– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is (...) a natural way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

This paper is a discussion note on Isaacs et al. (2022), who have claimed to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of their proposal. In particular, I show that if their proposal is applied to a bounded 3-dimensional space, then they have to reject at least one of the following: (i) If A is at most as probable as B and B is at most as (...) probable as C, then A is at most as probable as C. (ii) Let A ∩ C = B ∩ C = ∅. A is at most as probable as B iff (A ∪ C) is at most as probable as (B ∪ C). But rejecting either statement seems unattractive. (shrink)

In a recent paper, Yoaav Isaacs, Alan Hájek, and John Hawthorne argue for the rational permissibility of "credal imprecision" by appealing to certain propositions associated with non-measurable spatial regions: for example, the proposition that the pointer of a spinner will come to rest within a certain non-measurable set of points on its circumference. This paper rebuts their argument by showing that its premises lead to implausible consequences in cases where one is trying to learn, by making multiple observations, (...) whether a certain outcome is associated with a non-measurable region or a measurable one. (shrink)

This paper examines the role existence plays in measurement validity. I argue that existing popular theories of measurement and of validity follow a correspondence framework, which starts by assuming that an entity exists in the real world with certain properties that allow it to be measurable. Drawing on literature from the sociology of measurement, I show that the correspondence framework faces several theoretical and practical challenges. I suggested the validity-first framework of measurement, which starts with a practice-based validation process (...) as the basis for a measurement theory, and only posits objective existence when it is scientifically useful to do so. (shrink)

This article examines the biopower of non-Han bodies by considering the intersections of anthropology, racial science, and colonial regimes. During the 1930s and 1940s, when extensive anthropometric research was being undertaken on non-Han populations in the south-western borderlands of China, several anthropologists studied non-Han groups under the aegis of frontier administration. Chinese scholars sought to generate the physical characteristics of ethnic minority groups in the south-west of China through the methodology of body measurement, in order to identify forms of social (...) and political intervention in the management of the non-Han population in wartime. This article examines the global transmission of Western social science in China, highlighting the local reception of Western racial taxonomy. Non-Han bodies were represented as a subcategory of the Mongolian/‘Yellow’ race through anthropometric research. The body measurements of non-Han people were used to demonstrate physical similarities between the Han and various ethnic minority groups in order to evoke a unified Zhonghua minzu (Chinese ethnicity) that embraced both the Han Chinese and frontier ethnic minority groups. (shrink)

How to measure performance in charitable organisations continues to excite interest among academics and practitioners. Despite the intellectual interest, little consensus has emerged as to what are the best measures of performance in charities. This is against the backdrop of an increased demand by donors and other stakeholders on charities to provide information on their performance. Building on prior studies, this paper examines the measures of performance in charities using a hybrid methodological approach which consists of 14 exploratory interviews and (...) a quantitative survey of 105 chief executive officers/board of trustees of large British charities. The results of factor analysis and internal reliability produced five broad measures of performance of charities: financial measures; client satisfaction; management effectiveness; stakeholder involvement; and benchmarking, indicating that the overall performance of charities is best measured by a set of factors that reflect the multiple and diverse stakeholders associated with charities. Further analysis using structural equation modelling corroborates the results that non-financial measures such as management effectiveness, stakeholder involvement and benchmarking are important to the performance of charities. (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)

Non-perturbative quantum gravity prevents the formation of curvature singularities and may allow black holes to decay with a lifetime shorter than evaporation time. This, in connection with the existence of primordial black holes, could open a new window for quantum-gravity phenomenology. I discuss the possibility of observing astrophysical emissions from the explosion of old black holes in the radio and in the gamma wavelengths. These emissions can be discriminated from other astrophysical sources because of a peculiar way the emitted wavelength (...) scales with the distance. The spectrum of the diffuse radiation produced by those objects presents a peculiar distortion due to this scaling. (shrink)

Well-being measurements are frequently used to support conclusions about a range of philosophically important issues. This is a problem, because we know too little about the intervals of the relevant scales. I argue that it is plausible that well-being measurements are non-linear, and that common beliefs that they are linear are not truth-tracking, so we are not justified in believing that well-being scales are linear. I then argue that this undermines common appeals to both hypothetical and actual well-being measurements; I (...) first focus on the philosophical literature on prioritarianism and then discuss Kahneman’s Peak-End Rule as a systematic bias. Finally, I discuss general implications for research on well-being, and suggest a better way of representing scales. (shrink)

In this paper, we show within RCA 0 that weak Konig's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within WKL 0 , a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of WKL 0 has a proper initial part isomorphic to itself [10].

In a recent paper in this Journal San Pedro I formulated a conjecture relating Measurement Independence and Parameter Independence, in the context of common cause explanations of EPR correlations. My conjecture suggested that a violation of Measurement Independence would entail a violation of Parameter Independence as well. Leszek Wroński has shown that conjecture to be false. In this note, I review Wroński’s arguments and agree with him on the fate of the conjecture. I argue that what is interesting about the (...) conjecture, however, is not whether it is true or false in itself, but the reasons for the actual verdict, and their implications regarding locality. (shrink)

Consecutive measurements performed on the same quantum system can reveal fundamental insights into quantum theory’s causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after each measurement, erasing any memory of the prior state. We show here that counter to this view, un-amplified measurements have coherent ancilla density matrices that encode the memory of the entire set of quantum measurements (...) that came before, and that the chain of this entire set is therefore non-Markovian. In contrast, sequences of amplified measurements are equivalent to a quantum Markov chain. We argue that the non-Markovian nature of quantum measurement has empirical consequences that are incompatible with the assumption of wave function collapse, thus elevating the collapse assumption into a testable hypothesis. Finally, we find that all of the information necessary to reconstruct an arbitrary non-Markovian quantum chain of measurements is encoded on the boundary of that chain, reminiscent of the holographic principle. (shrink)

This paper discusses a relational modeling of measurement which is complementary to the standard representational point of view: by focusing on the experimental character of the measurand-related comparison between objects, this modeling emphasizes the role of the measuring systems as the devices which operatively perform such a comparison. The non-idealities of the operation are formalized in terms of non-transitivity of the substitutability relation between measured objects, due to the uncertainty on the measurand value remaining after the measurement. The metrological structure (...) of traceability is shown to be an effective solution to cope with the problem of the general non-transitivity of measurement results. A preliminary theory is introduced as a possible formalization for the presented model. (shrink)

In this paper, non-additivity of a set function is interpreted as a method to express relations between sets which are not modeled in a set theoretic way. Drawing upon a concept called “quasi-analysis” of the philosopher Rudolf Carnap, we introduce a transform for sets, functions, and set functions to formalize this idea. Any image-set under this transform can be interpreted as a class of (quasi-)components or (quasi-)properties representing the original set. We show that non-additive set functions can be represented as (...) signed σ-additive measures defined on sets of quasi-components. We then use this interpretation to justify the use of non-additive set functions in various applications like for instance multi criteria decision making and cooperative game theory. Additionally, we show exemplarily by means of independence, conditioning, and products how concepts from classical measure and probability theory can be transfered to the non-additive theory via the transform. (shrink)

The recently developed technique of Bohrification associates to a (unital) C*-algebra Athe Kripke model, a presheaf topos, of its classical contexts;in this Kripke model a commutative C*-algebra, called the Bohrification of A;the spectrum of the Bohrification as a locale internal in the Kripke model. We propose this locale, the ‘state space’, as a (n intuitionistic) logic of the physical system whose observable algebra is A.We compute a site which externally captures this locale and find that externally its points may be (...) identified with partial measurement outcomes. This prompts us to compare Scott-continuity on the poset of contexts and continuity with respect to the C*-algebra as two ways to mathematically identify measurement outcomes with the same physical interpretation. Finally, we consider the not-not-sheafification of the Kripke model on classical contexts and obtain a space of measurement outcomes which for commutative C*-algebras coincides with the spectrum. The construction is functorial on the category of C*-algebras with commutativity reflecting maps. (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our new (...) elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

Augé describes non-places as quantifiable and measureable physical space, but does not give an appropriate measure to do so. This contribution thinks about using crowd-harvested photo data, a specific kind of Big Data, to measure non-places in the context of tourism by giving a theory based discussion on Augé’s non-places, photography as key element of “doing” tourism, and the selection processes of photography and uploading photos. Solely using theoretical thoughts and propositional logic, this contribution indicates that it could be possible (...) to do so. Yet, there are plenty of empirical studies needed in order to verify the built hypothesis. (shrink)

For non-additive set functions, the independent product, in general, is not unique and the Fubini theorem is restricted to slice-comonotonic functions. In this paper, we use the representation theorem of Gilboa and Schmeidler (Math Oper Res 20:197–212, 1995) to extend the Möbius product for non-additive set functions to non-finite spaces. We extend the uniqueness result of Ghirardato (J Econ Theory 73:261–291, 1997) for products of two belief functions and weaken the requirements on the marginals necessary to obtain the Fubini property (...) in the product. More importantly, we show that for the Möbius product one side of the Fubini theorem holds for all integrable functions if one of the marginals either is a probability or a convex combination of a chain of unanimity games, i.e., we relax the requirement of slice-comonotonicity and enrich the set of possible applications. (shrink)

The Securities and Exchange Commission requires publicly held US corporations to disclose all information, whether it is positive or negative, that might be relevant to an investor's decision to buy, sell, or hold a company's securities. The decisions made by corporate managers to disclose such information can significantly affect the judgments and decisions of investors. This paper examines academic accounting research on corporate managers' voluntary disclosures of earnings forecasts and non-GAAP earnings measures. Much of the evidence from this research indicates (...) that some managers engage in opportunistic disclosure behavior that often benefits one group (managers and shareholders) at the expense of other groups (often other investors). The paper concludes by discussing the ethical implications of this behavior. (shrink)

To measure non-cognitive facets of competence, we developed and tested a new method that we refer to as Embedded Experience Sampling (EES). Domain-specific problem-solving competence is a multi-faceted construct that is not limited to cognitive facets such as domain knowledge or problem-solving strategies but also comprises non-cognitive facets in the sense of domain-specific emotional and motivational dispositions such as interest and self-concept. However, in empirical studies non-cognitive facets are usually either neglected or measured by generalized self-report questionnaires that are detached (...) from the performance assessment. To enable an integrated measurement, we developed the EES method to collect data on non-cognitive facets during scenario-based low-stakes assessments. Test-takers are requested to stop at certain times and spontaneously answer short items (EES items) regarding their actual experience of the problem situation. These EES items are embedded in an EES event that resembles typical social interactions with non-player characters. To evaluate the feasibility and validity of the method, we implemented EES in a series of three studies in the context of commercial vocational education and training (VET): A feasibility study with 77 trainees, a pilot study with 20 trainees, and the main study with 780 trainees who worked on three complex problem scenarios in a computer-based office simulation. In the present paper, we investigate how test-takers perceived the EES events, and whether social desirability biased their answers, and investigate the internal structure of the data and the relationship between EES data and data from several other sources. Interview data and survey data indicated no biases due to social desirability and no additional burden for the test-takers due to the EES events. A correlation analysis following the multitrait-multimethod approach as well as the calibration of a multidimensional model based on Item Response Theory (IRT) also supported the construct validity. Furthermore, EES data shows substantial correlations with test motivation but almost zero correlations with data from generalized retrospective self-report questionnaires on non-cognitive facets. Altogether, EES offers an alternative approach to measuring non-cognitive facets of competence under certain conditions. For instance, EES is also based on self-reporting and thus might not be suitable for high-stakes testing. (shrink)

This book provides an introduction to measurement theory for non-specialists and puts measurement in the social and behavioural sciences on a firm mathematical foundation. Results are applied to such topics as measurement of utility, psychophysical scaling and decision-making about pollution, energy, transportation and health. The results and questions presented should be of interest to both students and practising mathematicians since the author sets forth an area of mathematics unfamiliar to most mathematicians, but which has many potentially significant applications.

Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuously. In this article, written in dialogue form, we suggest that quantum mechanics can be taken even more seriously, if the many-worlds view is replaced by a many-measurements view. This allows not only to derive the (...) Born rule, thus solving the measurement problem, but also to deduce a one-world non-spatial reality, providing an even more fantastic scenario than that of the multiverse. (shrink)

In the last few decades the role played by models and modeling activities has become a central topic in the scientific enterprise. In particular, it has been highlighted both that the development of models constitutes a crucial step for understanding the world and that the developed models operate as mediators between theories and the world. Such perspective is exploited here to cope with the issue as to whether error-based and uncertainty-based modeling of measurement are incompatible, and thus alternative with one (...) another, as sometimes claimed nowadays. The crucial problem is whether assuming this standpoint implies definitely renouncing to maintain a role for truth and the related concepts, particularly accuracy, in measurement. It is argued here that the well known objections against true values in measurement, which would lead to refuse the concept of accuracy as non-operational, or to maintain it as only qualitative, derive from a not clear distinction between three distinct processes: the metrological characterization of measuring systems, their calibration, and finally measurement. Under the hypotheses that (1) the concept of true value is related to the model of a measurement process, (2) the concept of uncertainty is related to the connection between such model and the world, and (3) accuracy is a property of measuring systems (and not of measurement results) and uncertainty is a property of measurement results (and not of measuring systems), not only the compatibility but actually the conjoint need of error-based and uncertainty-based modeling emerges. (shrink)

In management literature, intellectual capital is considered the key driver of the competitive advantage of the third millennium enterprise firm; consequently, measuring, managing and reporting IC has become a critical issue. Frameworks addressed to measure and report IC have proliferated, nevertheless the adoption of these frameworks is not so widespread in practice. The strong call for critically investigating IC practices has been raised by several leading authors in the area. Doing a critical and performative IC research means empirically researching IC (...) organisational practices in specific contexts, in order to increase the understanding of the IC dynamics. By critically analysing the IC practices of ANPAS Piemonte, an Italian non-profit organisation chosen for its long-standing experience in issuing audited IC reports, the article contributes to the knowledge of how and why IC is measured and reported in a specific, outstanding NPO disclosing IC. Moreover, the case study analysis contributes to shed lights on the levers and barriers that should be faced by other managers intending to implement and effectively use an IC measurement, management and reporting system within organisation. (shrink)

Contemporary approaches to “non-market accounting” depend critically on methods of “monetization,” i.e., determining prices for goods outside the market. Monetization constitutes a case of economic measurement in a narrow sense that has not yet been analyzed in the literature on measurement in economics. Monetization, I will argue, uses homo economicus—originally created as a model to explain existing prices—as a measuring device, one that generates new prices for goods that are not traded on markets. Homo economicus, though long contested in microeconomics, (...) is thus enjoying a dubious revival in non-market accounting. (shrink)

The problem of measurement is often considered an inconsistency inside the quantum formalism. Many attempts to solve it have been made since the inception of quantum mechanics. The form of these attempts depends on the philosophical position that their authors endorse. I will review some of them and analyze their relevance. The phenomenon of decoherence is often presented as a solution lying inside the pure quantum formalism and not demanding any particular philosophical assumption. Nevertheless, a widely debated question is to (...) decide between two different interpretations. The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate. For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed, so explaining the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears. In this case, explaining why only one single definite outcome is observed remains to do. In this paper, I examine the arguments that have been given for and against both interpretations and defend a new position, the “Convivial Solipsism”, according to which the outcome that is observed is relative to the observer, different but in close parallel to the Everett’s interpretation and sharing also some similarities with Rovelli’s relational interpretation and Quantum Bayesianism. I also show how “Convivial Solipsism” can help getting a new standpoint about the EPR paradox providing a way out of the seemingly unavoidable non-locality of quantum mechanics. (shrink)

Extensive measurement theory is developed in terms of theratio of two elements of an arbitrary (not necessarily Archimedean) extensive structure; thisextensive ratio space is a special case of a more general structure called aratio space. Ratio spaces possess a natural family of numerical scales (r-scales) which are definable in non-representational terms; ther-scales for an extensive ratio space thus constitute a family of numerical scales (extensive r-scales) for extensive structures which are defined in a non-representational manner. This is interpreted as involving (...) arelational theory of quantity which contrasts in certain respects with thequalitative theory of quantity implicit in standard representational extensive measurement theory. The representational properties of extensiver-scales are investigated, and found to coincide withweak extensive measurement in the sense of Holman. This provides support for the thesis (developed in a separate paper) that weak extensive measurement is a more natural model of actual physical extensive scales than is the standard model using strong extensive measurement. Finally, the present apparatus is applied to slightly simplify the existing necessary and sufficient conditions for strong extensive measurement. (shrink)

This book traces how such a seemingly immutable idea as measurement proved so malleable when it collided with the subject matter of psychology. It locates philosophical and social influences reshaping the concept and, at the core of this reshaping, identifies a fundamental problem: the issue of whether psychological attributes really are quantitative. It argues that the idea of measurement now endorsed within psychology actually subverts attempts to establish a genuinely quantitative science and it urges a new direction. It relates views (...) on measurement by thinkers such as Holder, Russell, Campbell and Nagel to earlier views, like those of Euclid and Oresme. Within the history of psychology, it considers contributions by Fechner, Cattell, Thorndike, Stevens and Suppes, among others. It also contains a non-technical exposition of conjoint measurement theory and recent foundational work by leading measurement theorist R. Duncan Luce. (shrink)

This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann's classic treatise with this title. Fundamental non-classical features of quantum mechanics-indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality-are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and (...) operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective. The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory. (shrink)

In this essay I discuss a person’s freedom to choose whatever that person may reasonably prefer to choose. This type of freedom of choice may be regarded as a candidate for a social good, being a hybrid between freedom of choice and preference satisfaction utility. To separate this preference dependent freedom of choice from other types, we may call it opportunity. The essay is concerned with the question of how opportunity should be identified and measured. I discuss what conditions an (...) opportunity measure should satisfy and propose that an opportunity measure should satisfy at least four specific conditions. I then present a new class of measures which satisfy the four conditions (the Root measures). Last I prove that these measures are the only ones that satisfy the conditions, given the extra assumption that the measures are analytic functions with non-zero partial derivatives. (shrink)

Purpose: Performance measurement systems (PMS) in Nonprofit Organizations (NPOs) are more complex than in for-profit organizations. NPOs have an orientation towards social mission and values, and they consider not only organizational efficiency and viability, but also the social impact of the organization. This research provides a comprehensive synthesis of PMSs in NPOs. Design/methodology/approach: Using a literature review, supported by bibliometric and network analyses. A paper set of 240 articles related to this research field is examined. Topics that are the most (...) prevalent in this research area and their interrelationships are identified, presenting an outline of current efforts. Findings: Despite the descriptive analyses for the paper set, a framework is proposed for organizing the design-implementation factors of PMSs in nonprofit organizations, identifying the main requirements for their successful development. Originality/value: Investigation on performance measurement in nonprofit organizations is still in its early stages of development with many opportunities to further develop the field. Conceptual frameworks and models, as well as specific theories, are being generated for this field of research, and the process of adapting models from the general field of performance measurement is taking place. The meta-framework that organizes the main research topics of PMS in nonprofit organizations and the framework that consolidates factors that influence the design-implementation of PMSs in nonprofit organizations developed represents this paper contribution. (shrink)