ethics of care within which caregivers’ self-concern can be understood as fostering mutual respect. (shrink)

Suppose n Bayesian agents need to make a decision as a group. The groupas a whole is also supposed to be a Bayesian agent whose probabilities andutilities are derived or aggregated in reasonable ways from the probabilitiesand utilities of the group members. The aggregation could beex ante, i.e., interms of expected utilities, or it could be ex post, i.e., in terms of utilitiesonly, or in terms of utilities and probabilities separately. This study exploresthe ex post approach. (...) Using the Bolker/Jeffrey framework, we show thatex post aggregation is subject to an instability phenomenon. That is, it mayhappen that the group preference between actions ``flips back and forth'''' dependingon the level of detail in which the decision problem is described. Structurally verysimilar phenomena also occur elsewhere in social choice theory, in statistics (Simpson''sParadox), and in voting theory (Ostrogorski''s Paradox). (shrink)

This article identifies ‘the tragedy of the commons’ as an essentially aggregative harm and considers what agents in such a scenario owe to one another. It proposes that the duty to take reasonable precautions requires that agents make efforts to establish collective solutions to any essentially aggregative harm to which they would otherwise contribute. Baylor Johnson has argued that the general obligation to promote the common good requires that agents make efforts to establish a collective agreement to avert a potential (...) tragedy of the commons. This article agrees with Johnson's analysis but argues that there are also negative duties, which give commons users additional moral reason to take collective action to prevent the destruction of the utility of the commons. These duties link commons users to resolving this particular problem and provide grounds to demand that they make greater efforts to prevent the destruction of the commons compared to bystanders. The article suggests that fulfilling negative duties can require establishing collective institutions with the power to regulate human action and interaction. This analysis could be applied to a range of social problems which result from the aggregation of actions and practices. (shrink)

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)

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.

How might we extend aggregative moral theories to compare infinite worlds? In particular, how might we extend them to compare worlds with infinite spatial volume, infinite temporal duration, and infinitely many morally valuable phenomena? When doing so, we face various impossibility results from the existing literature. For instance, the view we adopt can endorse the claim that worlds are made better if we increase the value in every region of space and time, or that they are made better if we (...) increase the value obtained by every person. But they cannot endorse both claims, so we must choose. In this paper I show that, if we choose the latter, our view will face serious problems such as generating incomparability in many realistic cases. Opting instead to endorse the first claim, I articulate and defend a spatiotemporal, expansionist view of infinite aggregation. Spatiotemporal views such as this do face some difficulties, but I show that these can be overcome. With modification, they can provide plausible comparisons in cases that we care about most. (shrink)

The use of aggregated quality of life estimatesin the formation of public policy and practiceguidelines raises concerns about the moralrelevance of variability in values inpreferences for health care. This variabilitymay reflect unique and deeply held beliefs thatmay be lost when averaged with the preferencesof other individuals. Feminist moral theorieswhich argue for attention to context andparticularity underline the importance ofascertaining the extent to which differences inpreferences for health states revealinformation which is morally relevant toclinicians and policymakers. To facilitatethese considerations, we present (...) an empiricalstudy of preferences for the timing andoccurrence of health states associated withhormone replacement therapy (HRT). Sixteenwomen between the ages of 45 and 55 wereenrolled in this pilot study. Theirpreferences regarding five health statesassociated with HRT (menopausal symptoms, sideeffects of HRT, breast cancer, myocardialinfarction, and osteoporosis) were assessed inquantitative terms known as utilities. Twostandard methods, the visual analog scale (VAS) and the standard gamble (SG), were used toassess utility and time preference (calculatedas a discount rate). The wide variability ofresponses underlines the importance oftailoring health care to individual women'spreferences. Policy guidelines whichincorporate utility analysis must recognize thenormative limitations of aggregatedpreferences, and the moral relevance ofindividual conceptions of health. (shrink)

Suppose you found that the universe around you was infinite—that it extended infinitely far in space or in time and, as a result, contained infinitely many persons. How should this change your moral decision-making? Radically, it seems, according to some philosophers. According to various recent arguments, any moral theory that is ’minimally aggregative’ will deliver absurd judgements in practice if the universe is (even remotely likely to be) infinite. This seems like sound justification for abandoning any such theory. -/- My (...) goal in this thesis is simple: to demonstrate that we need not abandon minimally aggregative theories, even if we happen to live in an infinite universe. I develop and motivate an extension of such theories, which delivers plausible judgements in a range of realistic cases. I show that this extended theory can overcome key objections—both old and new—and that it succeeds where other proposals do not. With this proposal in hand, we can indeed retain minimally aggregative theories and continue to make moral decisions based on what will promote the good. (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)

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.

The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference and judgment (...) aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s :410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed. (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)

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)

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)

A TRADITIONAL VIEW OF UTILITY AND RIGHTS According to a conventional view, no project could be more hopelessly misconceived than the enterprise of attempting a utilitarian derivation of fundamental rights. We are all familiar – too familiar, perhaps – with the arguments that support this conventional view, but let us review them anyway. We may begin by recalling that, whereas the defining value of utilitarianism – pleasure, happiness or welfare – contains no mention of the dignity or autonomy of human (...) beings, it is this value which utilitarianism in all its standard forms invokes as the criterion of right action. Worse, insofar as utilitarian policy must have as its goal the maximization of welfare conceived as an aggregate summed over the utilities of everyone affected, legal and political utilitarianism seems bound to have a collectivist bias, trading on the dangerous fiction of a social entity and ignoring the distinctness of separate selves with their several incommensurable claims. It seems that, if individuals can appear in the utilitarian calculus at all, it will only be as ciphers, abstract place-holders for units of welfare. For, as an aggregative value, utility must be indifferent to distribution, and insensitive to the preeminently distributive considerations marked by claims about rights. So, if whatever has utility can be broken down into units or elements which are subject to measurement or at least comparison by a common standard, then it will always be possible that a very great loss of welfare for one man or a few men can be justified if it produces a great many small increments of welfare for a vast multitude of men. (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)

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)

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

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 (though not uncontroversial) 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)

Epistemic utility theory seeks to establish epistemic norms by combining principles from decision theory and social choice theory with ways of determining the epistemic utility of agents’ attitudes. Recently, Moss, 1053–69, 2011) has applied this strategy to the problem of finding epistemic compromises between disagreeing agents. She shows that the norm “form compromises by maximizing average expected epistemic utility”, when applied to agents who share the same proper epistemic utility function, yields the result that agents must form compromises by splitting (...) the difference between their credence functions. However, this “split the difference” norm is in conflict with conditionalization, since applications of the two norms don’t commute. A common response in the literature seems to be to abandon the procedure of splitting the difference in favor of compromise strategies that avoid non-commutativity. This would also entail abandoning Moss’ norm. I explore whether a different response is feasible. If agents can use epistemic utility-based considerations to agree on an order in which they will apply the two norms, they might be able to avoid diachronic incoherence. I show that this response can’t save Moss’ norm, because the agreements concerning the order of compromising and updating it generates are not stable over time, and hence cannot avoid diachronic incoherence. I also show that a variant of Moss’ norm, which requires that the weights given to each agent’s epistemic utility change in a way that ensures commutativity, cannot be justified on epistemological grounds. (shrink)

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and (...) are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent. (shrink)

Traditional act utilitarianism judges an action permissible just in case it produces as much aggregate utility as any alternative. It is often supposed that utilitarianism faces a serious problem if the future is infinitely long. For in that case, actions may produce an infinite amount of utility. And if that is so for most actions, then utilitarianism, it appears, loses most of its power to discriminate among actions. For, if most actions produce an infinite amount of utility, then few actions (...) produce non-maximal utility, and so most actions are permissible.1 I will argue that potentially infinite futures create no major problems for utilitarianism. Utilitarianism has, I argue, the resources to distinguish among actions all of which produce infinite amounts of utility -- judging some permissible and some impermissible. For brevity of expression I will focus on act utilitarianism, but all the points apply equally well to many other traditional forms of utilitarianism. (shrink)

The constitution of a collective judgment is analyzed from a contractarian point of view. The optimal collective judgment is defined as the one that maximizes the sum of the utility each member gets from the collective adoption of that judgment. It is argued that judgment aggregation is a different process from the aggregation of information and public deliberation. This entails that the adoption of a collective judgment should not make any rational member of the group change her individual (...) opinion, and so the collective judgment can not have any kind of epistemic superiority over the individual ones. ‡The author acknowledges Spanish Government's research projects HUM2005–01686/FISO and HUM2005-25447-E, as well as the grant PR2006-0108 which allowed a three months stay at the Helsinki Collegium for Advanced Studies, in which a big part of this paper was written. †To contact the author, please write to: Universidad Nacional de Educación a Distancia, Dpto. de Lógica, Historia y F. de la ciencia, Humanidades, Paseo de Senda del rey 7, 28040 Madrid, Spain; e-mail: [email protected]. (shrink)

Suppose we have a group of Bayesian agents, and suppose that theywould like for their group as a whole to be a Bayesian agent as well. Moreover, suppose that thoseagents want the probabilities and utilities attached to this group agent to be aggregated from theindividual probabilities and utilities in reasonable ways. Two ways of aggregating their individual data areavailable to them, viz., ex ante aggregation and ex post aggregation. The former aggregatesexpected utilities directly, whereas the (...) latter aggregates probabilities and utilities separately.A number of recent formal results show that both approaches have problematic implications. This studydiscusses the philosophical issues arising from those results. In this process, I hope to convincethe reader that these results about Bayesian aggregation are highly significant to decision theorists, butalso of immense interest to theorists working in areas such as ethics and political philosophy. (shrink)

Suppose we have a group of Bayesian agents, and suppose that theywould like for their group as a whole to be a Bayesian agent as well. Moreover, suppose that thoseagents want the probabilities and utilities attached to this group agent to be aggregated from theindividual probabilities and utilities in reasonable ways. Two ways of aggregating their individual data areavailable to them, viz., ex ante aggregation and ex post aggregation. The former aggregatesexpected utilities directly, whereas the (...) latter aggregates probabilities and utilities separately.A number of recent formal results show that both approaches have problematic implications. This studydiscusses the philosophical issues arising from those results. In this process, I hope to convincethe reader that these results about Bayesian aggregation are highly significant to decision theorists, butalso of immense interest to theorists working in areas such as ethics and political philosophy. (shrink)

Utilitarianism and other aggregationist moral theories view the public interest or the general welfare as an aggregate of individual goods. But critics of these theories question whether there is adequate justification for employing the concept of an aggregate social good. How are we supposed to sum up individual interests? Is it even possible to compare the utilities of different people or to assign values to individual utilities that can be added or subtracted? If not, how is the general (...) good to be aggregated? Critics have also raised concerns about the aggregative approach in ethics - concerns about its implications for distributive justice, individual liberty and democratic institutions. The essays in this volume explore these issues and address related questions. Some of them examine specific objections to aggregation, others analyze the very idea of a social good or social welfare. Other essays discuss the application of aggregative principles to particular problems. (shrink)

We introduce two novel frameworks for choice under complete uncertainty. These frameworks employ intervals to represent uncertain utility attaching to outcomes. In the first framework, utility intervals arising from one act with multiple possible outcomes are aggregated via a set-based approach. In the second framework the aggregation of utility intervals employs multi-sets. On the aggregated utility intervals, we then introduce min–max decision rules and lexicographic refinements thereof. The main technical results are axiomatic characterizations of these min–max decision rules and (...) these refinements. We also briefly touch on the independence of introduced axioms. Furthermore, we show that such characterizations give rise to novel axiomatic characterizations of the well-known min–max decision rule?mnx?mnx in the classical framework of choice under complete uncertainty. (shrink)

This paper examines Rosen's claim that Bentham's principle of utility was a distributive rather than an aggregative principle.

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

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)

That utility is not a sufficient test for a set of social rules to be morally binding upon a group of persons has been argued in a number of recent books and articles. Yet it is generally conceded in these arguments that a group's observance of rules makes possible greater benefits than would accrue if each did not associate himself with others under the rules. It is not denied that the practice of morality is socially advantageous. What is denied is (...) that social advantage is either the sole criterion or a sufficient criterion for the justifiability of any set of rules that could constitute the de facto system of moral requirements in a given society.What, then, is sufficient? The answer I am interested in defending in this paper is that both utility as an aggregative principle and justice as a distributive principle are each a necessary condition and together provide a sufficient condition for the justification of a moral code. In the first two parts of this paper, I shall explain how the concepts of justice and utility, respectively, are to be construed in the argument of the third part. (shrink)

We provide a simple model to measure the impact of aggregate risks. We consider agents whose rankings of lotteries over vectors of outcomes satisfy expected utility and separability. Such rankings are characterized in terms of aggregative utilities that measure sensitivity to aggregate uncertainty in a straightforward way. We consider applications to models of product variety, portfolio choice, and public attitudes towards catastrophic risks. The framework lends support to precautionary measures that penalize policies for exposure to correlation. The model rationalizes (...) a number of behavioral and policy patterns as attempts to hedge against aggregate uncertainty. (shrink)