"Golf day 2005 @ federal golf club, red hill." Ethos: Official Publication of the Law Society of the Australian Capital Territory, (196), pp. 7.

De Finetti introduced the concept of coherent previsions and conditional previsions through a gambling argument and through a parallel argument based on a quadratic scoring rule. He shows that the two arguments lead to the same concept of coherence. When dealing with events only, there is a rich class of scoring rules which might be used in place of the quadratic scoring rule. We give conditions under which a general strictly proper scoring rule can replace the quadratic scoring rule while (...) preserving the equivalence of de Finetti’s two arguments. In proving our results, we present a strengthening of the usual minimax theorem. We also present generalizations of de Finetti’s fundamental theorem of prevision to deal with conditional previsions. (shrink)

The score of Piece Four of Sylvano Bussotti's Five Piano Pieces for David Tudor is the most important image in A Thousand Plateaus. It serves as a prefatory image not only to the Rhizome plateau, but also to the work as a whole. It functions as the book's musical score, guiding readers in their performance of the text. Embracing John Cage's graphism and aleatory practices, Bussotti created his own ‘aserial’ new music, one that celebrated passion and Bussotti's open (...) homosexuality. The visual elements of Piece Four include a deterritorialisation of the standard piano score, a diagram of the composition's abstract machine, and a drawing that Bussotti had produced ten years before writing Five Piano Pieces for David Tudor. The drawing itself is a rhizomic artwork, with details that echo visual motifs throughout A Thousand Plateaus. The superimposition of the drawing on the deterritorialised framework of the standard piano score conjoins the visible and the audible, faciality and the refrain, in a single artefact. (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)

It is commonly assumed that when we assign different credences to a proposition, a perfect compromise between our opinions simply ‘splits the difference’ between our credences. I introduce and defend an alternative account, namely that a perfect compromise maximizes the average of the expected epistemic values that we each assign to alternative credences in the disputed proposition. I compare the compromise strategy I introduce with the traditional strategy of compromising by splitting the difference, and I argue that my strategy is (...) a reasonable characterization of epistemic compromise. (shrink)

We offer a case-study in irrationality, showing that even in a high stakes context, intelligent and well trained professionals may adopt dominated practices. In multiple-choice tests one cannot distinguish lucky guesses from answers based on knowledge. Test-makers have dealt with this problem by lowering the incentive to guess, through penalizing errors (called formula scoring), and by eliminating various cues for outperforming random guessing (e.g., a preponderance of correct answers in middle positions), through key balancing. These policies, though widespread and intuitively (...) appealing, are in fact ‘‘irrational’’, and are dominated by alternative solutions. Number-right scoring is superior to formula scoring, and key randomization is superior to key balancing. We suggest that these policies have persisted since all stake-holders – test-makers, test-takers and test-coaches – share the same faulty intuitions. (shrink)

Thomas Richardson and Peter Spirtes. Scoring Ancestral Graph Models.

Structural equation model trees are data-driven tools for finding variables that predict group differences in SEM parameters. SEM trees build upon the decision tree paradigm by growing tree structures that divide a data set recursively into homogeneous subsets. In past research, SEM trees have been estimated predominantly with the R package semtree. The original algorithm in the semtree package selects split variables among covariates by calculating a likelihood ratio for each possible split of each covariate. Obtaining these likelihood ratios is (...) computationally demanding. As a remedy, we propose to guide the construction of SEM trees by a family of score-based tests that have recently been popularized in psychometrics. These score-based tests monitor fluctuations in case-wise derivatives of the likelihood function to detect parameter differences between groups. Compared to the likelihood-ratio approach, score-based tests are computationally efficient because they do not require refitting the model for every possible split. In this paper, we introduce score-guided SEM trees, implement them in semtree, and evaluate their performance by means of a Monte Carlo simulation. (shrink)

A number of authors have recently put forward arguments pro or contra various rules for scoring probability estimates. In doing so, they have skipped over a potentially important consideration in making such assessments, to wit, that the hypotheses whose probabilities are estimated can approximate the truth to different degrees. Once this is recognized, it becomes apparent that the question of how to assess probability estimates depends heavily on context.

Consider an election in which each of the n voters casts a vote consisting of a strict preference ranking of the three candidates A, B, and C. In the limit as n→∞, which scoring rule maximizes, under the assumption of Impartial Anonymous Culture (uniform probability distribution over profiles), the probability that the Condorcet candidate wins the election, given that a Condorcet candidate exists? We produce an analytic solution, which is not the Borda Count. Our result agrees with recent numerical results (...) from two independent studies, and contradicts a published result of Van Newenhizen (Economic Theory 2, 69–83. (1992)). (shrink)

In this response, I focus on clarifying my arguments, highlighting consensus, and addressing competing views about the utility of polygenic scores (PGSs) for social science. I also discuss an assortment of expansions to my arguments and suggest alternative approaches. I conclude by reiterating the need for caution and appropriate scientific skepticism.

Epistemic decision theory aims to defend a variety of epistemic norms in terms of their facilitation of epistemic ends. One of the most important components of EpDT is known as a scoring rule. This thesis addresses some problems about scoring rules in EpDT. I consider scoring rules both for precise credences and for imprecise credences. For scoring rules in the context of precise credences, I examine the rationale for requiring a scoring rule to be strictly proper, and argue that no (...) satisfactory justification has been given. I then investigate one possible response to my argument and show the problems with this response. The conclusion is that there is a further need for justifying the requirement that a scoring rule should be strictly proper for precise credences. For scoring rules in the context of imprecise credences, an impossibility result has been established in the literature purporting to show that no strictly proper, continuous and real-valued scoring rule exists. However, a precise statement of the impossibility result requires precise definitions both of strict propriety and of continuity in the context of imprecise credences. Moreover, the result implies that we need to drop one of the three properties - strict propriety, continuity or being real-valued - to have a scoring rule for applying EpDT to imprecise credences. So, firstly, I offer definitions of strict propriety and of continuity and clarify the impossibility result. Then, I investigate what will happen if we drop one of the three properties. I argue that we should drop the property of being real-valued and I offer the general forms of two kinds of strictly proper, continuous and lexicographic scoring rules for imprecise credences. (shrink)

Research in the field of management has increasingly focused on strategies and tools related to corporate sustainability. Of the tools examined, codes of ethics have been found to play a primary role. Many studies have investigated the content of such codes, as well as their capacity to condition the behaviour of people within organizations. However, few studies have considered the intrinsic quality of codes of ethics. This study aims to investigate the impact that specific factors—firm size, degree of internationalization and (...) industry effect—can have on the quality of codes of ethics. Based on a sample of 248 listed Italian companies, the results of the empirical analysis show that the quality standard is particularly high in larger companies and in those firms operating in industries in which relationships established with critical stakeholders—and disclosure to those stakeholders—play a crucial role. These results have interesting implications for both researchers and practitioners. (shrink)

There is an ongoing debate about which rule we ought to use for scoring probability estimates. Much of this debate has been premised on scoring-rule monism, according to which there is exactly one best scoring rule. In previous work, I have argued against this position. The argument given there was based on purely a priori considerations, notably the intuition that scoring rules should be sensitive to truthlikeness relations if, and only if, such relations are present among whichever hypotheses are at (...) issue. The present paper offers a new, quasi-empirical argument against scoring-rule monism. This argument uses computational simulations to show that different scoring rules can have different economical consequences, depending on the context of use. (shrink)

This paper explores the interpretation and use of polygenic risk scores (PRSs). We argue that PRSs generally do not directly embody causal information. Nonetheless, they can assist us in tracking other causal relationships concerning genetic effects. Although their purely predictive/correlational use is important, it is this tracking feature that contributes to their potential usefulness in other applications, such as genetic dissection, and their use as controls, which allow us, indirectly, to "see" more clearly the role of environmental variables.

It is a hotly contested issue whether polygenic scores should play a major role in the social sciences. Here, we defend a methodologically pluralist stance in which sociogenomics should abandon its hype and recognize that it suffers from all the methodological difficulties of the social sciences, yet nevertheless maintain an optimistic stance toward a more cautious use.

This paper studies a ranking rule of the following type axiomatically: each voter places k candidates into n categories with ranks from n to 1 attached to these categories, the candidate(s) with the highest aggregate score is (are) the winner(s). We show that it is characterized by a monotonicity condition and a multi-stage cancellation property.

Suppose that beliefs come in degrees. How should we then measure the accuracy of these degrees of belief? Scoring rules are usually thought to be the mathematical tool appropriate for this job. But there are many scoring rules, which lead to different ordinal accuracy rankings. Recently, Fallis and Lewis [2016] have given an argument that, if sound, rules out many popular scoring rules, including the Brier score, as genuine measures of accuracy. I respond to this argument, in part by (...) noting that the argument fails to account for verisimilitude—that certain false hypotheses might be closer to the truth than other false hypotheses are. Oddie [forthcoming], however, has argued that no member of a very wide class of scoring rules (the so-called proper scores) can appropriately handle verisimilitude. I explain how to respond to Oddie's argument, and I recommend a class of weighted scoring rules that, I argue, genuinely measure accuracy while escaping the arguments of Fallis and Lewis as well as Oddie. (shrink)

Polygenic scores (PGSs) have several limitations. They are confounded with environmental effects on behavior and cannot be used to study how mutations affect brain function and behavior. For this, mutations with large effects, which often arise in only one geographical population are needed. Genome-wide association studies (GWASs), commonly used for identifying mutations, have difficulty detecting these mutations. A strategy that overcomes this challenge is discussed.

Sustainability reporting guidelines developed by Global Reporting Initiative provide a systematic approach for the companies to report their performance on social, environmental, and economic dimensions of sustainability. This study compared the sustainability reports of leading Indian public and private sector companies. Reports were analyzed based on GRI guidelines toward their reporting on sustainability. A numerical score from 0 to 3 was assigned for each of the 84 performance indicators of the GRI 2011 guidelines based on inclusiveness of sustainability report. (...) The analysis showed that reporting on economic dimension was comparatively better as compared to social and environmental dimensions. Sampled companies did not show much difference in their reporting practices on economic performances. However, considerable difference was observed in their reporting practices on environmental and social dimensions. Reporting practices of Tata Steel were better in all dimensions of sustainability and emerged as a responsible company on sustainability reporting. (shrink)

In a three-candidate election, a scoring rule s (s in [0,1]) assigns 1, s, and 0 points (respectively) to each first, second and third place in the individual preference rankings. The Condorcet efficiency of a scoring rule is defined as the conditional probability that this rule selects the winner in accordance with Condorcet criteria (three Condorcet criteria are considered in the paper). We are interested in the following question: What rule s has the greatest Condorcet efficiency? After recalling the known (...) answer to this question, we investigate the impact of social homogeneity on the optimal value of ?. One of the most salient results we obtain is that the optimality of the Borda rule (s=1/2) holds only if the voters act in an independent way. (shrink)

Thomas Richardson and Peter Spirtes. Parameterizing and Scoring Mixed Ancestral Graphs.

Polygenic score (PGS) computations assume an additive model of gene action because associations between phenotypes and alleles at different loci are compounded, ignoring interactions between alleles or loci let alone between genotype and environment. Consequently, PGSs are subject to the same objections that invalidated traditional heritability analyses in the 1970s. Thus, PGSs should not be used in the social sciences.

In lieu of an abstract, here is a brief excerpt of the content:A Bittersweet Score:A Father’s Account of His Family’s 20-Year Journey After a Pediatric Brain Tumor DiagnosisChristopher RileyI hadn’t seen him for 20 years, not since the day he drilled a hole in Peter’s head and left the stainless steel drill and bloody bit on the bedside table. He figured prominently in the story I often told of that day when he, a doctor in training, [End Page 3] (...) informed my wife Kathy and me that, “Wow,” our five-year-old son had “an impressive tumor” in his brain. He announced it with the admiration I reserve for a touchdown pass or stunning sunset. Since that day, he had become a venerable physician. Back then he was the resident who met us in the ER after our pediatrician told us that the MRI of Peter’s brain was “not normal,” that “there might be a growth.” As if there might not be. I imagined that Peter’s brain might simply have an unusual shape, or that the scan revealed some undiscovered fracture and the authorities only wanted to lock me up and all with my son would be well. The thrilled young doctor slew those hopes with an ice pick: “Wow, that’s an impressive tumor.” I said, “That’s the first time anyone has used the word tumor.” The doctor appeared mortified and started over.Now 20 years later we found ourselves at the same party and I felt a compulsion to introduce myself, remind him we’d met that day in 1993, and tell him what had become of Peter and his family in the decades since he’d made that mortifying mistake, one I hoped had become for him a defining moment. To my disappointment, he didn’t seem to remember.Peter was my red-haired boy. Fearless and whip smart, he told a stream of knock-knock jokes and performed dance routines choreographed by his 8-year-old sister Rachel. Six months of headaches, vomiting and clumsy falls led to discovery of the tumor. When I phoned my parents with the news, I couldn’t speak the words, words that felt as if they spelled my boy’s doom. My body refused to pronounce them.The war for Peter’s life began with surgery. I sat with Kathy in the surgical waiting area, fearing every minute that I would see the surgeon approaching with his shoulders slumped in mortal defeat. I learned during those hours that fear of your child’s death is a physical pain, a constriction in the chest, a suffocation. At the end of that wait, the surgeon told us the tumor was out and Peter had survived. The pathology indicated the tumor was a medulloblastoma. Without additional treatment, including radiation, it was certain to come back. Kathy’s knees buckled. Having just endured one life-and-death battle, we were plunged into another. To complicate matters, Peter wasn’t waking from surgery. Even after the anesthesia wore off, Peter remained groggy, unable to move or focus his eyes.Through the following days, Peter failed to rouse or speak. Sores formed at the back of his neck where his unswallowed saliva pooled. Neurologists doubted he knew us. His doctors hoped Peter would recover but it was possible he would remain as he was indefinitely. As I sat holding his useless hand, watching his useless body, I thought I’d never loved him as much as I did now.Peter’s doctors presented two treatment options. The first consisted of relatively high doses of daily radiation, the most effective known method for preventing the return of the cancer. But radiation wasn’t good for young brains. It “shaved IQ points,” they said in wild understatement. So they offered a second, experimental option, one that reduced radiation by a third and added months of chemotherapy. The doctors hoped this new regimen would be as effective as the old but cause less cognitive damage. They asked us to choose. It seemed impossible. We gathered the scant available data. We weighed the risks. We prayed. We took a leap. Without asking him, we made a decision for Peter we knew... (shrink)

Item response theory (IRT) is a modern psychometric framework for estimating respondents’ latent traits (e.g., ability, attitude, and personality) based on their responses to a set of questions in psychological tests. The current study adopted an item response tree (IRTree) method, which combines the tree model with IRT models for handling the sequential process of responding to a test item, to score individual moral inclination for the CNI test—a broadly adopted model for examining humans’ moral decision-making with three parameters (...) generated: sensitivity to moral norms, sensitivity to consequences, and inaction preference. Compared to previous models for the CNI test, the resulting EIRTree-CNI Model is able to generate individual scores without increasing the number of items (thus, less subject fatigue or compromised response quality) or employing a post hoc approach that is deemed statistically suboptimal. The model fits the data well, and the subsequent test also supported the concurrent validity and the predictive validity of the model. Limitations are discussed further. (shrink)

The coronavirus-19 (COVD-19) pandemic has resulted in strains on critical care resources throughout the world. Existing and newly developed guidelines for the allocation of scarce resources, including ventilators, frequently use the Sequential Organ Failure Assessment (SOFA) score for prognostic determination. This article will outline how SOFA scores were neither designed nor tested for this purpose and why guidelines based upon SOFA score groupings do not conform to ethical principles and community values.

Classification of the boys in 48 families of three or more brothers according to their Moray House Test (VIQ) scores awarded at age 11±1[fraction one-half] years in 1947–75 confirms the postulated existence of a total of nine male phenotypes for this X-linked trait in the score range <70 to 140 points. The phenotypic means lie close to the sequence 69(8)133. Recombination is shown to occur. An additive effect of three alleles at each of two X-chromosome loci is the most (...) likely simple scheme. An iterative approach matching the observed mixtures of proposed genotypes in the families with probabilities for variable levels of homozygosity, non-crossover/crossover heterozygosity, and maternal meiotic recombination yields a best goodness of fit where this last is 20%. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Uselessness of Polygenic Scores for Addressing Campus DrinkingBennett Knox (bio), Hannah Allen (bio), and Stephen M. Downes, PhD (bio)Here we articulate a negative answer to Turkheimer and Greer’s question: “Is it possible to envision a genetically informed program that ethically intervenes on campus drinking?” (Turkheimer & Greer, 2024). However, first, we note that the authors cover an immense amount of ground in their paper. They lend insight into (...) how psychiatric genetics, at its very core, is conducted through their detailed examination of a large body of work in one specific area of this large field. A main result of this is to explain the gulf between results and conclusions, work that provides an invaluable service not just to various areas in philosophy and bioethics, but that are deserving of readership by a very wide audience. This gulf is explained via a careful accounting of the statistical measures used to assess the impact of genes on alcohol-related behavior in the college students sampled and comparisons between the strength of these measures and the strength and scope of conclusions drawn by the Spit for Science (S4S) researchers.A brief mention of the statistical measures in question helps set up our main focus. As Turkheimer and Greer note, before advances in sequencing technology, human behavior geneticists generated heritability coefficients for traits of interest. These coefficients were standardly produced from twin study work, which historically was the best way of getting a sense of the relative contribution of genes to a trait of interest as we cannot, or rather should not, conduct breeding experiments on humans. Current descendants of heritability coefficients come from genome-wide association studies (GWAS), which can be conducted on large groups of unrelated people. One key measure of interest arising from GWAS is a polygenic score (PGS), which “can be thought of as an observed manifestation at the individual level of the abstract variance ratio estimated by a heritability” (Turkheimer & Greer, 2024). Turkheimer and Greer focus on R2 values, which roughly “describe the magnitude of the relationship between the polygenic score and the phenotypes [of interest]” [End Page 437] (Turkheimer & Greer, 2024). They point out that the largest R2 reported in an S4S study is 6.5% (0.065). R2 are taken to be small at 0.01, medium at 0.09, and large at 0.25 in many areas of social science research but there are fields, for example, drug assay work, where only much higher R2 values are considered indication of a large effect. By this assessment, most of the R2 values reported by the S4S researchers, or calculated by Turkheimer and Greer when not reported, are very, very small, sitting well below the level of small effect of 0.01.Given these very low R2 measures, we agree with Turkheimer and Greer that S4S researchers did not uncover genetic information that could be informative, let alone actionable, for administrators concerned with campus drinking. However, it is worth asking what it would have looked like if S4S had produced such information. Suppose that S4S had been wildly successful, producing the Gattaca-like genetic information of “polygenic scores making reliable predictions that individuals had a 35% chance of developing a psychiatric disorder [here, alcoholism]” (Turkheimer & Greer, 2024). If a student was given their PGS, how are they to interpret it and act on it? How would this information be put to use by an administrator to address the problem of campus drinking?For the information to be leveraged at all, it would require consent from a significant number of students to have their PGS calculated and made available to themselves or administrators. Were scores to be calculated without active consent from the student (perhaps by using the sample provided to S4S), this would be a serious ethical violation. But even if a sufficient number of students did consent to having their PGS for alcoholism calculated, it is still not clear how this information could be used in an ethical manner to address the problem of campus drinking.If this student was already aware of a family history of alcoholism, then the PGS might do little more than quantify... (shrink)

Polygenic scores cannot elucidate the mechanisms that produce behavioral phenotypes (including “intelligence”). Therefore, they are unlikely to yield helpful interventions. Moreover, they are poor predictors of individuals' developmental outcomes. Burt's critique is well-supported by the details of molecular biology. Specifically, experiences affect epigenetic factors that influence phenotypes via how the genome functions, a fact that lends support to Burt's conclusions.

We deal with the ranking problem of the nodes in a directed graph. The bilateral relationships specified by a directed graph may reflect the outcomes of a sport competition, the mutual reference structure between websites, or a group preference structure over alternatives. We introduce a class of scoring methods for directed graphs, indexed by a single nonnegative parameter α. This parameter reflects the internal slackening of a node within an underlying iterative process. The class of so-called internal slackening scoring methods, (...) denoted by λα, consists of the limits of these processes. It is seen that λ0 extends the invariant scoring method, while λ∞ extends the fair bets scoring method. Method λ1 corresponds with the existing λ-scoring method of Borm et al. (Ann Oper Res 109(1):61–75, 2002) and can be seen as a compromise between λ0 and λ∞. In particular, an explicit proportionality relation between λα and λ1 is derived. Moreover, the internal slackening scoring methods are applied to the setting of social choice situations where they give rise to a class of social choice correspondences that refine both the Top cycle correspondence and the Uncovered set correspondence. (shrink)

In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. Regarding a bet on one event given another event, only logarithmic versions preserve the probability of the given event. Logarithmic versions also preserve the conditional probabilities of other events, and so preserve conditional independence relations. Given logarithmic rules that elicit relative probabilities of (...) base event pairs, it costs no more to elicit estimates on all combinations of these base events. (shrink)

Conversational contextualism states that the truth-conditions expressed by knowledge-attributing sentences vary relative to the context of utterance. This context is determined partly by different standards the person involved must meet in order to make the sentence true. I am concerned with the question of how these standards can be raised or lowered, and especially what happens to the standards and the conversational score when parties in a discussion push the conversational scores in different directions. None of the available options (...) for an answer seems satisfying. I argue that this results from a misunderstanding of the characteristics of the situation at hand. (shrink)

In the United States, at least 6% of all hospital beds are in the intensive care unit or coronary care unit. The cost of treating a patient in an intensive care unit averages from $2,000 to $3,500 per day. At least 10–40% of intensive care patients will not survive to hospital discharge. Today, every major category of disease may be found in the modern ICU; common diagnoses are septicemia, postsurgical complications, cerebrovascular accidents, gastrointestinal bleeding, neoplasia, and respiratory failure. ICUs employ (...) some of the most sophisticated medical technology, routinely monitoring the cardiopulmonary performance of patients and often providing assisted ventilation. ICUs are high intensity in terms of their staffing, involving 24-hour physician supervision and nurse:patient ratios from 1:3 to 1:1. (shrink)

The last lecture on leadership by the NFL's greatest coach: Bill Walsh Bill Walsh is a towering figure in the history of the NFL.

The internal structure of ability emotional intelligence tests at item level has been hardly studied, and if studied often the predicted structure did not show. In the present study, an a priori model for responses to EI ability items using Likert response scales with a Situational Judgement Test format is investigated with confirmatory factor analysis. The model consists of a target EI ability factor, an acquiescence factor, which is a method factor induced by the Likert response scales, and design-based error (...) covariances, which are induced by the SJT format. It is investigated whether this a priori model can account for the observed associations between the raw item responses of the Components of Emotion Understanding Test-24. The CEUT-24 is a new test developed to assess emotion understanding, a key aspect of the EI ability construct, based on the componential emotion framework. The sample consisted of 1184 participants from four European countries speaking four different languages. Findings showed that the a priori model fitted the data well in all four languages. Furthermore, measurement invariance testing gave evidence for a well-fitting configural, metric, and partial scalar invariance model. The conclusion is that within a regular CFA framework using raw observed items responses, method factors can be disentangled from the targeted EI ability factor. (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)

In many voting systems, voters’ preferences on a set of candidates are represented by linear orderings. In this context, scoring rules are well-known procedures to aggregate the preferences of the voters. Under these rules, each candidate obtains a fixed number of points, sk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s_k$$\end{document}, each time he/she is ranked k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}th by one voter and the candidates are ordered according to the total number of (...) points they receive. In order to identify the best scoring rule to use in each situation, we need to know which properties are met by each of these procedures. Although some properties have been analyzed extensively, there are other properties that have not been studied for all scoring rules. In this paper, we consider two desirable social choice properties, the Pareto-optimality and the immunity to the absolute loser paradox, and establish characterizations of the scoring rules that satisfy each of these specific axioms. Moreover, we also provide a proof of a result given by Saari and Barney, where the scoring rules meeting reversal symmetry are characterized. From the results of characterization, we establish some relationships among these properties. Finally, we give a characterization of the scoring rules satisfying the three properties. (shrink)

We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifi es the connection of coherence and proper scoring rules to Bregman divergence.