This paper presents a new kind of problem in the ethics of distribution. The problem takes the form of several “calibration dilemmas,” in which intuitively reasonable aversion to small-stakes inequalities requires leading theories of distribution to recommend intuitively unreasonable aversion to large-stakes inequalities. We first lay out a series of such dilemmas for prioritarian theories. We then consider a widely endorsed family of egalitarian views and show that they are subject to even more forceful calibration dilemmas than prioritarian (...) theories. Finally, we show that our results challenge common utilitarian accounts of the badness of inequalities in resources. (shrink)

To study consciousness, scientists need to determine when participants are conscious and when they are not. They do so with consciousness detection procedures. A recurring skeptical argument against those procedures is that they cannot be calibrated: there is no way to make sure that detection outcomes are accurate. In this article, I address two main skeptical arguments purporting to show that consciousness scientists cannot calibrate detection procedures. I conclude that there is nothing wrong with calibration in consciousness science.

In 2012, the Geological Time Scale, which sets the temporal framework for studying the timing and tempo of all major geological, biological, and climatic events in Earth’s history, had one-quarter of its boundaries moved in a widespread revision of radiometric dates. The philosophy of metrology helps us understand this episode, and it, in turn, elucidates the notions of calibration, coherence, and consilience. I argue that coherence testing is a distinct activity preceding calibration and consilience, and I highlight the (...) value of discordant evidence and trade-offs scientists face in calibration. The iterative nature of calibration, moreover, raises the problem of legacy data. (shrink)

This chapter examines the role of parameterParametercalibrationCalibration in the confirmation and validation of complex computer simulation models. I examine the question to what extent calibration data can confirm or validate the calibrated model, focusing in particular on Bayesian approaches to confirmation. I distinguish several different Bayesian approaches to confirmation and argue that complex simulation models exhibit a predictivist effect: Complex computer simulation models constitute a case in which predictive success, as opposed to the mere accommodation of evidence, provides a (...) more stringent test of the model. DataData used in tuning do not validate or confirm a model to the same extent as data successfully predicted by the model do. (shrink)

We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness (...) notions going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness based on definitions along the lines of Schnorr [117].These notions have complex interrelationships, and connections to classical notions from computability theory such as relative computability and enumerability. Computability figures in obvious ways in definitions of effective randomness, but there are also applications of notions related to randomness in computability theory. For instance, an exciting by-product of the program we describe is a more-or-less naturalrequirement-freesolution to Post's Problem, much along the lines of the Dekker deficiency set. (shrink)

This paper assesses the comparative reliability of two belief-revision rules relevant to the epistemology of disagreement, the Equal Weight and Stay the Course rules. I use two measures of reliability for probabilistic belief-revision rules, calibration and Brier Scoring, to give a precise account of epistemic peerhood and epistemic reliability. On the calibration measure of reliability, epistemic peerhood is easy to come by, and employing the Equal Weight rule generally renders you less reliable than Staying the Course. On the (...) Brier-Score measure of reliability, epistemic peerhood is much more difficult to come by, but employing the Equal Weight rule always renders you more reliable than Staying the Course. I conclude with some normative lessons we can draw from these formal results. (shrink)

Over the last twenty-five years, climate scientists working on the attribution of climate change to humans have developed increasingly sophisticated statistical models in a process that can be understood as a kind of calibration: the gradual changes to the statistical models employed in attribution studies served as iterative revisions to a measurement(-like) procedure motivated primarily by the aim of neutralizing particularly troublesome sources of error or uncertainty. This practice is in keeping with recent work on the evaluation of models (...) more generally that views models as tools for particular tasks: what drives the process is the desire for models that provide more reliable grounds for inference rather than accuracy to the underlying mechanisms of data-generation. (shrink)

This paper deals with calibration in scientific practices which investigate relatively well-understood natural phenomena by means of already standardized instrumental devices. Calibration is a crucial topic, since it conditions the reliability of instrumental procedures in science. Yet although important, calibration is a relatively neglected topic. We think more attention should be devoted to calibration. The paper attempts to take a step in this direction. The aims are two-fold: (1) to characterize calibration in a relatively simple (...) kind of scientific practices; (2) to provide conceptual and taxonomic tools of broader scope that help to get a better understanding of calibration in more complex cases and other kinds of scientific practices. For this purpose, we first provide indications for why a conceptual framework is needed. Second, a bibliographic survey of works dealing with calibration is attempted. Third, we introduce different tools to enable a better understanding of calibration. Fourth, we turn to the elaboration of what we call a “simple exemplar” of calibration, illustrated through the case of the calibration of an equal-arm balance. Fifth, the tools previously introduced, and the framework of the simple exemplar, are applied to a more complex case of calibration: calibration procedures in X-ray experiments. This serves to show the work accomplished by the simple exemplar and to emphasize features of more complex cases of calibration. Eventually, we revisit and specify the nature, status, scope and value of the proposed framework. (shrink)

Comparative valuation of different policy interventions often requires interpersonal comparability of benefit. In the field of health economics, the metric commonly used for such comparison, quality adjusted life years (QALYs) gained, has been criticized for failing to respect the equality of all persons’ intrinsic worth, including particularly those with disabilities. A methodology is proposed that interprets ‘full quality of life’ as the best health prospect that is achievable for the particular individual within the relevant budget constraint. This calibration is (...) challenging both conceptually and operationally as it shifts dramatically when technology or budget developments alter what can be achieved for incapacitated individuals. The proposal nevertheless ensures that the maximal achievable satisfaction of one person’s preferences can carry no more intrinsic value than that of another. This approach, which can be applied to other domains of social valuation, thus prevents implicit discrimination against the elderly and those with irremediable incapacities. (shrink)

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of (...) a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line. (shrink)

The epistemic theory of causality is analogous to epistemic theories of probability. Most proponents of epistemic probability would argue that one's degrees of belief should be calibrated to chances, insofar as one has evidence of chances. The question arises as to whether causal beliefs should satisfy an analogous calibration norm. In this paper, I formulate a particular version of a norm requiring calibration to chances and argue that this norm is the most fundamental evidential norm for epistemic probability. (...) I then develop an analogous calibration norm for epistemic causality, argue that it is the *only* evidential norm required for epistemic causality, and show how an epistemic account of causality that incorporates this norm can be used to analyse objective causal relationships. (shrink)

Calibration, the use of a surrogate signal to standardize an instrument, is an important strategy for the establishment of the validity of an experimental result. In this paper, I present several examples, typical of physics experiments, that illustrate the adequacy of the surrogate. In addition, I discuss several episodes in which the question of calibration is both difficult to answer and of paramount importance. These episodes include early attempts to detect gravity waves, the question of the existence of (...) a 17–keV neutrino, and the question of the existence of a Fifth Force in gravity. I argue that in these more complex cases, the adequacy of calibration, in an extended sense, was both considered and established. (shrink)

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing (...) how it answers or sidesteps problems that have been raised for previous work in this area. (shrink)

The practice of appealing to esoteric intuitions, long standard in analytic philosophy, has recently fallen on hard times. Various recent empirical results have suggested that philosophers are not currently able to distinguish good intuitions from bad. This paper evaluates one possible type of approach to this problematic methodological situation: calibration. Both critiquing and building on an argument from Robert Cummins, the paper explores what possible avenues may exist for the calibration of philosophical intuitions. It is argued that no (...) good options are currently available, but leaves open the real possibility of such a calibration in the future. (shrink)

Can there be good reasons for judging one set of probabilistic assertions more reliable than a second? There are many candidates for measuring "goodness" of probabilistic forecasts. Here, I focus on one such aspirant: calibration. Calibration requires an alignment of announced probabilities and observed relative frequency, e.g., 50 percent of forecasts made with the announced probability of.5 occur, 70 percent of forecasts made with probability.7 occur, etc. To summarize the conclusions: (i) Surveys designed to display calibration curves, (...) from which a recalibration is to be calculated, are useless without due consideration for the interconnections between questions (forecasts) in the survey. (ii) Subject to feedback, calibration in the long run is otiose. It gives no ground for validating one coherent opinion over another as each coherent forecaster is (almost) sure of his own long-run calibration. (iii) Calibration in the short run is an inducement to hedge forecasts. A calibration score, in the short run, is improper. It gives the forecaster reason to feign violation of total evidence by enticing him to use the more predictable frequencies in a larger finite reference class than that directly relevant. (shrink)

Prediction is more than testing established theory by examining whether the prediction matches the data. To show this, I examine the practices of a community of scientists, known as threaders, who are attempting to predict the final, folded structure of a protein from its primary structure, i.e., its amino acid sequence. These scientists employ a careful and deliberate methodology of prediction. A key feature of the methodology is calibration. They calibrate in order to construct better models. The construction leads (...) to knowledge of how to construct or build an object. Thus, prediction serves a cognitive goal of model construction and not just model or theory testing. The kind of knowledge that results is relevantly different than theoretical knowledge. (shrink)

The assessment of models in an experiment depends on their material nature and their function in the experiment. Models that are used to make the phenomenon under investigation visible - sensors - are assessed by calibration. However, calibration strategies assume material intervention. The experiment discssed in this paper is an experiment in economics to measure the influence of technology shocks on business cycles. It uses immaterial, mathematical instruments. It appears that calibration did not work for these kinds (...) of models, it did not provide reliable evidence for the facts of the business cycle. (shrink)

Jablonka & Lamb (J&L) have presented a number of different possible mechanisms for finessing design. The extra-genetic nature of these mechanisms has led them to challenge orthodox neo-Darwinian views. However, these mechanisms are for calibration and have been designed by natural selection. As such, they add detail to our knowledge, but neo-Darwinism is sufficiently resourced to account for them.

Schervish (1985b) showed that every forecasting system is noncalibrated for uncountably many data sequences that it might see. This result is strengthened here: from a topological point of view, failure of calibration is typical and calibration rare. Meanwhile, Bayesian forecasters are certain that they are calibrated---this invites worries about the connection between Bayesianism and rationality.

: This paper explores the calibration of laboratory models in population genetics as an experimental strategy for justifying experimental results and claims based upon them following Franklin (1986, 1990) and Rudge (1996, 1998). The analysis provided undermines Coyne et al.'s (1997) critique of Wade and Goodnight's (1991) experimental study of Wright's (1931, 1932) Shifting Balance Theory. The essay concludes by further demonstrating how this analysis bears on Diamond's (1986) claims regarding the weakness of laboratory experiments as evidence, and further (...) how the calibration strategy fits within Lloyd's (1987, 1988) account of the confirmation of ecological and evolutionary models. (shrink)

Study is recently re-invoked as an alternative educational formation to disrupt the learning trap and trope. This paper calibrates study and learning as two hermeneutic principles and correlates them with seeing, hearing, and observing as three onto-epistemic modes that respectively underpin Greco-Christian, Rabbinic, and ancient Chinese exegetical traditions. Linking study and learning with the hermeneutic issues of language, text, meaning, and reality, my calibration unfolds in four steps. First, I introduce an epistemic aporia encountered in interpreting some Chinese educational (...) “wind” texts, exposing our naturalized reasoning of learning along a representational enclosure. Second, turning to Susan Handelman’s writing, I trace this learning-as-representation enclosure as being conditioned upon the Greco-Christian exegetical mode of seeing, meanwhile correlating study back with the Rabbinic hearing hermeneutic. Third, I move on to explicate an onto-cosmological Yijing observing, proffering a study hermeneutic as a movement of observing, following, and attuning to wendao, literally put, “a crisscrossing pattern that turns with dao.” Finally, I re-observe and study the crisscrossing Chinese educational “wind” texts, evoking a Chinese “wind-teaching” sensibility so far rarely discerned through representational thinking and learning. (shrink)

Recent discussion of the calibration of probability assessments is related to the earlier influential attitudes of Fréchet. The limiting frequency criterion of good calibration is criticised as being of no relevance to the evaluation of the probability of any event. An operational definition of good calibration is proposed which treats calibration properties as characteristics of the assessor's entire body of opinion, not of opinion about some particular event or events. In these terms a result is shown (...) which says that every coherent opinion distribution is well-calibrated. Scoring rule representations as calibration plus refinement scores are discussed. It is proposed that a subjectivist could well attribute particular bad experiences to 'luck', and must balance this sense of luck with a sense of the inadequacy of his/her own knowledge when evaluating previous knowledge and experience. (shrink)

“This one,” she said, pointing at a chocolate in the box she was handing to me, “is absolutely evil.” And she was right or, at least, half-right: I’ve never tasted chocolate like that before, or since. Should I refrain from doing so?

We argue that concerns about double-counting—using the same evidence both to calibrate or tune climate models and also to confirm or verify that the models are adequate—deserve more careful scrutiny in climate modelling circles. It is widely held that double-counting is bad and that separate data must be used for calibration and confirmation. We show that this is far from obviously true, and that climate scientists may be confusing their targets. Our analysis turns on a Bayesian/relative-likelihood approach to incremental (...) confirmation. According to this approach, double-counting is entirely proper. We go on to discuss plausible difficulties with calibrating climate models, and we distinguish more and less ambitious notions of confirmation. Strong claims of confirmation may not, in many cases, be warranted, but it would be a mistake to regard double-counting as the culprit. 1 Introduction2 Remarks about Models and Adequacy-for-Purpose3 Evidence for Calibration Can Also Yield Comparative Confirmation3.1 Double-counting I3.2 Double-counting II4 Climate Science Examples: Comparative Confirmation in Practice4.1 Confirmation due to better and worse best fits4.2 Confirmation due to more and less plausible forcings values5 Old Evidence6 Doubts about the Relevance of Past Data7 Non-comparative Confirmation and Catch-Alls8 Climate Science Example: Non-comparative Confirmation and Catch-Alls in Practice9 Concluding Remarks. (shrink)

Pains are subject to obvious, well-documented, and striking top-down influences. This is in stark contrast to visual perception, where the debate over cognitive penetrability tends to revolve around fairly subtle experimental effects. Several authors have recently taken up the question of whether top-down effects on pain count as cognitive penetrability, and what that might show us about traditional debates. I review some of the known mechanisms for top-down modulation of pain, and suggest that it reveals an issue with a relatively (...) neglected part of the cognitive penetrability literature. Much of the debate inherits Pylyshyn’s stark contrast between transducers and cognition proper. His distinction grew out of his running fight with Gibson, and is far too strong to be defensible. I suggest that we might therefore view top-down influences on pain as a species of transducer calibration. This provides a novel but principled way to distinguish between several varieties of top-down effect according to their architectural features. (shrink)

To improve the positioning accuracy of industrial robots and avoid using the coordinates of the end effector, a novel kinematic calibration method based on the distance information is proposed. The kinematic model of an industrial robot is established. The relationship between the moving distance of the end effector and the kinematic parameters is analyzed. Based on the results of the analysis and the kinematic model of the robot, the error model with displacements as the reference is built, which is (...) linearized for the convenience of the following identification. The singular value decomposition is used to eliminate the redundant parameters of the error model. To solve the problem that traditional optimization algorithms are easily affected by data noise in high dimension identification, a novel extended Kalman filter and regularized particle filter hybrid identification method is presented. EKF is used in the preidentification of the linearized error model. With the preidentification results as the initial parameters, RPF is used to identify the kinematic parameters of the linearized error model. Simulations are carried out to validate the effectiveness of the proposed method, which shows that the method can identify the error of the parameters and after compensation the accuracy of the robot is improved. (shrink)

This note responds to some criticisms of my recent book In Defence of Objective Bayesianism that were provided by Gregory Wheeler in his ‘Objective Bayesian Calibration and the Problem of Non-convex Evidence’.

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools (...) adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

Our beliefs can have, or fail to have, a significant epistemic virtue: they can be true. What about our partial beliefs – that is, credences or subjective probabilities? Is there an epistemic virtue that credences can have or fail to have, whose nature or role with respect to credences is analogous to the role that truth has with respect to full beliefs? Van Fraassen argued in the 1980s that there is indeed such an analog virtue, and he claimed that it (...) is calibration: our credences should match, or be in tune with, some appropriately chosen frequencies of events. For example, if your credence in the proposition ‘It will rain today’ is 0.3 for any day that starts out like today did, and in fact it does rain on approximately 30% of such days, then your credence level is well‐calibrated, and is vindicated by the actual frequency of rain.In an unpublished paper Alan Hájek rejects this calibrationist answer, and proposes instead that having credences in agreement with the relevant objective chances is what it is to have vindicated credences, in the relevant sense analogous to truth for full beliefs. Although there are problems that afflict both van Fraassen's and Hájek's proposals, I will argue that Hájek and the calibrationist are both largely right – although the calibrationist answer is at bottom more right. In section I will propose an account of being in tune with the world that divides types of propositions into a few different classes; for one of those classes, Hájek's answer is exactly right, while for the others the calibrationist account gives the right answer. (shrink)

Variable-Value axiologies avoid Parfit’s Repugnant Conclusion while satisfying some weak instances of the Mere Addition principle. We apply calibration methods to two leading members of the family of Variable-Value views conditional upon: first, a very weak instance of Mere Addition and, second, some plausible empirical assumptions about the size and welfare of the intertemporal world population. We find that such facts calibrate these two Variable-Value views to be nearly totalist, and therefore imply conclusions that should seem repugnant to anyone (...) who opposes Total Utilitarianism only due to the Repugnant Conclusion. (shrink)

Based on an original ethnographic study of a translational cancer research institute in the United States, we propose calibration as a process that makes interdisciplinary collaboration without consensus possible. Calibration refers to ongoing, day-to-day negotiation and alignment of personal identities, disciplinary commitments, and research group customs that occur during face-to-face group deliberations around everyday research concerns. Calibration provides a mechanism that explains how collaboration without consensus is possible. Crucially, it does not presuppose that interdisciplinary collaboration either indicates (...) or causes the blurring or softening of disciplinary boundaries. We argue that at the microsociological level it may be disciplinary robustness, rather than synthesis, that contributes to interdisciplinary innovation. (shrink)

When discussing AI alignment, we usually refer to the problem of teaching or training advanced autonomous AI systems to make decisions that are aligned with human values or preferences. Proponents of this approach believe it can be employed as means to stay in control over sophisticated intelligent systems, thus avoiding certain existential risks. We identify three general obstacles on the path to implementation of value alignment: a technological/technical obstacle, a normative obstacle, and a calibration problem. Presupposing, for the purposes (...) of this discussion, that the technical and normative problems are solved, we focus on the problem of how to calibrate a system, for a specific value, to be on a specific location within a spectrum stretching between righteous and normal or average human behavior. Calibration, or more specifically mis-calibration, also raises the issue of trustworthiness. If we cannot trust AI systems to perform tasks the way we intended, we would not use them on our roads and at our homes. In an era where we strive to construct autonomous machines endowed with common sense, reasoning abilities and a connection to the world, so they would be able to act in alignment with human values, such mis-calibrations can make the difference between trustworthy and untrustworthy systems. (shrink)

We analyze the set-theoretic strength of determinacy for levels of the Borel hierarchy of the form$\Sigma _{1 + \alpha + 3}^0 $, forα<ω1. Well-known results of H. Friedman and D.A. Martin have shown this determinacy to requireα+ 1 iterations of the Power Set Axiom, but we ask what additional ambient set theory is strictly necessary. To this end, we isolate a family of weak reflection principles, Π1-RAPα, whose consistency strength corresponds exactly to the logical strength of${\rm{\Sigma }}_{1 + \alpha + (...) 3}^0 $determinacy, for$\alpha < \omega _1^{CK} $. This yields a characterization of the levels ofLby or at which winning strategies in these games must be constructed. Whenα= 0, we have the following concise result: The leastθso that all winning strategies in${\rm{\Sigma }}_4^0 $games belong toLθ+1is the least so that$L_\theta \models {\rm{``}}{\cal P}\left$exists, and all wellfounded trees are ranked”. (shrink)

We propose a new account of calibration according to which calibrating a technique shows that the technique does what it is supposed to do. To motivate our account, we examine an early twentieth-century debate about chlorophyll chemistry and Mikhail Tswett’s use of chromatographic adsorption analysis to study it. We argue that Tswett’s experiments established that his technique was reliable in the special case of chlorophyll without relying on either a theory or a standard calibration experiment. We suggest that (...) Tswett broke the experimenters’ regress by appealing to material facts in the common ground for chemists at the time. (shrink)

In this article, I argue that Heidegger’s political failures haunt Arendt’s complex “phenomenology of thinking,” and, in the words of Richard Bernstein, “Arendt’s most novel and striking thesis—that there is an intrinsic connection between our ability or inability to think and evil—depends on discriminating the thinking that may prevent catastrophes from the thinking that does not.” The key to doing so, I suggest, is to attend more closely to Arendt’s persistent use of the language of stabilization, orientation, and navigation: in (...) other words, how we “take our bearings” in a world of perpetual change and motion. The ability to locate oneself in relation to the world is a recurrent theme in Arendt’s writings, and the metaphors of orientation appear frequently in her attempts to understand totalitarianism and Heidegger’s turn to National Socialism. Whereas most theorists collapse the idea of “taking our bearings” into judging, I argue that the activity of orientation should be theorized in its own right. As such, I explore the disorientation experienced during the traversal between thinking and acting via a close reading of Heidegger’s “Conversation on a Country Path About Thinking.” My reading illustrates how certain elements of the world, crucial to maintaining our bearings, fade from view while one is thinking. I conclude by discussing representative thinking as an explicitly political mode of thought that escapes some of the difficulties inherent in pure thinking—showing how it shores up those elements of the world that enable us to take our bearings. (shrink)

Abner Shimony argues that degrees of belief satisfy the axioms of probability because their epistemic goal is to match estimates of objective probabilities. Because the estimates obey the axioms of probability, degrees of belief must also obey them to reach their epistemic goal. This calibration argument meets some objections, but with a few revisions it can surmount those objections. It offers a good alternative to the Dutch book argument for compliance with the probability axioms. The defense of Shimony's (...) class='Hi'>calibration argument examines rational pursuit of an epistemic goal, introduces strength of evidence and its measurement, and distinguishes epistemic goals and functions. (shrink)

The signals in numerous complex systems of engineering can be regarded as nonlinear parameter trend with noise which is identically distributed random signals or deterministic stationary chaotic signals. The commonly used methods for parameter estimation of nonlinear trend in signals are mainly based on least squares. It can cause inaccurate estimation results when the noise is complex. This paper proposes a calibration method for this issue in the case of single parameter via nonstationarity measure from the perspective of the (...) stationarity of residual sequence. Some numerical studies are conducted for validation. Results of numerical studies show that the proposed calibration method performs well for various models with different noise strengths and types and can significantly improve the accuracy of initial estimates obtained by least squares method. This is the first time that the nonstationarity measure is applied to the parameter calibration. All these results will be a guide for future studies of other parameter calibrations. (shrink)

We introduce and study the D-model, which reflects the simplest situation in which one wants to calibrate an observable. We discuss the question of representing the statistics of the D-model in the context of an effect algebra.

The Representational Theory of Measurement conceives measurement as establishing homomorphisms from empirical relational structures into numerical relation structures, called models. Models function as measuring instruments by transferring observations of an economic system into quantitative facts about that system. These facts are evaluated by their accuracy. Accuracy is achieved by calibration. For calibration standards are needed. Then two strategies can be distinguished. One aims at estimating the invariant (structural) equations of the system. The other is to use known stable (...) facts about the system to adjust the model parameters. For this latter strategy, the requirement of models as homomorphic mappings is not required anymore. (shrink)