Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.

Richard Jeffrey's generalization of Bayes' rule of conditioning follows, within the theory of belief functions, from Dempster's rule of combination and the rule of minimal extension. Both Jeffrey's rule and the theory of belief functions can and should be construed constructively, rather than normatively or descriptively. The theory of belief functions gives a more thorough analysis of how beliefs might be constructed than Jeffrey's rule does. The inadequacy of Bayesian conditioning is much more general than (...) Jeffrey's examples of uncertain perception might suggest. The ``parameter α '' that Hartry Field has introduced into Jeffrey's rule corresponds to the "weight of evidence" of the theory of belief functions. (shrink)

In a recent monograph, I advocated a new theory—the theory of belief functions—as an alternative to the Bayesian theory of epistemic probability. In this paper I compare the two theories in the context of a simple but authentic example of assessing evidence.The Bayesian theory is ostensibly the theory that assessment of evidence should proceed by conditioning additive probability distributions; this theory dates from the work of Bayes and Laplace in the second half of the eighteenth century. It is indisputably the (...) dominant theory of epistemic probability today.The theory of belief functions differs from the Bayesian theory in that it uses certain non-additive set functions in the place of additive probability distributions and in that it generalizes the rule of conditioning to a general rule for combining evidence. As a mathematical theory its apparent origin is rather recent and abrupt; it first appears in work of A. P. Dempster, published in the 1960’s. (shrink)

I show that Dempster's Rule of combination can be represented in the theory of Markov chains and use this representation to derive limit theorems concerning the long term effect of updating belief with Dempster's rule.

Introduction -- Part I: The good life -- Hedonism : its powerful appeal -- Is happiness all that matters? -- Getting what you want -- Problems for the desire theory -- Part II: Doing the right thing -- Morality and religion -- Natural law theory -- Psychological egoism -- Ethical egoism -- Consequentialism : its nature and attractions -- Consequentialism : its difficulties -- The kantian perspective : fairness and justice -- The kantian perspective : autonomy and respect -- The (...) social contract tradition : theory and attractions -- The social contract tradition : problems and prospects -- Ethical pluralism and absolute moral rules -- Ethical pluralism : prima facie duties and ethical particularism -- Virtue ethics -- Feminist ethics -- Part III: The status of morality -- Ethical relativism -- Moral nihilism -- Ten arguments against moral objectivity. (shrink)

The traditional conception of ethical theory sees it as the project of developing a coherent set of rules from which one can infer all determinate moral verdicts. I am not optimistic about the prospects for constructing such a theory. To explain this pessimism, we need to understand what moral rules are and what roles they might play in ethical theory.

Choquet expected utility substitutes capacities for subjective probabilities to explain uncertainty aversion and related phenomena. This paper studies capacities as models of belief. The notions of inner and outer acceptance context are defined. These are shown to be the natural acceptance contexts when belief expansion is described by naïve Bayesian and Dempster–Shafer updating of capacities respectively. We also show that Eichberger and Kelsey's use of Dempster–Shafer updating as a model of belief revision may lead to violations of the (...) AGM axioms for rational belief change. (shrink)

The Dempster–Shafer approach to expressing beliefabout a parameter in a statistical model is notconsistent with the likelihood principle. Thisinconsistency has been recognized for some time, andmanifests itself as a non-commutativity, in which theorder of operations (combining belief, combininglikelihood) makes a difference. It is proposed herethat requiring the expression of belief to be committed to the model (and to certain of itssubmodels) makes likelihood inference very nearly aspecial case of the Dempster–Shafer theory.

Previous work has shown that the Complex Conceptual Spaces − Single Observation Mathematical framework is a useful tool for event characterization. This mathematical framework is developed on the basis of Conceptual Spaces and uses integer linear programming to find the needed similarity values. The work of this paper is focused primarily on space event characterization. In particular, the focus is on the ranking of threats for malicious space events such as a kinetic kill. To make the Conceptual Spaces framework work, (...) the similarity values between the contents of observations on the one hand and the properties of the entities observed on the other needs to be found. This paper shows how to exploit Dempster-Shafer theory to implement a statistical approach for finding these similarities values. This approach will allow a user to identify the uncertainty involved in similarity value data, which can later be propagated through the developed mathematical model in order for the user to know the overall uncertainty in the observation-to-concept mappings needed for space event characterization. (shrink)

An introduction to Dempster-Shafter Theory, from a lecture at the Northern Institute of Philosophy in 2010.

Let Ln be a sentential language with n atomic sentences {A1, . . . , An}. Let Sn = {s1, . . . , s2n} be the set of 2n state descriptions of Ln, in the following, canonical lexicographical truth-table order: State Description A1 A2 · · · An−1 An T T T T T s1 = A1 & A2 & · · · &An−1 & An T T T T F s1 = A1 & A2 & · · · (...) &An−1 & ¬An T T T F T s3 = A1 & A2 & · · · & ¬An−1 & An T T T F F s4 = A1 & A2 & · · · & ¬An−1 & ¬An.. (shrink)

Combining testimonial reports from independent and partially reliable information sources is an important epistemological problem of uncertain reasoning. Within the framework of Dempster–Shafer theory, we propose a general model of partially reliable sources, which includes several previously known results as special cases. The paper reproduces these results on the basis of a comprehensive model taxonomy. This gives a number of new insights and thereby contributes to a better understanding of this important application of reasoning with uncertain and incomplete information.

Analyzing situations where information is partial, incomplete or contradictory has created a demand for quantitative belief measures that are weaker than classic probability theory. In this paper, we compare two frameworks that have been proposed for this task, Dempster-Shafer theory and non-standard probability theory based on Belnap-Dunn logic. We show the two frameworks to assume orthogonal perspectives on informational shortcomings, but also provide a partial correspondence result. Lastly, we also compare various dynamical rules of the two frameworks, all seen as (...) generalizations of classic Bayes’ conditioning. (shrink)

This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas (...) to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster?Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values.We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005. (shrink)

Sometimes appearances provide epistemic support that gets undercut later. In an earlier paper I argued that standard Bayesian update rules are at odds with this phenomenon because they are ‘rigid’. Here I generalize and bolster that argument. I first show that the update rules of Dempster–Shafer theory and ranking theory are rigid too, hence also at odds with the defeasibility of appearances. I then rebut three Bayesian attempts to solve the problem. I conclude that defeasible appearances pose a more (...) difficult and pervasive challenge for formal epistemology than is currently thought. 1 The Challenge for Bayesianism1.1 Updating and experience1.2 The problem1.3 Objections2 The Challenge for Dempster–Shafer Theory2.1 Background on Dempster–Shafer theory2.2 The problem for Dempster–Shafer theory3 The Challenge for Ranking Theory4 The Appeal to Metacognition5 The Appeal to Richer Inputs6 The Appeal to a Generic Underminer7 Conclusion. (shrink)

Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason for the epistemological success of (...) probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability theory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositions2 to be true (or to be false or neither). Probability theory, however, offers no formal counterpart to this notion. Believing A is not the same as having probability 1 for A, because probability 1 is incorrigible3; but plain belief is clearly corrigible. And believing A is not the same as giving A a probability larger than some 1 - c, because believing A and believing B is usually taken to be equivalent to believing A & B.4 Thus, it seems that the formal representation of plain belief has to take a non-probabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or, since I make the common assumption that plain belief is deductively closed, by the conjunction of all propositions believed true in it. But this does not yet provide a theory of induction, i.e. an answer to the question how epistemic states so represented are changed tbrough information or experience. There is a convincing partial answer: if the new information is compatible with the old epistemic state, then the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. This answer is partial because it does not cover the quite common case where the new information is incompatible with the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise, we would not represent plain belief as conigible. The crucial problem is that there is no good completion. When epistemic states are represented simply by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed, as far as I know, which provides a complete solution to this problem. In this paper, I want to suggest such a solution. In [4], I have more fully argued that this is the only solution, if certain plausible desiderata are to be satisfied. Here, in section 2, I will be content with formally defining and intuitively explaining my proposal. I will compare my proposal with probability theory in section 3. It will turn out that the theory I am proposing is structurally homomorphic to probability theory in important respects and that it is thus equally easily implementable, but moreover computationally simpler. Section 4 contains a very brief comparison with various kinds of logics, in particular conditional logic, with Shackle's functions of potential surprise and related theories, and with the Dempster - Shafer theory of belief functions. (shrink)

Fitelson and McCarthy have proposed an accuracy measure for confidence orders which favors probability measures and Dempster-Shafer belief functions as accounts of degrees of belief and excludes ranking functions. Their accuracy measure only penalizes mistakes in confidence comparisons. We propose an alternative accuracy measure that also rewards correct confidence comparisons. Thus we conform to both of William James’ maxims: “Believe truth! Shun error!” We combine the two maxims, penalties and rewards, into one criterion that we call prioritized accuracy optimization. That (...) is, PAO punishes wrong comparisons and rewards right comparisons. And it requires to prioritize being right und avoiding to be wrong in a specific way. Thus PAO is both, a scoring rule and a decision rule. It turns out that precisely confidence orders representable by two-sided ranking functions satisfy PAO. The point is not to argue that PAO is the better accuracy goal. The point is only that ranking theory can also be supported by accuracy considerations. Thus, those considerations by themselves cannot decide about rational formats for degrees of belief, but are part and parcel of an overall normative assessment of those formats. (shrink)

Merging logic and mathematics in deductive inference-an innovative, cutting-edge approach. Optimization methods for logical inference? Absolutely, say Vijay Chandru and John Hooker, two major contributors to this rapidly expanding field. And even though "solving logical inference problems with optimization methods may seem a bit like eating sauerkraut with chopsticks... it is the mathematical structure of a problem that determines whether an optimization model can help solve it, not the context in which the problem occurs." Presenting powerful, proven optimization techniques for (...) logic inference problems, Chandru and Hooker show how optimization models can be used not only to solve problems in artificial intelligence and mathematical programming, but also have tremendous application in complex systems in general. They survey most of the recent research from the past decade in logic/optimization interfaces, incorporate some of their own results, and emphasize the types of logic most receptive to optimization methods-propositional logic, first order predicate logic, probabilistic and related logics, logics that combine evidence such as Dempster-Shafer theory, rule systems with confidence factors, and constraint logic programming systems. Requiring no background in logic and clearly explaining all topics from the ground up, Optimization Methods for Logical Inference is an invaluable guide for scientists and students in diverse fields, including operations research, computer science, artificial intelligence, decision support systems, and engineering. (shrink)

The theory of random propositions is a theory of confirmation that contains the Bayesian and Shafer—Dempster theories as special cases, while extending both in ways that resolve many of their outstanding problems. The theory resolves the Bayesian problem of the priors and provides an extension of Dempster's rule of combination for partially dependent evidence. The standard probability calculus can be generated from the calculus of frequencies among infinite sequences of outcomes. The theory of random propositions is generated analogously from (...) the calculus of frequencies among pairs of infinite sequences of suitably generalized outcomes and in a way that precludes the inclusion of contrived orad hoc elements. The theory is also formulated as an uninterpreted calculus. (shrink)

In this paper we propose a semantic analysis of Lewis' counterfactuals. By exploiting the structural properties of the recently introduced boolean algebras of conditionals, we show that counterfactuals can be expressed as formal combinations of a conditional object and a normal necessity modal operator. Specifically, we introduce a class of algebras that serve as modal expansions of boolean algebras of conditionals, together with their dual relational structures. Moreover, we show that Lewis' semantics based on sphere models can be reconstructed in (...) this framework. As a consequence, we establish the soundness and completeness of a slightly stronger variant of Lewis' logic for counterfactuals with respect to our algebraic models. In the second part of the paper, we present a novel approach to the probability of counterfactuals showing that it aligns with the uncertainty degree assigned by a belief function, as per Dempster-Shafer theory, to its associated conditional formula. Furthermore, we characterize the probability of a counterfactual in terms of Gärdenfors' imaging rule for the probabilistic update. (shrink)

In his recent monograph [7], Professor Shafer has offered us an alternative to Bayesian inference with his novel theory of belief functions and, in his current paper [8], has characterized his position by pointing to two basic differences it shares with Bayesianism. First, belief functions are non-additive so that the degree of belief assigned to the disjunction ‘A1 or A2’ may be larger than the sum of the degrees of belief assigned to the separate disjuncts. Second, the theory of belief (...) functions has its own rule for determining the commitments to changes in degrees of belief when evidence is compounded. So, instead of the Bayesian postulate of conditionalization, that is, in place of using Bayes’ theorem to identify the commitments to changes in probability when evidence accumulates, the theory advocated by Professor Shafer relies on a proposal he traces to A.P.Dempster, which he calls Dempster’s rule for combination of belief functions. (shrink)

This study investigates the relations among Machiavellianism, the stakeholder orientation, and Italian managers' support for corporate social and environmental reporting (SER). These relationships have not previously been investigated among a sample of experienced managers but have important implications. As anticipated, Machiavellianism had a strong negative association with the support for SER. Machiavellianism was also negatively related to the stakeholder orientation, which in turn was positively correlated with the support for SER. Support for the stakeholder orientation partially mediated the association between (...) Machiavellianism and SER. The findings advance our understanding of the motivations for sustainability reporting by documenting that managers' fundamental personality traits and economic ideologies are closely associated and are important determinants of normative support for social and environmental disclosures. We further suggest that the results support the case for mandated compliance‐with‐standard sustainability reports coupled with a requirement that such reports be independently audited. (shrink)

Living Ethics: An Introduction with Readings is an ideal all-in-one resource for courses in introduction to ethics and contemporary moral problems. In this hybrid textbook/reader, Russ Shafer-Landau brings moral theory and contemporary moral issues to life with a comprehensive and balanced set of readings, uniquely engaging explanations, and clear analysis of arguments. The book balances coverage of moral reasoning (in Part 1) with highly relevant contemporary moral problems (in Part 2).

Should we allow performance-enhancing substances in competitive athletics? The first book of its kind, Well Played answers this question by urging us to a deeper appreciation for the purpose of sport. Giving special reference to performance-enhancing substances, Shafer challenges the incompleteness of the ethical arguments and contributes a Christian voice to the discussion. He initiates a theological conversation that is both scholarly and accessible, arguing that a distinctively Christian understanding of sport will have far-reaching implications for how we treat ethical (...) issues like doping. The values, beliefs, and practices within the Christian tradition show an alternative that prioritizes humility and friendship, grace and gratitude over the "win at all costs" mentality that drives the use of performance-enhancing substances for a competitive advantage. This groundbreaking book ventures into new theological territory as it explores the intersections of theology, philosophy of sport, and the ethics of doping. Theologians, ethicists, and pastors, as well as coaches, athletes, and sports fans will benefit from this book's thoughtful reflection on how Christians can play well in the modern sports culture. (shrink)

Our project in this essay is to showcase nonnaturalistic moral realism’s resources for responding to metaphysical and epistemological objections by taking the view in some new directions. The central thesis we will argue for is that there is a battery of substantive moral propositions that are also nonnaturalistic conceptual truths. We call these propositions the moral fixed points. We will argue that they must find a place in any system of moral norms that applies to beings like us, in worlds (...) similar to our own. By committing themselves to true propositions of these sorts, nonnaturalists can fashion a view that is highly attractive in its own right, and resistant to the most prominent objections that have been pressed against it. (shrink)

Introduction -- Value theory : the nature of the good life -- Epicurus letter to Menoeceus -- John Stuart Mill, Hedonism -- Aldous Huxley, Brave new world -- Robert Nozick, The experience machine -- Richard Taylor, The meaning of life -- Jean Kazez, Necessities -- Normative ethics : theories of right conduct -- J.J.C. Smart, Eextreme and restricted utilitarianism -- Immanuel Kant the good will & the categorical imperative -- Thomas Hobbes, Leviathan -- Philippa Foot, Natural goodness -- Aristotle, Nicomachean (...) ethics -- W.D. Ross, What makes right acts right? -- Hilde Lindemann, What is feminist ethics? -- Metaethics : the status of morality -- David Hume, Moral distinctions not derived from reason -- J.L. Mackie, The subjectivity of values -- Gilbert Harman, Ethics and observation -- Mary Midgley, Trying out one's new sword -- Michael Smith, Rrealism -- Renford Bambrough, Pproof -- Moral problems -- Peter Singe, The Singer solution to world poverty -- Heidi Malm, Paid surrogacy: arguments and responses -- Ronald Dworkin, Playing God : genes, clones, and luck -- James Rachels, The morality of euthanasia -- John Harris, The survival lottery -- Peter Singer, Unsanctifying human life -- William F. Baxter, People or penguins : the case for optimal pollution -- Judith Jarvis, Tthomson a defense of abortion -- Don Marquis, Why abortion is immoral -- Jonathan Bennett, The conscience of Huckleberry Finn -- Michael Walzer, Terrorism : a critique of excuses -- David Luban, Liberalism, torture, and the ticking bomb -- Martin Luther King, Jr., Letter from Birmingham City Jail -- Igor Primoratz, Justifying legal punishment -- Stephen Nathanson, An eye for an eye -- Michael Huemer, America's unjust drug war -- John Corvino, Why shouldn't Tommy and Jimmy have sex? : a defense of homosexuality -- Bonnie Steinbock, Adultery -- Hugh Lafollette, Licensing parents -- Jane English, What do grown children owe their parents? (shrink)

Simon Blackburn has developed an interesting challenge to moral realism based on its alleged inability to account for supervenience relations between the moral and nonmoral. If supervenience holds, then any base property once giving rise to a supervening one must always do so. The realist accepts supervenience, but also (according to Blackburn) accepts the claim that nonmoral base properties do not necessitate the moral ones that supervene on them. This combination is thought deadly, because it leaves the realist without an (...) explanation of why ethical supervenience should be true. I offer three responses on behalf of the moral realist. The first rejects the need for explanation, arguing that supervenience should be understood as closely analogous to Leibniz's law, which, I argue, needs no defense. I next argue that ethical naturalism may be right, and if so, would provide an adequate response to Blackburn. Lastly, I show that the success of Blackburn's arguments implies a global antirealism, and so does not, as he claims, amount to a special problem for realism in ethics. (shrink)

There is a long-running debate among legal scholars regarding the propriety and enforceability of SEC attempts to mandate disclosures of antisocial or illegal corporate activities that do not materially impact a company’s financial statements. This debate was recently revived by the issuance of SEC Staff Accounting Bulletin 99, Materiality in Financial Statements (SEC 1999), which suggests that quantitatively immaterial information relating to unlawful transactions or regulatory non-compliance should be considered for disclosure. This issue has important implications for the accounting profession, (...) although it has generally been ignored in the accounting literature. This paper reviews legal and ethical considerations raised by the issue of qualitative disclosures, and also presents the results of a preliminary empirical test of the impact of such disclosures on financial statement users’ judgments. The results of this study indicate that investors consider the nondisclosure of immaterial illegal acts to be unethical, and reject suggestions that such information lacks moral intensity. The results also suggest that immaterial illegal acts have a significant effect on investors’perceptions of the quality of corporate management and the likelihood of investment in a company. This effect was more pronounced when the illegal act was combined with self-dealing on the part of corporate executives. (shrink)

The contents of the inaugural volume of Oxford Studies in Metaethics nicely mirror the variety of issues that make this area of philosophy so interesting. The volume opens with Peter Railton's exploration of some central features of normative guidance, the mental states that underwrite it, and its relationship to our reasons for feeling and acting. In the next offering, Terence Cuneo takes up the case against expressivism, arguing that its central account of the nature of moral judgments is badly mistaken. (...) Terence Horgan and Mark Timmons, two of the most prominent contemporary expressivists, then offer their take on how expressivism manages to avoid a different objection-that of collapsing into an objectionable form of relativism. Daniel Jacobson and Justin D'Arms next offer an article that continues their research program devoted to exploring the extent to which values might depend upon, or be constrained by, human psychology. Ralph Wedgwood engages in some classical metaethical conceptual analysis, seeking to explicate the meaning of ought. Mark van Roojen then contributes a new take on the Moral Twin Earth Argument, a prominent anti-realist puzzle advanced in the early 1990s by Horgan and Timmons. -/- Allan Gibbard next presents his latest thoughts on the nature of moral feelings and moral concepts, crucial elements in the overall project of defending the expressivism he is so well known for. James Dreier then takes up the details of Gibbard's recent efforts to provide a solution to what many view as the most serious difficulty for expressivism, namely, the Frege-Geach problem. Dreier identifies difficulties in Gibbard's expressivist account, and offers a suggestion for their solution. Sergio Tenenbaum explores the concept of a direction of fit, relied on so heavily nowadays in accounts of moral motivation. Nadeem Hussain and Nishiten Shah then consider the merits of Christine Korsgaard's influential critique of moral realism. T. M. Scanlon's widely-discussed buck-passing account of value attracts the critical eye of Pekka Väyrynen, who attempts to reveal the reasons that we might resist it. Derek Parfit's contribution concludes this volume, with an article on normativity that presents his most recent thinking on this fundamental notion. (shrink)

This study examined the effects of social integration on the psychological well-being of American women who were wives and mothers of young children in the 1950s. The sample, drawn from a 1956 data archive, consisted of 358 married mothers with children under age 13 who lived in upstate New York. The authors focused on two measures of psychological well-being, self-esteem and general life satisfaction, and three measures of women's subjective appraisal of the mother role. Using hierarchical multiple regression and controlling (...) for potentially important individual and structural variables, the authors found that the number of nonfamily roles beyond those of wife and mother that this sample of women occupied was positively related to both self-esteem and general life satisfaction and was negatively related to feelings of detachment from the mothering role. These effects remained regardless of whether or not women were in the labor force and regardless of their social class. The paid worker role per se was not related to self-esteem or general life satisfaction but was related to feelings of maternal discontent and maternal inadequacy. (shrink)

This article offers a pragmatist conception of multiplicitous subjectivity that captures the best features of Richard Rorty’s private ironist and John Dewey’s social self while rejecting anti-democratic implications I identify in each. On the one hand, Rorty rightly sees that having a plural self is crucial for self-creation but fails to see the connection between self-creation and social justice. On the other hand, Dewey rightly sees the interrelationship between personal and social growth but fails to appreciate the danger implicit in (...) his emphasis on integration of differences (both within the self and in the community). To see how we can achieve a compelling synthesis of these two views, I turn to Gloria Anzaldúa’s theory of “mestiza consciousness,” which points us toward a model of democratic citizenship that brings together Rorty’s tolerance for multiplicity and ambivalence with Dewey’s relational understanding of personal development and social progress. (shrink)