How should we respond to cases of disagreement where two epistemic agents have the same evidence but come to different conclusions? Adam Elga has provided a Bayesian framework for addressing this question. In this paper, I shall highlight two unfortunate consequences of this framework, which Elga does not anticipate. Both problems derive from a failure of commutativity between application of the equal weight view and updating in the light of other evidence.

In the last decade, analytic epistemologists have engaged in a lively debate about Equal Weight, the claim that you should give the credences of epistemic peers the same consideration as your own credences. In this paper, I explore the implications of the debate about Equal Weight for how we should respond to religious disagreement found in the diversity of models of God. I first claim that one common argument against religious exclusivism and for religious pluralism can be articulated (...) as an Equal Weight argument. I then argue that to avoid this argument, religious exclusivists must reject Equal Weight. Next, I maintain that, while the exclusivist complaint that pluralism is self-undermining is incorrect, exclusivists can rightly object that the pluralist’s Equal Weight argument is self-undermining. Thus both exclusivists and pluralists have an interest in rejecting Equal Weight. My final discussion is speculative: I suggest that the goals of those of pluralist persuasion might be better met by religious permissivism, the view that some forms of both exclusivism and pluralism are rational responses to religious disagreement. (shrink)

Some philosophers believe that when epistemic peers disagree, each has an obligation to accord the other's assessment the same weight as her own. I first make the antecedent of this Equal-Weight View more precise, and then I motivate the View by describing cases in which it gives the intuitively correct verdict. Next I introduce some apparent counterexamples – cases of apparent peer disagreement in which, intuitively, one should not give equal weight to the other party's assessment. To defuse (...) these apparent counterexamples, an advocate of the View might try to explain how they are not genuine cases of peer disagreement. I examine David Christensen's and Adam Elga's explanations and find them wanting. I then offer a novel explanation, which turns on a distinction between knowledge from reports and knowledge from direct acquaintance. Finally, I extend my explanation to provide a handy and satisfying response to the charge of self-defeat. (shrink)

Much of the literature on the epistemology of disagreement focuses on the rational responses to disagreement, and to disagreement with an epistemic peer in particular. The Equal Weight View claims that in cases of peer disagreement each dissenting peer opinion is to be given equal weight and, in a case of two opposing equally-weighted opinions, each party should adopt the attitude which ‘splits the difference’. The Equal Weight View has been taken by both its critics and its (...) proponents to have quite drastic skeptical ramifications given contingent empirical facts that we are aware of regarding disagreements in philosophy, religion, science, and politics. In this paper,we begin by clarifying the central claims of the Equal Weight View (Section 2) and then examine two routes from the Equal Weight View to skepticism about such matters that have been explored in the literature. The first claims that our awareness of peers or experts who disagree with us about such issues requires that we abandon our beliefs on these issues (Section 3). The second claims that our awareness of merely possible peers or experts who disagree with us requires us to abandon our beliefs (Section 4). We find both routes from the Equal Weight View to a form of skepticism defective. However, there are nearby considerations, explored in Sections 5 and 6,which (for better or worse) do lead to at least some skeptical consequences for the Equal WeightView, albeit for different reasons. (shrink)

We present a minimal pragmatic restriction on the interpretation of the weights in the “Equal Weight View” regarding peer disagreement and show that the view cannot respect it. Based on this result we argue against the view. The restriction is the following one: if an agent, $$\hbox {i}$$ i, assigns an equal or higher weight to another agent, $$\hbox {j}$$ j,, he must be willing—in exchange for a positive and certain payment—to accept an offer to let a completely (...) rational and sympathetic $$\hbox {j}$$ j choose for him whether to accept a bet with positive expected utility. If $$\hbox {i}$$ i assigns a lower weight to $$\hbox {j}$$ j than to himself, he must not be willing to pay any positive price for letting $$\hbox {j}$$ j choose for him. Respecting the constraint entails, we show, that the impact of disagreement on one’s degree of belief is not independent of what the disagreement is discovered to be. (shrink)

In this paper, we investigate various possible (Bayesian) precisifications of the (somewhat vague) statements of “the equal weight view” (EWV) that have appeared in the recent literature on disagreement. We will show that the renditions of (EWV) that immediately suggest themselves are untenable from a Bayesian point of view. In the end, we will propose some tenable (but not necessarily desirable) interpretations of (EWV). Our aim here will not be to defend any particular Bayesian precisification of (EWV), but rather (...) to raise awareness about some of the difficulties inherent in formulating such precisifications. (shrink)

Dawid, DeGroot and Mortera showed, a quarter century ago, that any agent who regards a fellow agent as a peer--in particular, defers to the fellow agent's prior credences in the same way that she defers to her own--and updates by split-the-difference is prone to diachronic incoherence. On the other hand one may show that there are special scenarios in which Bayesian updating approximates difference splitting, so it remains an important question whether it remains a viable response to ``generic" peer update. (...) We look at arguments by two teams of philosophers against difference splitting. (shrink)

There are several proposals to resolve the problem of epistemic peer disagreement which concentrate on the question of how to incorporate evidence of such a disagreement. The main positions in this field are the equal weight view, the steadfast view, and the total evidence view. In this paper we present a new argument in favour of the equal weight view. As we will show, this view results from a general approach of forming epistemic attitudes in an optimal way. (...) By this, the argument for equal weighting can be massively strengthened from reasoning via epistemic indifference to reasoning from optimality. (shrink)

Standardly, epistemic peers regarding a given matter are said to be people of equal competence who share all relevant evidence. Alternatively, one can define epistemic peers regarding a given matter as people who are equally likely to be right about that matter. I argue that a definition in terms of likelihood captures the essence of epistemic peerhood better than the standard definition or any variant of it. What is more, a likelihood definition implies the truth of the central thesis (...) in the debate on peer disagreement, the so-called Equal Weight View, according to which we should give the opinions of our peers the same weight we give our own. Adopting a likelihood definition, however, does not end the debate on peer disagreement, because the alleged theoretical alternatives to the Equal Weight View, reinterpreted in the light of a likelihood definition, can in fact be shown to be compatible with this view—though the reinterpreted versions may appear less plausible than the original ones. (shrink)

In the debate of epistemic peer disagreement the equal-weight view suggests to split the difference between one's own and one's peer's opinions. An argument in favour of this view---which is prominently held by Adam Elga---is that by such a difference-splitting one may make some use of a so-called wise-crowd effect. In this paper it is argued that such a view faces two main problems: First, the problem that the standards for making use of a wise-crowd effect are quite low. (...) And second, the problem that following the equal-weight view decreases such effects and by this the argument's own basis is defeated. We therefore come to the conclusion that an argument for the equal-weight view with the help of wise-crowd effects as provided more or less explicitly by Elga does not succeed. (shrink)

If a colleague of mine, whose opinion I respect, disagrees with me about some claim, this might give me pause regarding my position on the matter. The Equal Weight view proposes that in such cases of peer disagreement I ought to give my colleague’s opinion as much weight as my own, and decrease my certainty in the disputed claim. One prominent criticism of the Equal Weight view is that treating higher-order (indirect) evidence in this way invariably swamps first-order (...) (direct) evidence. While the opinions of our peers matter in our deliberations, the Equal Weight view counter-intuitively requires that evidence of mere disagreement is more important than standard kinds of evidence. I offer a proposal for how we should idealize epistemic agents that identifies the variable feature of disagreements that accounts for the shifting significance of direct and indirect evidence in different disagreement contexts. Specifically, by idealizing epistemic agents as deriving functions that characterize the non-subjective relationship between a body of evidence and the reasonableness of believing the various propositions supported by that evidence, we can accommodate the intuition to compromise that motivates the Equal Weight view, without accepting the counter-intuitive results. (shrink)

There is a controversy, within social epistemology, over how to handle disagreement among epistemic peers. Call this the problem of peer disagreement. There is a solution, i.e. the equal-weight view, which says that disagreement among epistemic peers is a reason for each peer to lower the credence they place in their respective positions. However, this solution is susceptible to a serious challenge. Call it the merely modal peers challenge. Throughout parts of modal space, which resemble the actual world almost (...) completely, there are hordes of epistemic peers, who disagree with almost any arbitrarily chosen belief had by residents of the actual world. Further, the mere modality of these peers is not itself an epistemic difference-maker. Thus, on the equal-weight view, we should significantly lower the credence we place in most of our beliefs. Surely, this is seriously mistaken. Thus, there are serious considerations that cut against the equal-weight view. (shrink)

Self-regarding acts are frequently classified as non-moral; even more frequently, they are assumed to have less moral weight than parallel other-regarding acts. I argue briefly against the first claim, and at greater length against the second. Our intuitions about the lesser moral weight of self-regarding acts arise from imperfectly recognized, and morally relevant, differences between acts which are ordinarily described in misleadingly parallel phrases. ‘Love of self,’ for instance, and ‘love of another’ are not symmetrical attitudes, in spite of the (...) symmetrical grammar. More obviously, one cannot steal from, lie to, nor force oneself in the same way one can do these things to others. I conclude, therefore, that difference in moral weight never stems merely from a difference in the person concerned, but rather from differences between the actions themselves; furthermore, that whatever it is wrong to do to a willing other, it is wrong to do to oneself. (shrink)

New and recent axioms for cooperative games with transferable utilities are introduced. The non-negative player axiom requires to assign a non-negative payoff to a player that belongs to coalitions with non-negative worth only. The axiom of addition invariance on bi-partitions requires that the payoff vector recommended by a value should not be affected by an identical change in worth of both a coalition and the complementary coalition. The nullified solidarity axiom requires that if a player who becomes null weakly loses (...) from such a change, then every other player should weakly lose too. We study the consequence of imposing some of these axioms in addition to some classical axioms. It turns out that the resulting values or set of values have all in common to split efficiently the worth achieved by the grand coalition according to an exogenously given weight vector. As a result, we also obtain new characterizations of the equal division value. (shrink)

Although the concept of corporate social responsibility is fundamentally multidimensional, most studies use composite scores to assess corporate social performance. How relevant are such composite scores? How the CSR dimensions are weighted? Should the weighting scheme be the same across sectors? This article proposes an original weighting scheme of CSR strengths and concerns, at the sector level, which is proportional to media and nongovernmental organizations scrutiny. The authors show that previous CSP assessments underweight environmental and corporate governance concerns. (...) Moreover, findings suggest that firms that are exposed to the closest scrutiny are usually criticized on one single dimension: for instance, banks for bad corporate governance, and basic-resource firms for environmental damage. Composite scores based on equal weights hence misrepresent CSP and the difference in CSR between sectors. (shrink)

Is the assessment of motor milestones valid and scaled equivalently for all infants? It is not only important to understand if the way we use gross and fine motor scores are appropriate for monitoring motor milestones but also to determine if these scores are confounded by specific infant characteristics. Therefore, the aim of the study is to investigate the latent structure underlying motor milestone assessment in infancy and measurement invariance across sex, birth weight, and gestational age. For this study, the (...) birth cohort data from the United Kingdom Millennium Cohort Study was used, which includes the assessment of eight motor milestone tasks from the Denver Developmental Screening Test in 9-month-old infants, depicting early motor development of the first children of generation Z. Confirmatory factor analyses showed a better model fit for a two-factor structure compared to a one-factor structure, and multiple indicators multiple causes modeling revealed no differential item functioning related to sex, birth weight, and gestational age. The study provides support for the use of gross and fine motor scores when assessing motor milestones in infants—both boys and girls with different birth weights and of varying gestational ages. Further investigation into widely adopted assessment tools is recommended to support the use of valid composite scores in early childhood research and practice. (shrink)

Faced with a choice between saving one stranger and saving a group of strangers, some people endorse weighted lotteries, which give a strictly greater chance of being saved to the group of strangers than the single stranger. In this paper I attempt to criticize this view. I first consider a particular version of the weighted lotteries, Frances Kamm's procedure of proportional chances, and point out two implausible implications of her proposal. Then, I consider weighted lotteries in general, and claim (1) (...) that the correct thing to distribute is not the chance of being saved but the good of being saved, (2) that assigning some chance to the single stranger is not the only way to give a positive (and equal) respect to the people concerned, and (3) that the weighted lottery appears to be deceptive since it would show the respect to the single stranger in a negligible way. (shrink)

In many scientific, economic and policy-related problems, pieces of information from different sources have to be aggregated. Typically, the sources are not equally competent. This raises the question of how the relative weights and competences should be related to arrive at an optimal final verdict. Our paper addresses this question under a more realistic perspective of measuring the practical loss implied by an inaccurate verdict.

Weights of evidence and logistic regression are two loglinear methods for mineral potential mapping. Both models are limited by their respective basic assumptions in application. Ideally, WofE indicator patterns have the property of conditional independence with respect to the point pattern of mineral deposits to be predicted; in LR, there supposedly are no interactions between the point pattern and two or more of the indicator patterns. If the CI assumption is satisfied, estimated LR coefficients become approximately equal to WofE (...) contrasts and the two methods produce similar results; additionally, bias then is avoided in that the sum of all estimated posterior probabilities becomes approximately equal to the number of observed discrete events. WofE allows construction of input layers that have missing data as a separate category in addition to known presence-absence type input, while logistic regression as such is not capable of handling missing data. As an improved WofE model based on LR, modified weights of evidence inherit the advantages of both LR and WofE, i.e., eliminates bias due to lack of CI and can handle missing data as well. Pixel or unit area input for MWofE consists of positive and negative weights for presence and absence of a pattern plus zeros for missing data. MWofE first is illustrated by application to simple examples. Next, it is applied to a study area with 20 known gold occurrences in southwestern Nova Scotia in relation to four input layers based on geological and lake geochemical data. Assuming that geochemical data were missing for the northern part of the study area, MWofE, like WofE but unlike LR, provides posterior probabilities for the entire area. (shrink)

House of Lords authority in Tesco v Secretary of State for the Environment [1995] 1 WLR 759 has reinforced the well-established principle that judicial review will distinguish between relevant and irrelevant considerations pertaining to the exercise of a power, and leave the weighing of the relevant ones to the decision-maker. It has also problematized the principle by insisting that relevant factors may adequately be taken into account even where the decision-maker allows them no influence (subject to challenge for irrationality). It (...) is difficult to accept that a legislative identification of relevant factors need not influence the decision-maker, and the article begins by observing that this proposition would probably not have been accepted at the time of Roberts v Hopwood [1925] AC 578. It is argued in the article, however, that the proper influence of the relevant can be accommodated within the decision-making process while upholding the Tesco principle. The article therefore charts the activities which are logically implicit in a decision-making process including the consideration and weighing of relevant factors, and locates opportunities for legal challenge. The influence of the expressly relevant must be felt when the decision-maker has to decide whether other factors are impliedly relevant. It will equally be registered when a basis for the assessment of weight is established (weight being impossible to gauge without the prior formulation of criteria of influence). The process of weighing itself is shown to require two separate assessments; the first particular to each factor, the second comparative. This distinction allows explanation of those explanation of those authorities which require substantial weight to be given to certain protected factors, and helps to define the nature of irrationality challenges to absurd weighing. In summary, the article takes a rigorous look at what weight is, how it is assessed, how it differs from relevance, and to what extent a flawed assessment of it can be challenged. (shrink)

Are there any prima facie reasons that democracies might have for disenfranchising older citizens? This question reflects increasingly salient, but often incompletely theorized complaints that members of democratic publics advance about older citizens’ electoral influence. Rather than rejecting these complaints out of hand, we explore whether, suitably reconstructed, they withstand democratic scrutiny. More specifically, we examine whether the account of political equality that seems to most fittingly capture the logic of these complaints – namely, equal opportunity of political influence (...) over electoral outcomes – can justify disenfranchising older citizens. We conclude that equal opportunity of influence cannot ground a blanket disenfranchisement of older people and that, taken in conjunction with other general considerations that apply to all sound electoral policies, partial disenfranchisement proposals (i.e. proposals for reducing the electoral influence of older citizens via age-weighted voting) are both quasi-inapplicable and practically unrobust across a relevant range of political contexts. (shrink)

In this commentary we discuss a predictive sensorimotor illusion, the size-weight illusion, in which the smaller of two objects of equal weight is perceived as heavier. We suggest that Grush's emulation theory can explain this illusion as a mismatch between predicted and actual sensorimotor feedback, and present preliminary data suggesting that the cerebellum may be critical for implementing the emulator.

Research providing consistent evidence of pervasive discrimination against overweight job applicants and employees in the American workplace raises important questions for organizational stakeholders. To what extent is the disparate treatment of job applicants or employees based on their weight ethically justified? Are there aspects of weight discrimination that make it more acceptable than discrimination based on other characteristics, such as race or gender? What operational steps can employers take to address concerns regarding the ethical treatment of overweight individuals in the (...) workplace? This article investigates these and related questions. Its purpose is to provide information and analysis that will assist organizations in formulating ethical responses to a widespread phenomenon: weight discrimination in the workplace. Although its focus is the American workplace, the proposed employer ethical obligations and the practical guidance that is provided are viewed as generalizing across countries and cultures. (shrink)

The three most common responses to Taurek’s ‘numbers problem’ are saving the greater number, equal chance lotteries and weighted lotteries. Weighted lotteries have perhaps received the least support, having been criticized by Scanlon What We Owe to Each Other ( 1998 ) and Hirose ‘Fairness in Life and Death Cases’ ( 2007 ). This article considers these objections in turn, and argues that they do not succeed in refuting the fairness of a weighted lottery, which remains a potential solution (...) to cases of conflict. Moreover, it shows how these responses actually lead to a new argument for weighted lotteries, appealing to fairness and Pareto-optimality. (shrink)

Two prominent relational egalitarians, Elizabeth Anderson and Niko Kolodny, object to giving people in a democratic community differential voting weights on the grounds that doing so would lead to unequal relations between them. Their claim is that deviating from a “one-person, one-vote” scheme is incompatible with realizing relational egalitarian justice. In this article, I argue that they are wrong. I do so by showing that people can relate as moral, epistemic, social, and empirical equals in a scheme with differential voting (...) weights. I end the article by showing that from the perspective of relational egalitarianism, it is sometimes true that differential voting weights are more just than equal voting weights. (shrink)

Many philosophers argue that individuals have duties to do their fair shares of the demands of achieving important common ends. But what happens when some individuals fail to do their fair shares?...

I demonstrate that a set of well-known objections defeat John Stuart Mill’s plural voting proposal, but do not defeat plural voting as such. I adopt the following as a working definition of political equality: a voting system is egalitarian if and only if departures from a baseline of equally weighted votes are normatively permissible. I develop an alternative proposal, called procedural plural voting, which allocates plural votes procedurally, via the free choices of the electorate, rather than according to a substantive (...) standard of competence. The alternative avoids standards objections to Mill’s proposal. Moreover, reflection on the alternative plural voting scheme disrupts our intuitions about what counts as an egalitarian voting system. Undue emphasis on Mill’s version of plural voting obscures three important reasons to reject plural voting in favor of strictly egalitarian voting systems: that certain choices that generate inequalities of political power are morally impermissible; that even... (shrink)

How important is it for managers to have the “nice” virtues of modesty, civility, and humility? While recent scholarship has tended to focus on the organizational consequences of leaders having or lacking these traits, I want to address the prior, deeper question of whether and how these traits are intrinsically morally important. I argue that certain aspects of modesty, civility, and humility have intrinsic importance as the virtues of relational equality – the attitudes and dispositions by which we relate as (...) moral equals. I provide a novel account of the normative grounds of the virtues of relational equality and develop a corresponding framework for how these virtues can be enacted by managers. The virtues are grounded in the value of opposing objectionable forms of social hierarchy, which requires social norms that grant all persons the same personal authority over their lives and interactions. I show how this view of virtue contrasts with prevailing Aristotelian, Personalist, and Smithian views in business ethics. I then explain how, for managers, sustaining and enacting the virtues of relational equality involves a distinctive cluster of role-specific traits: respect for employees’ equal personal authority, a commitment to express such respect, and a disposition to give equal weight and deference to employees’ relevant interests. (shrink)

In this article I criticize the non-consequentialist Weighted Lottery (WL) solution to the choice between saving a smaller or a larger group of people. WL aims to avoid what non-consequentialists see as consequentialism's unfair aggregation by giving equal consideration to each individual's claim to be rescued. In so doing, I argue, WL runs into another common objection to consequentialism: it is excessively demanding. WL links the right action with the outcome of a fairly weighted lottery, which means that an (...) agent can only act rightly if s/he has actually run the lottery. In many actual cases, this involves epistemic demands that can be almost impossible to meet. I argue that plausible moral principles cannot make such extreme epistemic demands. (shrink)

A leading international expert on environmental issues, Shrader-Frechette brings a new standard of rigor to philosophical discussions of environmental justice in her latest work. Observing that environmental activists often value environmental concerns over basic human rights, she points out the importance of recognising that minority groups and the poor in general are frequently the biggest victims of environmental degradation, a phenomenon with serious social and political implications that the environmental movement has failed to adequately address. She argues for their (...) class='Hi'>equal rights to 'environmental justice' and maintains that they should not have to bear most of the weight of the burdens of pollution and resource depletion. Advocating a greater awareness on the part of professionals in a position to help these victims, Shrader-Frechette proposes a more equitable distribution of environmental resources and, in doing so, makes an important contribution to the fields of environmental ethics and applied philosophy. (shrink)

In a recent article, Thomas Christiano defends the intrinsic justice of democracy grounded in the principle of equal consideration of interests. Each citizen is entitled to a single vote, equal in weight to all other citizens. The problem with this picture is that all citizens must meet a threshold of minimal competence. -/- My argument is that Christiano is wrong to claim a minimum threshold of competency is fully consistent with the principle of equality. While standards of minimal (...) competency may be justifiable, these standards justify political inequality. -/- This paper explores the relationship between equality and democracy in terms of minimal competency, demonstrating how minimal competency is justified and why it is inegalitarian in interesting ways. (shrink)

The recent decision of the House of Lords in Stack v. Dowden appears, at first sight, to endorse a new approach to the jointly owned family home. However, upon closer inspection, this proves to be something of an illusion: the new approach is remarkably similar to the traditional resulting trust in that it attaches more weight to financial payments than to other contributions. A further problem is that the disjunction between the reasoning of the judges and the actual result makes (...) it a difficult decision to apply to future cases. This case-note will consider the legal and social issues raised by the case and will argue that it has the potential to disadvantage women who do not make an equal financial contribution to the purchase of the home. (shrink)

If we can save the lives of only one of multiple groups of people, we might be inclined simply to save whichever group is largest. We may worry, though, that automatically saving the largest group fails to take each saveable individual sufficiently into account, offering some of these individuals no chance at all of being rescued. Still wanting to give larger groups higher chances of survival, we may then say that we ought to employ a proportionally weighted lottery to determine (...) which group to save. In this paper, I argue that this would be a mistake. Given the most plausible way of specifying it, the weighted-lottery view itself fails to treat each saveable individual with equal moral respect. (shrink)

This article is an attempt to evaluate the Oregon plan from the perspective of a Scandinavian national health care system. The Nordic welfare states are marked by a strong emphasis on equality. As an example of an egalitarian system we present the Norwegian health care model in part one. In part two, the arguments in favor of a one tier system in Norway are presented and compared to Oregon's two tier system. Although we argue, in part three, that a comparison (...) of the degree of explicitness in the prioritization process shows that Norway has much to learn from Oregon, we do believe that the Norwegian system has some attractive elements that may function as an important corrective. In part four we present the Norwegian Guidelines for priority-setting and discuss the weight assigned to the severity of disease criterion. It is argued that the exclusion of information about the severity of disease partly explains the counterintuitive ranking of treatment-condition pairs in Oregon's initial method based on the principle of health maximization. A normative analysis of the conflicting norms of efficiency and equality of results is called for. The final part of the paper is devoted to the problem of rigidity. Henry J. Aaron has argued that the Oregon system is insensitive to inter-individual variations within each diagnosis-treatment pair. This objection is a severe one, since the system might end up treating patients unfairly on the individual level. To overcome this problem, we suggest a selection rule that should be more capable of dealing with the problem of rigidity. (shrink)

Bioethicists often present ‘saving lives’ as a goal distinct from, and competing with, that of extending lives by as much as possible. I argue that this usage of the term is misleading, and provides unwarranted rhetorical support for neglecting the magnitudes of the harms and benefits at stake in medical allocation decisions, often to the detriment of the young. Equal concern for all persons requires weighting equal interests equally, but not all individuals have an equal interest (...) in ‘life-saving’ treatment. (shrink)

This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker showed that a simple game is non-weighted if and only if there exists a trading transform of finite size. They also provided an upper bound on the size of such a trading transform, if it exists. Gvozdeva and Slinko improved that upper bound; their proof employed a property of (...) linear inequalities demonstrated by Muroga. In this study, we provide a new proof of the existence of a trading transform when a given simple game is non-weighted. Our proof employs Farkas’ lemma, and yields an improved upper bound on the size of a trading transform. We also discuss an integer-weight representation of a weighted simple game, improving the bounds obtained by Muroga. We show that our bound on the quota is tight when the number of players is less than or equal to five, based on the computational results obtained by Kurz. Furthermore, we discuss the problem of finding an integer-weight representation under the assumption that we have minimal winning coalitions and maximal losing coalitions. In particular, we show a performance of a rounding method. Finally, we address roughly weighted simple games. Gvozdeva and Slinko showed that a given simple game is not roughly weighted if and only if there exists a potent certificate of non-weightedness. We give an upper bound on the length of a potent certificate of non-weightedness. We also discuss an integer-weight representation of a roughly weighted simple game. (shrink)

This study further examined the negative association between boys77, differences in height and log-transformed weight were judged using analysis of covariance (ANCOVA) with measurement age as a covariate, and parental education level (four levels), number of sisters (0, 1, 2 or 3+) and number of brothers (0, 1, 2+) as predictors. The relative importance of birth order and sibling sex was examined among the near majority of boys with one sibling (47%, 278/596). The sibling composition variable was defined using mutually (...) exclusive categories representing individuals with one sibling: either one older or younger brother or sister. All boys contributed information before leaving middle school at a mean age of 14·9±0·4 years SD. The results were compared with similar analyses of data for 154 of these same boys for whom measurements were available from primary school entry at a mean age of 6·4±0·3 years SD onward. Results were also compared with data for a cohort of 153 boys who entered primary school later in 1986. Results confirm that boys from the Da-an area born in the mid-1970s who did not have sisters were significantly taller (2·23·9 kg, p[less-than-or-equal]0·016) than those with one or two sisters. However, the 26 boys with three or more sisters, most of whom were last-born, were somewhat taller than those with one or two sisters. The same curvilinear relationships in height and weight appeared both among boys as they prepared to leave middle school and among the subset also measured just after entering primary school. When numbers of sisters were statistically controlled, the presence of two or more brothers was also significantly negatively associated with mean stature, but not weight, among middle school boys. Analyses among boys with one sibling revealed that birth order was associated with mean stature, but only if the sibling was female; an older sister was associated with a greater deficit in mean stature than a younger sister. Evidence of rising educational expectations, continued declines in family size with fewer gender-related differences in numbers of siblings, and a clear secular increase in body size in this community among children entering primary school from 1982 to 1986 suggest a possible explanatory model. (shrink)

Specifying accurate informative prior distributions is a question of carefully selecting studies that comprise the body of comparable background knowledge. Psychological research, however, consists of studies that are being conducted under different circumstances, with different samples and varying instruments. Thus, results of previous studies are heterogeneous, and not all available results can and should contribute equally to an informative prior distribution. This implies a necessary weighting of background information based on the similarity of the previous studies to the focal (...) study at hand. Current approaches to account for heterogeneity by weighting informative prior distributions, such as the power prior and the meta-analytic predictive prior are either not easily accessible or incomplete. To complicate matters further, in the context of Bayesian multiple regression models there are no methods available for quantifying the similarity of a given body of background knowledge to the focal study at hand. Consequently, the purpose of this study is threefold. We first present a novel method to combine the aforementioned sources of heterogeneity in the similarity measure ω. This method is based on a combination of a propensity-score approach to assess the similarity of samples with random- and mixed-effects meta-analytic models to quantify the heterogeneity in outcomes and study characteristics. Second, we show how to use the similarity measure ωas a weight for informative prior distributions for the substantial parameters in Bayesian multiple regression models. Third, we investigate the performance and the behavior of the similarity-weighted informative prior distribution in a comprehensive simulation study, where it is compared to the normalized power prior and the meta-analytic predictive prior. The similarity measure ω and the similarity-weighted informative prior distribution as the primary results of this study provide applied researchers with means to specify accurate informative prior distributions. (shrink)

This paper is an engagement with Equality by John Baker, Kathleen Lynch, Judy Walsh and Sara Cantillon. It identifies a dilemma for educational egalitarians, which arises within their theory of equality, arguing that sometimes there may be a conflict between advancing equality of opportunity and providing equality of respect and recognition, and equality of love care and solidarity. It argues that the latter values may have more weight in deciding what to do than traditional educational egalitarians have usually thought.

In this dissertation, I discuss two distributive principles in moral philosophy: Derek Parfit's Prioritarianism and Egalitarianism. I attempt to defend a version of Egalitarianism, which I call Weighted Egalitarianism. Although Parfit claims that Egalitarianism is subject to what he calls the Levelling Down Objection, I show that my proposed Weighted Egalitarianism is not subject to the Objection, and that it gives priority to the worse off people. The real difference between the two principles lies in how the weight of each (...) person's well-being is determined. Prioritarianism assumes that there is a moral scale of the goodness of well-being, independently of distributions of people's well-being. I raise two objections to this claim: firstly, it is hard to believe that the choice of the level of well-being affects our distributive judgement; secondly, it is hard to believe that there is such a moral scale independently of distributions of people's well-being. On the other hand, Weighted Egalitarianism claims that the weight is given by the rank order position of the person in the ranking by well-being level. This means that, in Weighted Egalitarianism, the goodness of a distribution is an increasing, linear function of people's well-being. Weighted Egalitarianism is not affected by the choice of the level of people's well-being. Nor does it require require the moral scale of the goodness of well-being independently of distributions of people's well-being. Leximin, which might be a version of Prioritarianism, avoids my objections. But it is hard to support Leximin, because it rules out the trade off between the better off and the worse off. I conclude that Weighted Egalitarianism is more acceptable than Prioritarianism. (shrink)

The (moral) permissibility of an act is determined by the relative weights of reasons, or so I assume. But how many weights does a reason have? Weight Monism is the idea that reasons have a single weight value. There is just the weight of reasons. The simplest versions hold that the weight of each reason is either weightier than, less weighty than, or equal to every other reason. We’ll see that this simple view leads to paradox in at least (...) two ways. We must complicate the picture somehow. I consider two candidate complications. The first, Parity Monism, is inspired by Ruth Chang’s suggestion that parity is a fourth comparative beyond the traditional three (>, <, =). This view complicates the single weight relation by allowing that the weights of reasons can be on a par. Unfortunately, Parity Monism resolves only one of the two paradoxes that afflict simple versions of Weight Monism. To resolve both paradoxes, we need our second candidate complication, Weight Pluralism. This view holds that reasons have at least two weight values (e.g., justifying weight and requiring weight) and these two values aren’t always equivalent. Parity is no substitute for Pluralism. (shrink)

The principle that each individual is entitled to an equal opportunity to benefit from any public health care system, and that this entitlement is proportionate neither to the size of their chance of benefitting, nor to the quality of the benefit, nor to the length of lifetime remaining in which that benefit may be enjoyed, runs counter to most current thinking about the allocation of resources for health care. It is my contention that any system of prioritisation of the (...) resources available for healthcare or of rationing such resources must be governed by this principle. -/- This can have apparently paradoxical conclusions in that it can seem wasteful to give someone with a very slim chance of a lifesaving treatment the same priority as someone with a much better chance. In an important and thoughtful recent paper, Julian Savulescu has concentrated on this apparent weakness and has argued for a particular conception of the good or benefit to be achieved by a healthcare system which purports to demonstrate the inadequacies of an equal opportunities approach to prioritisation and to replace it with an altogether better account. This paper will show that a rational ‘reasons based consequentialism’ is more in line with the equal opportunities approach, which I defended some time ago in these pages, than with that of Savulescu. I shall then examine more closely the conception of equal opportunities in health care and show that if we give weight to an individual's reasons, and what is expected to be good for them, we will opt for exactly the equality based account of distributive justice that I have recommended. (shrink)

It is a precept of commonsense morality that parents have permissions to be partial toward their own children in various ways: they are permitted to act in a variety of ways that favor the interests of their own children. But how are such permissions to be reconciled with more general principles of justice? In this article, I discuss this question as it arises for one kind of liberal egalitarian theory of justice. Given their robust commitment to an ideal of equality, (...) such theories face prima facie difficulties in accommodating the commonsense permissions of parental partiality. After sketching the contours of the apparent conflict between equality and parental partiality, I survey some of the ways in which some writers have attempted to reconcile equality and parental partiality, and I criticize these reconciliation proposals, which in different ways subordinate a concern for equality to a concern for parental partiality. I then suggest a different direction for reconciliation, which subordinates a concern for partiality to a concern for equality. This alternative reconciliation strategy, I argue, deserves to be taken seriously by liberal egalitarians; whether it is the most plausible way to reconcile equality and parental partiality depends on one’s view about the moral weight of people’s interest in parenting. (shrink)

By enacting equality laws the liberal state decides the limits of liberal tolerance by relying on content-based rather than content-neutral considerations. Equality laws are not and cannot be neutral. They reflect a content-based moral decision about the importance and weight of the principle of equality vis-à-vis other rights or interests. This leads to the following conclusions: First, since equality laws in liberal democracies reflect moral-liberal values, conscientious objections to equality laws rely, almost by definition, on unjustly intolerant, anti-liberal and morally (...) repugnant values. Secondly, we should not shy away from explicitly relying on moral-liberal views when deciding whether it is justified to grant exemptions from equality laws. Thirdly, conscientious objections to equality laws should normally not be tolerated or accommodated by the state, because conscientious objections that rely on what is rightly perceived as unjustly intolerant, anti-liberal and morally repugnant values should not be tolerated in a tolerant-liberal democracy. (shrink)

Social egalitarianism holds that individuals ought to have equal power over outcomes within relationships. Egalitarian philosophers have argued for this ideal by appealing to features of political society. This way of grounding the social egalitarian principle renders it dependent on empirical facts about political culture. In particular, egalitarians have argued that social equality matters to citizens in political relationships in a way analogous to the value of equality in a marriage. In this paper, we show how egalitarian philosophers are (...) committed to psychological premises, and then illustrate how to test the social egalitarian’s empirical claims. Using a nationally representative survey experiment, we find that citizens will sometimes prioritize equality over competing values, but that the weight of social equality diminishes when moving from personal to political cases. These findings raise questions for thinking about how to explain the normative significance of social equality. (shrink)

The purpose of this study is to explore the impact of constraining class-specific residual variances to be equal by examining and comparing the parameter estimation of a free model and a constrained model under various conditions. A Monte Carlo simulation study was conducted under several conditions, including the number of predictors, class-specific intercepts, sample size, class-specific regression weights, and class proportion to evaluate the results for parameter estimation of the free model and the restricted model. The free model yielded (...) a more accurate estimation than the restricted model for most of the conditions, but the accuracy of the free model estimation was impacted by the number of predictors, sample size, the disparity in the magnitude of class-specific slopes and intercepts, and class proportion. When equality constraints were imposed in residual variance discrepant conditions, the parameter estimates showed substantial inaccuracy for slopes, intercepts, and residual variances, especially for those in Class 2. When the residual variances were equal between the classes, the restricted model showed better performance under some conditions. (shrink)