This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling (...) rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists. (shrink)

When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model (...) for the data but who holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an "improper" prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive. (shrink)

When can a Bayesian investigator select an hypothesis H and design an experiment to make certain that, given the experimental outcome, the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model for the data but who (...) holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an "improper" prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive. (shrink)

The Sleeping Beauty problem has spawned a debate between “Thirders” and “Halfers” who draw conflicting conclusions about Sleeping Beauty’s credence that a coin lands Heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the Experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. (...) We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the Experiment. (shrink)

Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Also we address Adam Elga’s rebuttal to Belot’s analysis, (...) which focuses attention on the role that the assumption of countable additivity plays in Belot’s criticisms. (shrink)

Methodology for conducting clinical trials of new drugs and treatments on people need not be regarded as fixed. After reviewing the currently most popular method (randomization) and its ethical problems, this paper explores the possibilities of a new method for conducting such trials. It relies on new Bayesian technology for eliciting the opinions of medical experts. These opinions are conditioned on specific predictor variables, and are held in a computer. At any stage in a trial, these opinions can be updated (...) in the computer using the information collected in the trial up to that point. Consider as an admissible treatment for a patient having specific values of predictor variables only those treatments that at least one expert regards as best (in the computer model) for this patient. It is proposed that only admissible treatments, so defined, be allowed to be assigned to the patient. The ethical and statistical consequences of this principle are explored. Experience to date with a trial at Johns Hopkins designed on this principle is reported. Keywords: Bayesian statistics, information, clinical trial CiteULike Connotea Del.icio.us What's this? (shrink)

The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. (...) We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the experiment. (shrink)

According to Mark Rubinstein ‘In 1952, anticipating Kenneth Arrow and John Pratt by over a decade, he [de Finetti] formulated the notion of absolute risk aversion, used it in connection with risk premia for small bets, and discussed the special case of constant absolute risk aversion.’ The purpose of this note is to ascertain the extent to which this is true, and at the same time, to correct certain minor errors that appear in de Finetti's work.

A donation paradox occurs when a player gives an apparently valuable prerogative to another player, but ‘does better’, according to some criterion. Peremptory challenges, used in choosing a American jury, permit each side to veto a certain number of potential jurors. With even a very simple model of jury selection, it is shown that for one side to give a peremptory challenge to the other side may lead to a more favorable jury, an instance of the donation paradox. Both a (...) theorem and examples are given concerning the existence of the donation paradox in the optimal use of peremptory challenges. (shrink)

Experimenters sometimes insist that it is unwise to examine data before determining how to analyze them, as it creates the potential for biased results. I explore the rationale behind this methodological guideline from the standpoint of an error statistical theory of evidence, and I discuss a method of evaluating evidence in some contexts when this predesignation rule has been violated. I illustrate the problem of potential bias, and the method by which it may be addressed, with an example from the (...) search for the top quark. A point in favor of the error statistical theory is its ability, demonstrated here, to explicate such methodological problems and suggest solutions, within the framework of an objective theory of evidence. (shrink)

Sometimes conducting an experiment to ascertain the state of a system changes the state of the system being measured. Kahneman & Tversky modelled this effect with ‘support theory’. Quantum physics models this effect with probability amplitude mechanics. As this paper shows, probability amplitude mechanics is similar to support theory. Additionally, Viscusi's proposed generalized expected utility model has an analogy in quantum mechanics.

In the longstanding foundational debate whether to require that probability is countably additive, in addition to being finitely additive, those who resist the added condition raise two concerns that we take up in this paper. (1) _Existence_: Settings where no countably additive probability exists though finitely additive probabilities do. (2) _Complete Additivity_: Where reasons for countable additivity don’t stop there. Those reasons entail complete additivity—the (measurable) union of probability 0 sets has probability 0, regardless the cardinality of that union. Then (...) probability distributions are discrete, not continuous. We use Easwaran’s (Easwaran, Thought 2:53–61, 2013) advocacy of the _Comparative_ principle to illustrate these two concerns. Easwaran supports countable additivity, both for numerical probabilities and for finer, qualitative probabilities, by defending a condition he calls the _Comparative_ principle [ \({\mathcal{C}}\) ]. For numerical probabilities, principle \({\mathcal{C}}\) contrasts pairs, P 1 and P 2, defined over a common partition \(\prod\) = {a _i_ : _i_ ∈ I} of measurable events. \({\mathcal{C}}\) requires that no P 1 may be pointwise dominated, i.e., no (finitely additive) probability P 2 exists such that for each _i_ ∈ I, P 2 (a _i_ ) > P 1 (a _i_ ). By design, the cardinality of \(\prod\) is not limited in \({\mathcal{C}}\), which Easwaran asserts is important when arguing that the principle does not require more, or less, than that probability is countably additive. We agree that a numerical probability P satisfies principle \({\mathcal{C}}\) in all partitions just in case P is countably additive. However, we show that for numerical probabilities, by considering the size of the algebra of events to which probability is applied, principle \({\mathcal{C}}\) is subject to each of the above concerns, (1) and (2). Also, Easwaran considers principle \({\mathcal{C}}\) with non-numerical, qualitative probabilities, where a qualitative probability may be finer than an almost agreeing numerical probability P. A qualitative probability is regular if possible events are strictly more likely than impossible events. Easwaran motivates and illustrates regular qualitative probabilities using a continuous, almost agreeing quantitative probability that is uniform on the unit interval. We make explicit the conditions for applying principle \({\mathcal{C}}\) with qualitative probabilities and show that \({\mathcal{C}}\) restricts regular qualitative probabilities to those whose almost agreeing quantitative probabilities are completely additive. For instance, Easwaran’s motivating example of a regular qualitative probability is precluded by principle \({\mathcal{C}}\). (shrink)

We give necessary and sufficient conditions for a scoring rule to be proper for a quantile if utility is linear, and the distribution is unrestricted. We also give results when the set of distributions is limited, for example, to distributions that have first moments.

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. (...) We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. (shrink)

We review de Finetti’s two coherence criteria for determinate probabilities: coherence1defined in terms of previsions for a set of events that are undominated by the status quo – previsions immune to a sure-loss – and coherence2 defined in terms of forecasts for events undominated in Brier score by a rival forecast. We propose a criterion of IP-coherence2 based on a generalization of Brier score for IP-forecasts that uses 1-sided, lower and upper, probability forecasts. However, whereas Brier score is a strictly (...) proper scoring rule for eliciting determinate probabilities, we show that there is no real-valuedstrictly proper IP-score. Nonetheless, with respect to either of two decision rules – Γ-maximin or E-admissibility-+-Γ-maximin – we give a lexicographic strictly proper IP-scoring rule that is based on Brier score. (shrink)

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of whatcounts as a constant outcome. Although it is sometimes clear what should be considered constant, in many cases there are several possible (...) choices. Each choice can lead to a different "unique" probability and utility. By focusing attention on statedependent utilities, we determine conditions under which a truly unique probability and utility can be determined from an agent's expressed preferences among acts. Suppose that an agent's preference can be represented in terms of a probability P and a utility U.That is, the agent prefers one act to another iff the expected utility of that act is higher than that of the other. There are many other equivalent representations in terms of probabilities Q, which are mutually absolutely continuous with P, and state-dependent utilities V, which differ from U by possibly different positive affine transformations in each state of nature. We describe an example in which there are two different but equivalent state-independent utility representations for the same preference structure. They differ in which acts count as constants. The acts involve receiving different amounts of one or the other of two currencies, and the states are different exchange rates between the currencies. It is easy to see how it would not be possible for constant amounts of both currencies to have simultaneously constant values across the differentstates. Savage (1954, sec. 5.5) discovered a situation in which two seemingly equivalent preference structures are represented by different pairs of probability and utility. He attributed the phenomenon to the construction of a "small world." We show that the small world problem is just another example of two different, but equivalent, representations treating different actsas constants. Finally, we prove a theorem (similar to one of Karni 1985) that shows how to elicit a unique state-dependent utility and does not assume that there are prizes with constant value. To do this, we define a new hypothetical kind of act in which both the prize to be awarded and the state of nature are determined by an auxiliary experiment. (shrink)

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably additive probability has (...) conditional probabilities that fail to be conglomerable in some countable partition. (shrink)

The degree of incoherence, when previsions are not made in accordance with a probability measure, is measured by either of two rates at which an incoherent bookie can be made a sure loser. Each bet is considered as an investment from the points of view of both the bookie and a gambler who takes the bet. From each viewpoint, we define an amount invested (or escrowed) for each bet, and the sure loss of incoherent previsions is divided by the escrow (...) to determine the rate of incoherence. Potential applications include the treatment of arbitrage opportunities in financial markets and the degree of incoherence of classical statistical procedures. We illustrate the latter with the example of hypothesis testing at a fixed size. (shrink)

When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the status quo, (...) then preferences over rich sets of unbounded variables, such as variables used in the St. Petersburg paradox, cannot preserve indifference between all pairs of equivalent variables. In such circumstances, preference is not a function only of probability and utility for outcomes. Then the preference ordering is not defined in terms of lotteries. (shrink)

We investigate differences between a simple Dominance Principle applied to sums of fair prices for variables and dominance applied to sums of forecasts for variables scored by proper scoring rules. In particular, we consider differences when fair prices and forecasts correspond to finitely additive expectations and dominance is applied with infinitely many prices and/or forecasts.

It has long been known that the practice of testing all hypotheses at the same level , regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti’s “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to measure the rate at which incoherent procedures are sure (...) to lose, so that we can distinguish slightly incoherent procedures from grossly incoherent ones. We present an analysis of testing a simple hypothesis against a simple alternative as a case‐study of how the method can work. (shrink)

It has long been known that the practice of testing all hypotheses at the same level , regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti’s “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to measure the rate at which incoherent procedures are sure (...) to lose, so that we can distinguish slightly incoherent procedures from grossly incoherent ones. We present an analysis of testing a simple hypothesis against a simple alternative as a case‐study of how the method can work. (shrink)

Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unit-less numerical measures of value for consequences. Here, we address the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisions. When multiple currencies are available for paying the loss, one must take explicit (...) account of which currency is used as well as the exchange rates between the various available currencies. (shrink)

We give an extension of de Finetti’s concept of coherence to unbounded random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to unbounded random variables that we believe has advantages over Lebesgue-style integrals in the finitely additive setting. We also give a general version of the Fundamental Theorem of Prevision to deal with conditional previsions and unbounded random variables.

uniquely into a convex combination of a countably additive probability and a purely finitely additive (PFA) one. The coefficient of the PFA probability..

Ever since the publication of Placide Tempel's epoch-making work Bantu Philosophy, African philosophers have worked to dispel the myth that there is no metaphysics in Africa.

The standard “gladiatorial” interpretation of the Modes of Agrippa has undergone several recent attacks. Scholars have criticized it because it seems to portray the skeptic as a dogmatist about logical support and because it does not treat all five Modes as part of the system. Although some have attempted to patch up the standard interpretation to address these issues, I raise a further problem: The gladiatorial interpretation cannot make sense of the skeptic using the Modes on herself, to suspend her (...) own judgment. In light of these problems, I propose a fresh interpretation: The Agrippan Modes should be understood, not as arguments (or argument forms), but as types of dialectical challenge that the skeptic can use in an endless inquiry into any dogmatic position. (shrink)

Machine generated contents note: Contributors ix -- Foreword by Douglas A. Boyd andJoseph D. Straubhaar xiii -- Preface byMariaHenson xv -- Acknowledgments xvii -- Part I. Introduction 1 -- Chapter 1. Journalism as a Mission: Ethics and Purpose -- from an International Perspective -- by Joseph B. Atkins 3 -- Chapter 2. Chaos and Order: Sacrificing the Individual for the -- Sake of Social Harmony -- by John C. Merrill 17 -- Part II. In the United States and Latin (...) America 37 -- Chapter 3. Ways of a Muckraker -- by Jerry Mitchell 39 -- Chapter 4. A Sinister Zone of Likeness: Journalists as Heroes and -- Villains in the U.S. South and in Central and Eastern -- Europe -- by Joseph B. Atkins 45 -- Chapter 5. From Collusion to Independence: The Press, The Ruling -- Party, and Democratization in Mexico -- byMichaelSnodgrass 55 -- Chapter 6. The Outspoken Journalist Is an Expression, a Symbol -- of Colombia -- by Stephen E Jackson 69 -- Part III. In Europe 77 -- Chapter 7. The Stranger: Minorities and Their Treatment -- in the German Media -- by Georg Ruhrmann 79 -- Chapter 8. Between State Control and the Bottom Line: -- Journalism and Journalism Ethics in Hungary -- by Ildiko Kaposi and Eva Vajda 91 -- Chapter 9. SITA: Slovakia's First Independent News Service and -- Its Battles with the Huey Long of the Danube -- byPavol Mudry 101 -- Chapter 10. Holding Politicians' Feet to the Fire in Slovenia -- by Bernard Nezmah 111 -- Part IV. In the Middle East and Africa 121 -- Chapter 11. Lebanese Television: Caught Between the -- Government and the Private Sector -- by Nabil Dajani 123 -- Chapter 12. Press Freedom and the Crisis of Ethical Journalism -- in Southern Africa -- by Regina Jere-Malanda 143 -- Chapter 13. Nigerian Press Ethics and the Politics of Pluralism -- by Minabere Ibelema 153 -- Part V. In South and East Asia 169 -- Chapter 14. The Indian Press: Covering an Enigma -- byJayanti Ram-Chandran 171 -- Chapter 15. Palace Intrigue in Katmandu and the Press in Nepal -- byAkhilesh Upadhyay 181 -- Chapter 16. The Press in Japan: Job Security versus -- Journalistic Mission -- by Takehiko Nomura 187 -- Part VI. Three Journalists and Their Missions 201 -- Chapter 17. A Journey in Journalism: From Idealism -- to Bankruptcy -- by Neil White III 203 -- Chapter 18. Reclaiming Responsibility: A Journalist and Artist -- in the Catholic Worker Movement -- by Chuck Trapkus 211 -- Chapter 19. Ryszard Kapuscinski: The Empathetic Existentialist -- by Joseph B. Atkins and Bernard Nezmah 217 -- Postscript The White Rose: On the Martyrdom of Student Pamphleteers in -- Nazi Germany and Their Legacy -- by Joseph B. Atkins 227 -- References 233 -- Index 243. (shrink)

Multifunctionality poses significant challenges for human brain mapping. Cathy Price and Karl Friston argue that brain regions perform many functions in one sense and a single function in another. Thus, neuroscientists must revise their “cognitive ontologies” to obtain systematic mappings. Colin Klein draws a different lesson from these findings: neuroscientists should abandon systematic mappings for context-sensitive ones. I claim that neither account succeeds as a general treatment of multifunctionality. I argue that brain areas, like genes or organs, are multifunctional in (...) different ways. I call this the “functional heterogeneity hypothesis.” I contend that different multifunctional parts require different mapping strategies. (shrink)

Ancient Greek philosophical schools are said to share a common structure in their ethical theories which is characterized by a eudaimonistic teleology based in an understanding of human nature. At first glance, the skepticism of Sextus Empiricus as described in the Outlines of Pyrrhonism seems to fit into this model insofar as he describes the end of the skeptic as ataraxia, a common account of the expression of human happiness. I argue that this is a misunderstanding of Sextus’s philosophy for (...) several reasons. “The end of skepticism” cannot be eudaimonistic or teleological in the way that other ancient ethical theories are typically understood; moreover, ataraxia is not an end derived from a theory about human nature. For these reasons, the skeptical way of life is radically different than the ethical theories proposed by other schools. I argue that this difference is a result of the character of the skeptical enterprise which involves the implicit rejection of norms in both the epistemological and the ethical spheres. (shrink)

Functional localization is a central aim of cognitive neuroscience. But the nature and extent of functional localization in the human brain have been subjects of fierce theoretical debate since the 19th Century. In this essay, I first examine how concepts of functional localization have changed over time. I then analyze contemporary challenges to functional localization drawing from research on neural reuse, neural degeneracy, and the context-dependence of neural functions. I explore the consequences of these challenges for topics in philosophy of (...) science and philosophy of mind including localizationist versus anti-localizationist approaches to cognitive neuroscience, multiple realizability, reverse inference in functional neuroimaging, and the modularity of mind. (shrink)

Researchers are beginning to transition from studying human–automation interaction to human–autonomy teaming. This distinction has been highlighted in recent literature, and theoretical reasons why the psychological experience of humans interacting with autonomy may vary and affect subsequent collaboration outcomes are beginning to emerge (de Visser et al., 2018;Wynne and Lyons, 2018). In this review, we do a deep dive into human–autonomy teams (HATs) by explaining the differences between automation and autonomy and by reviewing the domain of human–human teaming to make (...) inferences for HATs. We examine the domain of human–human teaming to extrapolate a few core factors that could have relevance for HATs. Notably, these factors involve critical social elements within teams that are central (as argued in this review) for HATs. We conclude by highlighting some research gaps that researchers should strive toward answering, which will ultimately facilitate a more nuanced and complete understanding of HATs in a variety of real-world contexts. (shrink)

SummaryUtah has the highest total fertility of any state in the United States and also the highest proportion of population affiliated with the Church of Jesus Christ of Latter-day Saints. Data were used from the 1996 Utah Health Status Survey to investigate how annual household income, education and affiliation with the LDS Church affect fertility for married women in Utah. Younger age and higher education were negatively correlated with fertility in the sample as a whole and among non-LDS respondents. Income (...) was negatively associated with fertility among non-LDS respondents. However, income was positively correlated with fertility among LDS respondents. This association persisted when instrumental variables were used to address the potential simultaneous equations bias arising from the potential endogeneity of income and fertility. The LDS religion's pronatalist stance probably encourages childbearing among those with higher income. (shrink)