We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) (...) gave an axiomatisation of binary preferences—on horse lotteries, rather than on gambles—that also leads to a unique representation in terms of sets of probability mass functions. To reach this goal, they use two devices, which we will call ‘SSK–Archimedeanity’ and ‘SSK–extension’. In this paper, we will make the arguments of Seidenfeld et al. (1995) explicit in the language of gambles, and show how their ideas imply even convexity and allow for conservative reasoning with evenly convex sets of desirable gambles, by deriving an equivalence between the SSK–Archimedean natural extension, the SSK–extension, and the evenly convex natural extension. (shrink)

Teddy Seidenfeld – CMU An old, wise, and widely held attitude in Statistics is that modest intervention in the design of an experiment followed by simple statistical analysis may yield much more of value than using very sophisticated statistical analysis on a poorly designed existing data set.

Given the unprecedented novel nature and scale of coronavirus and the global nature of this public health crisis, which upended many public/environmental research norms almost overnight. However, with further waves of the virus expected and more pandemics anticipated. The COVID-19 pandemic of 2020 opened our eyes to the ever-changing conditions and uncertainty that exists in our world today, particularly with regards to environmental and public health practices disruption. This paper explores environmental and public health evidence-based practices toward responding to Covid-19. (...) A literature review tried to do a deep dive through the use of various search engines such as Mendeley, Research Gate, CAB Abstract, Google Scholar, Summon, PubMed, Scopus, Hinari, Dimension, OARE Abstract, SSRN, Academia search strategy toward retrieving research publications, “gray literature” as well as reports from expert working groups. To achieve enhanced population health, it is recommended to adopt widespread evidence-based strategies, particularly in this uncertain time. As only together can evidence-informed decision-making (EIDM) can become a reality which include effective policies and practices, transparency and accountability of decisions, and equity outcomes; these are all more relevant in resource-constrained contexts, such as Nigeria. Effective and ethical EIDM though requires the production as well as use of high-quality evidence that are timely, appropriate and structured. One way to do so is through co-production. Co-production (or co-creation or co-design) of environmental/public health evidence considered as a key tool for addressing complex global crises such as the high risk of severe COVID-19 in different nations. A significant evidence-based component of environmental/public health (EBEPH) consist of decisions making based on best accessible, evidence that is peer-reviewed; using data as well as systematic information systems; community engagement in policy-making; conducting sound evaluation; do a thorough program-planning frameworks; as well as disseminating what is being learned. As researchers, scientists, statisticians, journal editors, practitioners, as well as decision makers strive to improve population health, having a natural tendency toward scrutinizing the scientific literature aimed at novel research findings serving as the foundation for intervention as well as prevention programs. The main inspiration behind conducting research ought to be toward stimulating and collaborating appropriately on public/environmental health action. Hence, there is need for a “Plan B” of effective behavioral, environmental, social as well as systems interventions (BESSI) toward reducing transmission. (shrink)

The field of of imprecise probability has matured, in no small part because of Teddy Seidenfeld’s decades of original scholarship and essential contributions to building and sustaining the ISIPTA community. Although the basic idea behind imprecise probability is (at least) 150 years old, a mature mathematical theory has only taken full form in the last 30 years. Interest in imprecise probability during this period has also grown, but many of the ideas that the mature theory serves can be (...) difficult to apprehend to those new to the subject. Although these fundamental ideas are common knowledge in the ISIPTA community, they are expressed, when they are expressed at all, obliquely, over the course of years with students and colleagues. -/- A single essay cannot convey the store of common knowledge from any research community, let alone the ISIPTA community. But, this essay nevertheless is an attempt to guide those familiar with the basic Bayesian framework to appreciate some of the elegant and powerful ideas that underpin the contemporary theory of lower previsions, which is the theory that most people associate with the term ‘imprecise probabilities’. (shrink)

We study whether it is possible to generalise Seidenfeld et al.’s representation result for coherent choice functions in terms of sets of probability/utility pairs when we let go of Archimedeanity. We show that the convexity property is necessary but not sufficient for a choice function to be an infimum of a class of lexicographic ones. For the special case of two-dimensional option spaces, we determine the necessary and sufficient conditions by weakening the Archimedean axiom.

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

Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show (...) that there is no strictly proper scoring rule for imprecise probabilities. -/- The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption — called strict immodesty— should be rejected, and we prove a representation theorem that characterizes all “mildly” immodest measures of inaccuracy. (shrink)

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices, partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually (...) endorsed by practicing experimentalists. (shrink)

We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware (...) of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1] have called S-independence. We show that neither is more general than the other. (shrink)

We introduce an independence notion for choice functions, which we call ‘epistemic independence’ following the work by De Cooman et al. [17] for lower previsions, and study it in a multivariate setting. This work is a continuation of earlier work of one of the authors [29], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [11]. We obtain the many-to-one independent natural extension in this (...) framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less expressive imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [28], which De Bock and De Cooman [2] have called S-independence. We show that neither is more general than the other. (shrink)

Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation, since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We explicitly investigate (...) the short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging. (shrink)

This essay argues that literature is neither an intrinsic good (like oxygen) nor a constructed good (like a teddy-bear) but instead a conditional good, like a blueprint. It has immense potential value, but that potential can be actualized only if readers do a certain kind of work; and readers are likely to do that work only if, as a culture, we retain an understanding of what novels and poems both need from us and can give us. This means we (...) need to be wary of theories that are excessively deflationary (all literature is mere entertainment), cynical (all literature is a vehicle for state ideology), or over-optimistic (all literature makes us more altruistic) and instead embrace a pluralism of effect. Some fictions, like The Wire, invite us to reflect on our own beliefs; some, like Plato’s dialogues, help us fine-tune our mental capacities; some, like Toni Morrison’s Song of Solomon, offer us a choice of genres; some help us feel our feelings; some offer formal models for the shape of a life. Literature can continue to matter in all of these ways—but only as long as we allow it to. (shrink)