Culture is used as a sortal term in philosophical, political and scientific projects. This sortal picks out particular cultural groups as countable, classifiable and comparable entities. The best current accounts of this sortal develop an analogy between cultures and species. Just as species are lineages of organisms linked by biological reproduction, cultures are lineages of entities linked by cultural reproduction. Here I highlight an underappreciated problem for these accounts: the ranking problem. Cultural reproduction supports multiple lineages at (...) various levels of organization and scale – so which of these, if any, are at the ‘culture’ rank? That is, which lineages are the particulars the sortal should be capturing? After suggesting that current accounts lack the resources to answer the problem, I argue the most plausible route forward drops the requirement that ‘cultural’ lineages are found at a particular rank. Sortal cultures are rank-free. (shrink)

Partial order optimality theory is a conservative generalization of classical optimality theory that makes possible the modeling of free variation and quantitative regularities without any numerical parameters. Solving the ranking problem for PoOT has so far remained an outstanding problem: allowing for free variation, given a finite set of input/output pairs, i.e., a dataset, \ that a speaker S knows to be part of some language L, how can S learn the set of all grammars G under (...) some constraint set C compatible with \?. Here, allowing for free variation, given the set of all PoOT grammars GPoOT over a constraint set C, for an arbitrary \, I provide set-theoretic means for constructing the actual set G compatible with \. Specifically, I determine the set of all STRICT ORDERS of C that are compatible with \. As every strict total order is a strict order, our solution is applicable in both PoOT and COT, showing that the ranking problem in COT is a special instance of a more general one in PoOT. (shrink)

The outranking methods usually contain two main steps: determination of a (sometimes valued) relation which aggregates the preferences and exploitation of this relation in order to choose, sort or rank the actions. In a ranking problem, the second step is the construction of a (complete or partial) preorder from a (valued) relation. We have considered it was interesting to list the ‘good properties’ such a construction should verify and to analyze some procedures in this context. We present here (...) the first results of this study, which concern the construction of a complete preorder from a non valued relation. (shrink)

An organizing theme of the dissertation is the issue of how to make philosophical theories useful for scientific purposes. An argument for the contention is presented that it doesn’t suffice merely to theoretically motivate one’s theories, and make them compatible with existing data, but that philosophers having this aim should ideally contribute to identifying unique and hard to vary predictions of their theories. This methodological recommendation is applied to the ranking-theoretic approach to conditionals, which emphasizes the epistemic relevance and (...) the expression of reason relations as part of the semantics of the natural language conditional. As a first step, this approach is theoretically motivated in a comparative discussion of other alternatives in psychology of reasoning, like the suppositional theory of conditionals, and novel approaches to the problems of compositionality and accounting for the objective purport of indicative conditionals are presented. In a second step, a formal model is formulated, which allows us to derive quantitative predictions from the ranking-theoretic approach, and it is investigated which novel avenues of empirical research that this model opens up for. Finally, a treatment is given of the problem of logical omniscience as it concerns the issue of whether ranking theory (and other similar approaches) makes too idealized assumptions about rationality to allow for interesting applications in psychology of reasoning. Building on the work of Robert Brandom, a novel solution to this problem is presented, which both opens up for new perspectives in psychology of reasoning and appears to be capable of satisfying a range of constraints on bridge principles between logic and norms of reasoning, which would otherwise stand in a tension. (shrink)

Ranking finite subsets of a given set X of elements is the formal object of analysis in this article. This problem has found a wide range of economic interpretations in the literature. The focus of the article is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn (1996), Journal of Mathematical Psychology 40, 64–77 showed that the number of sufficient and necessary conditions that are (...) needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this article proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu’s (1990), Recherches Economiques de Louvain 56, 383–390) characterization of the cardinality-based rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of “focal” elements is not given ex-ante; but brought out by the axioms. (shrink)

Ranking Theory has been developed as an alternative to subjec- tive probability for modelling partial belief. It goes further than probability in that it jointly models both full and partial belief. One selling feature is that the Lottery Paradox does not arise in Ranking Theory. However, all is not well when it comes to modelling lottery beliefs with ranks. In this paper, I show how lotteries create problems for Ranking Theory.

BackgroundCodes of conduct mainly focus on research misconduct that takes the form of fabrication, falsification, and plagiarism. However, at the aggregate level, lesser forms of research misbehavior may be more important due to their much higher prevalence. Little is known about what the most frequent research misbehaviors are and what their impact is if they occur.MethodsA survey was conducted among 1353 attendees of international research integrity conferences. They were asked to score 60 research misbehaviors according to their views on and (...) perceptions of the frequency of occurrence, preventability, impact on truth (validity), and impact on trust between scientists on 5-point scales. We expressed the aggregate level impact as the product of frequency scores and truth, trust and preventability scores, respectively. We ranked misbehaviors based on mean scores. Additionally, relevant demographic and professional background information was collected from participants.ResultsResponse was 17% of those who were sent the invitational email and 33% of those who opened it. The rankings suggest that selective reporting, selective citing, and flaws in quality assurance and mentoring are viewed as the major problems of modern research. The “deadly sins” of fabrication and falsification ranked highest on the impact on truth but low to moderate on aggregate level impact on truth, due to their low estimated frequency. Plagiarism is thought to be common but to have little impact on truth although it ranked high on aggregate level impact on trust.ConclusionsWe designed a comprehensive list of 60 major and minor research misbehaviors. Our respondents were much more concerned over sloppy science than about scientific fraud (FFP). In the fostering of responsible conduct of research, we recommend to develop interventions that actively discourage the high ranking misbehaviors from our study. (shrink)

While numerous studies have shown diverse effects of rankings, rather little is known about their production. This article contributes to a broader understanding of rankings in society, and does so by focusing on underlying worldviews. I argue that the existence of a ranking and its concrete methodology can be explained by the producer’s paradigmatic assumptions about a world-to-be-ranked. Referring to the sociology of knowledge and studies on commensuration, comparisons, quantification and valuation, I provide a general heuristic to analyze this (...) relation between underlying worldviews and observational regimes through which order is constructed systematically. Presenting empirical results on a ranking for the most famous artists in the world, I show how the review device’s initial problem and its construction of order derive from consistent assumptions about contemporary art, its symbolic structures and its social embeddedness. These findings have implications for both research on rankings and sociology of the arts. (shrink)

We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.

Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of first-order structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we solve a problem of the second author by showing that certain injective envelopes have the maximum possible positive Deissler rank complexity. The proof shows that this complexity naturally reflects the internal structure of the (...) injective extension in the form of the levels of the Matlis hierarchy. (shrink)

To aggregate rankings into a social ranking, a natural approach is to use scoring systems such as Plurality, Veto, and Borda that assign scores to candidates. We distinguish three types of methods built on scoring systems: ranking by score, ranking by repeatedly choosing a winner, and ranking by repeatedly choosing a loser. The latter method captures the frequently studied voting rules Instant Runoff Voting (IRV), Coombs, and Baldwin. We compare these classes of methods axiomatically, referencing prior (...) results. In an experimental analysis, we show that the three types of methods produce different rankings in practice. We also provide evidence that sequentially selecting winners is most suitable to detect a ground truth ranking of candidates. For different rules in our classes, we then study the (parameterized) computational complexity of deciding in which positions a given candidate can appear in the chosen ranking. As part of our analysis, we also consider the Winner Determination problem for IRV, Coombs, and Baldwin and determine their complexity when there are few voters or candidates. (shrink)

In this paper I revisit nineteenth-century debates over historical objectivity and the political functions of historiography. I focus on two central contributors to these debates: Leopold von Ranke and Johann Gustav Droysen. In their takes on objectivity and subjectivity, impartiality and political engagement I reveal diametrically opposed solutions to shared concerns: how can historians reveal history to be meaningful without taking recourse to speculative philosophy? And how can they produce a knowledge that is relevant to the present when the project (...) of “exemplary” history has been abandoned? I put a special focus on the relativist themes in Ranke’s and Droysen’s answers to these questions. Ranke’s demand for impartiality leads him to think of all historical epochs as equally valid, while Droysen’s emphasis on the historian’s subjectivity relativizes historical truth. In order to explain why Ranke and Droysen nevertheless remained unfazed by the problem of historical relativism, I analyze their normative conceptions of the historian’s disciplinary ethos. I show that Ranke and Droysen think of objective impartiality and subjective partiality not only in methodological terms, but also in terms of justice and ethic duty. This normative element secures the professional study of history an ethical-political relevance for the present. (shrink)

Belief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I, I have first presented the AGM theory of belief revision. Then I have focused on the problem of iterated belief revisions. In part II, I will first present ranking theory (Spohn 1988). Then I will show how it solves the problem of iterated belief revisions. I will conclude by sketching two areas of future research.

Ranke (1795-1886) championed objective writing based on source material and established the study of history as a major university discipline. These essays, presented in October 1986 at a conference held to mark the centennial of his death, place the German historian in the context of the developing discipline and introduce important issues and problems in European historiography. Annotation copyrighted by Book News, Inc., Portland, OR.

We tend to think that there are different types of biological taxa: some taxa are species, others are genera, while others are families. Linnaeus gave us his ranks in 1731. Biological theory has changed since Linnaeus’s time. Nevertheless, the vast majority of biologists still assign Linnaean ranks to taxa, even though that practice is at odds with evolutionary theory and even though it causes a number of practical problems. The Linnaean ranks should be abandoned and alternative methods for displaying the (...) hierarchical relations of taxa should be adopted. (shrink)

In this chapter I turn to the question of how the value of alternatives can be incorporated in freedom rankings such that freedom’s agency value is captured. I do so in a two step approach. In the first step I identify the formal and interpretational conditions under which a freedom ranking suffers the problem of desire dependency or the impossibility of paternalism. Given that the occurrence of these problems, as I have argued in Chap. 2, indicates a failure (...) to take freedom’s agency value into account, this allows me to rule out approaches that fail to capture that value. The somewhat puzzling finding, however, is that nearly all existing freedom rankings fail to capture freedom’s agency value. That is, given a widely accepted (formal) condition, both ways to interpret the preferences invoked to identify the valuable alternatives in a set face either the problem of desire dependency or the impossibility of paternalism. In the second step I suggest a way to capture freedom’s agency value. For this purpose I define freedom’s agency value more precisely, taking it to be the value freedom has in virtue of allowing a person to reflect and deliberate upon the relative priority of her plural identities at the moment of choice. I use a procedural criterion of ‘reasonableness’ to identify the valuable alternatives in a set on the basis of a person’s identity profile. It turns out that the same condition that -as it was shown in Chap. 4 – restricts the conflict among a person’s plural identities and allows for the transitivity of her all-things-considered preference, provides a way to account for the value the availability of options has for a person’s agency without suffering the problems of desire dependency or the impossibility of paternalism. (shrink)

Sustainable development calls for choices among alternative policy options. It is a common view that such choices can be justified by appealing to an evaluative ranking of the options with respect to how their consequences affect a broad range of prudential and moral values. Three philosophically motivated proposals for analysing evaluative rankings are discussed: the measured merits model (e.g. Chang), the ordered values model (e.g. Griffin), and the permissible preference orderings model (Rabinowicz). The analysis focuses on the models’ potential (...) for making transparent how an evaluative ranking can contribute to a justified choice among options, particularly in situations that involve diverse values as typically found in debates on sustainable development. Such transparency plays a crucial role when policy rankings are going to be used as arguments in political decision processes. The measured merits model is found to have questionable consequences for the concept of sustainability, while the ordered values model calls for an axiological framework that cannot plausibly be spelled out for sustainability. The permissible preference orderings model is more promising. Its formal structure and its ability to deal with value-pluralism provide an interesting re-structuring of the problem of justifying choices in sustainability issues. (shrink)

Motivated by the search for a logic for polynomial time, we study rank logic which extends fixed-point logic with counting by operators that determine the rank of matrices over finite fields. WhileFPRcan express most of the known queries that separateFPCfromPtime, almost nothing was known about the limitations of its expressive power.In our first main result we show that the extensions ofFPCby rank operators over different prime fields are incomparable. This solves an open question posed by Dawar and Holm and also (...) implies that rank logic, in its original definition with a distinct rank operator for every field, fails to capture polynomial time. In particular we show that the variant of rank logic${\text{FPR}}^{\text{*}}$with an operator that uniformly expresses the matrix rank over finite fields is more expressive thanFPR.One important step in our proof is to consider solvability logicFPSwhich is the analogous extension ofFPCby quantifiers which express the solvability problem for linear equation systems over finite fields. Solvability logic can easily be embedded into rank logic, but it is open whether it is a strict fragment. In our second main result we give a partial answer to this question: in the absence of counting, rank operators are strictly more expressive than solvability quantifiers. (shrink)

Supererogatory acts are, in some sense, morally better their non-supererogatory alternatives. In this sense, what is it for one option A to be better than an alternative B? I argue for three main conclusions. First, relative rankings are a type of all-in action guidance. If A is better than B, then morality recommends that you A rather than B. Such all-in guidance is useful when acts have the same deontic status. Second, I argue that Right > Wrong: permissible acts are (...) always better than their impermissible alternatives. If Right > Wrong were false, then morality’s deontic verdicts would sometimes conflict with its relative rankings. Such conflict would undermine the thought that morality is a coherent, authoritative guide to action. Third, the All or Nothing Problem is not a counterexample to Right > Wrong as is commonly thought. Instead, it involves an interesting ranking reversal: whether A > B can depend on whether a certain alternative is added as a third option. (shrink)

A vast number of real-world problems can be associated with multi-criteria decision-making (MCDM). This paper discusses MCDM in agricultural industry. Methodological hybrid analytical hierarchy processes, ELECTRE I and genetic algorithm method are proposed here, and it is shown how such a model can be used for complete ranking model. The proposed hybrid bio-inspired method is implemented on real-world data set collected from agricultural industry in Serbia.

Ratings and rankings are criticized for being simplistic, obscurantist, inaccurate, and subjective, yet they are becoming an increasingly influential social form. We elaborate the criticisms of ratings and rankings in various fields but go on to argue that analysis should shift its target. The problem that ratings deal with is not observation of an independent world. Instead, the challenge they face is the circularity of second-order observation in which observations must take into account the observations of others. To this (...) purpose they function well enough not because they mirror how things are but because they offer a highly visible reference point to which others are attentive and thereby provide an orientation to navigate uncertainty. The concluding section places the problem of ratings and rankings in a broader historical perspective, contrasting the ranked society to the society of rankings. Responding to uncertainty, ratings and rankings perpetuates rather than eliminates anxiety. (shrink)

Supererogatory acts are, in some sense, morally better their non-supererogatory alternatives. In this sense, what is it for one option A to be better than an alternative B? This chapter argues for three main conclusions. First, relative rankings are a type of all-in action guidance. If A is better than B, then morality recommends that you A rather than B. Such all-in guidance is useful when acts have the same deontic status. Second, Right > Wrong: permissible acts are always better (...) than their impermissible alternatives. If Right > Wrong were false, then morality’s deontic verdicts would sometimes conflict with its relative rankings. Such conflict would undermine the thought that morality is a coherent, authoritative guide to action. Third, the All or Nothing Problem is not a counterexample to Right > Wrong, as is commonly thought. Instead, it involves an interesting ranking reversal: whether A > B can depend on whether a certain alternative is added as a third option. (shrink)

We apply a cognitive modeling approach to the problem of measuring expertise on rank ordering problems. In these problems, people must order a set of items in terms of a given criterion (e.g., ordering American holidays through the calendar year). Using a cognitive model of behavior on this problem that allows for individual differences in knowledge, we are able to infer people's expertise directly from the rankings they provide. We show that our model-based measure of expertise outperforms self-report (...) measures, taken both before and after completing the ordering of items, in terms of correlation with the actual accuracy of the answers. These results apply to six general knowledge tasks, like ordering American holidays, and two prediction tasks, involving sporting and television competitions. Based on these results, we discuss the potential and limitations of using cognitive models in assessing expertise. (shrink)

While much attention has been given to the use of principles in biomedical ethics and increasing attention is given to alternative theoretical approaches, relatively little attention has been devoted to the critical task of how one resolves conflicts among competing principles. After summarizing the system of principles and some problems in conceptualizing the principles, several strategies for reconciling conflicts among principles are examined including the use of single-principle theories (pure libertarianism, pure utilitarianism, and pure Hippocratism), balancing theories, conflicting appeals theories, (...) and lexical ordering. Then a mixed strategy is proposed in which consequentialist principles are balanced between themselves as are nonconsequentialist principles, after which the result of balancing the nonconsequentialist principles is lexically ranked over the result of balancing the consequentialist ones. Finally, strategies involving specifying and rule generation are discussed concluding that most current specification and rule-generating theories must involve some degree of lexical ordering of principles. (shrink)

In this paper, we shall discuss some recent contributions to the project [15, 14, 2, 18, 22, 23] of explaining why no satisfactory system of complete invariants has yet been found for the torsion-free abelian groups of finite rank n ≥ 2. Recall that, up to isomorphism, the torsion-free abelian groups of rank n are exactly the additive subgroups of the n-dimensional vector space ℚn which contain n linearly independent elements. Thus the collection of torsion-free abelian groups of rank at (...) most n can be naturally identified with the set S of all nontrivial additive subgroups of ℚn. In 1937, Baer [4] solved the classification problem for the class Sof rank 1 groups as follows.Let ℙ be the set of primes. If G is a torsion-free abelian group and 0 ≠ x ϵ G, then the p-height of x is defined to behx = sup{n ϵ ℕ ∣ There exists y ϵ G such that pny = x} ϵ ℕ ∪{∞}; and the characteristic χ of x is defined to be the function. (shrink)

This paper analyzes the problem of deriving a ranking of fixed-cardinality subsets of a universal set from a given ranking of the elements of this universal set. Only subsets with a given number of elements are being ranked, which is where the approach in this paper differs from the literature on extension rules that establish preference relations on the power set of the universal set. Common examples for areas where such preferences on subsets with a fixed cardinality (...) are needed are elections of committees of a given size, many-to-one matchings, and decision problems under ignorance. The main result of the paper is a characterization of a class oflexicographic rank-ordered rules by means of two axioms, namely, aresponsiveness condition used in the matching literature and a well-knownneutrality requirement which ensures that the names of the alternatives are irrelevant for the ranking of the sets. (shrink)

Traditional accounts of belief change have been criticized for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is a framework for non-prioritized belief change based on default theories (Ghose and Goebel, 1998). A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. This (...) approach is, however, restrictive in assuming a linear ordering of reliability on the received inputs. In this paper, we replace the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced. This extension brings along with it the problem of dealing with inputs of equal rank. We provide a semantic solution to this problem which contains, as a special case, AGM belief change on closed theories. (shrink)

The implementation of the UN Sustainable Development Goals and the Lisbon Strategy sets the task of a comprehensive study of the citizens` well-being, determining the state and trends in the level and quality of life not only by traditional methods of social statistics, but also through comprehensive sociological research. This approach has significant advantages since it allows us to generalize the state of social development of a society based on the population`s opinions, to study the emerging social risks that concern (...) the population, to determine the differentiation of countries by indicators of well-being. The foundations of the new approach to the analysis of social processes were laid by the scientific achievements of the 60s of the last century. The dominant paradigm was the economic goals and parameters of statistically measured national income, household income, wages and their differentiation. The environmental risks that threaten the future of civilization were identified and analyzed in the 70s of the XX century. The production contradiction, which raised the question of measuring the quality of life in a new way, was articulated. The economic component was mixed and replaced with the welfare parameter. The sustainable development, including the indicators of well-being, the fight against poverty, and the environment were declared to be the goals of the society. The tasks of monitoring the solution of these problems are solved by sociological research, whose mathematical formalization can become a structural element of economic and mathematical modeling of social processes. (shrink)

If preference-based freedom rankings are based on all-things-considered preferences, they risk judging phenomena of adaptive preferences as freedom enhancing. As a remedy, it has been suggested to base preference-based freedom rankings on reasonable preferences. But this approach is also problematic. This article argues that the quest for a remedy is unnecessary. All-things-considered preferences retain information on whether the availability of an option contributes to the value that freedom has for a person’s self-expression. If preference-based freedom rankings use all-things-considered preferences to (...) evaluate whether an option contributes to a person’s self-expression, they are immune to the problem posed by adaptive preferences. (shrink)

A decision under ‘complete uncertainty’ is one where the decision maker knows the set of possible outcomes for each decision, but cannot assign probabilities to those outcomes. This way, the problem of ranking decisions is reduced to a problem of ranking sets of outcomes. All rankings that have emerged in the literature in this domain imply transitivity. In the current study, transitivity is subjected to an empirical evaluation in two experiments, where subjects are asked to choose (...) between sets of monetary consequences. After analysis with a Bayes Factor, very few violations of transitivity were found. It can be concluded that transitivity seems a plausible condition for the ranking of sets of monetary consequences. (shrink)

The fecund growth of open source knowledge goods in the global communicative environment underlines their public good character. Once knowledge goods are disseminated, their cost and price tend towards zero. It is now obvious (as apparent in recent OECD policy documents) that commercial research and trade in intellectual property capture only a small fraction of open source knowledge, which is expanding even more rapidly than global markets. But for policy makers this poses the problem of how to assign stable (...) and defensible value to free floating knowledge goods. Across the world, research universities have been positioned in a networked competition of institutions with globally mobile personnel and converging goals and organizational cultures. In rapid time global university ranking and the associated technologies of publication and citation ordering and counting have proved potent in arranging status, assigning value and shaping behaviours in higher education. We find that public goods are readily annexed to the longer-standing projects of producing university status and sustaining an imperial global geo-politics of knowledge. Here the relation between status production and free open source cultural production is not so much a contradiction as an antinomy. These issues are discussed in the light of the flourishing and fall of the lowland city-states of the Maya in Mesoamerica, a notable example of a status economy and of the interplay between status reproduction and cultural goods, a dynamic only partly nested in economic production. The article reviews the rankings technologies, led by the Shanghai Jiao Tong University research metrics, the global strategies of university executives, changing national policies on universities and research, and the aggregation of these effects in the emerging `arms race' in investment in innovation. (shrink)

In recruitment, promotion, admission, and other forms of wealth and power apportion, an evaluator typically ranks a set of candidates in terms of their perceived competence. If the evaluator is prejudiced, the resulting ranking will misrepresent the candidates’ actual ranking. This constitutes not only a moral and a practical problem, but also an epistemological one, which begs the question of what we should do – epistemologically – to mitigate it. The article is an attempt to begin to (...) answer this question. I first explore the presuppositions that must obtain for individual interventions to likely yield positive epistemological effects in ranking situations. I then compare these with the corresponding presuppositions of a novel, ‘post hoc’ approach to deprejudicing due to Jönsson and Sjödahl (Episteme 14(4):499–517, 2017), which does not attempt to change evaluators but attempts to increase the veracity of the rankings they produce after the fact (but before the rankings give rise to discriminatory effects) using statistical methods. With these two sets of presuppositions in place, I describe the limitations imposed by each presupposition on its intervention, compare presuppositions across the two kinds of interventions, and conclude that the two kinds of interventions importantly complement each other by having fairly disjoint, but non–conflicting, presuppositions. The post hoc intervention can thus complement an individual intervention (and vice versa) in situations where both are applicable (by adding further increases in veracity), but also by applying to situations where that intervention is not applicable (and thereby increase veracity in situations beyond the reach of that intervention). (shrink)

Ranks are cardinal degrees of belief (that also represent belief). This calls for a theory of measurement of those numerical ranks. The chapter provides no less than three different methods of measurement. The basic theory is that of difference measurement. The main measurement method uniquely reconstructs a ranking function from its iterated contraction behavior on a ratio scale. Thereby, it offers a complete set of laws of iterated contraction, thus solving an old problem of belief revision theory. The (...) chapter should be understood as providing additional justification of ranking theory. At the end, two possible further lines of justification, a Cox-type of justification and an analogy to the Dutch book argument, are presented and discussed. (shrink)

In spite of our good intentions and explicit egalitarian convictions, we habitually disfavor the underprivileged. The rapidly growing literature on implicit bias – unconscious, automatic tendencies to associate negative traits with members of particular social groups – points towards explanations of this dissonance, although rarely towards generalizable solutions. In a recent paper, Jennifer Saul draws attention to the alarming epistemological problems that implicit bias carries with it; since our judgments about each other are likely influenced by implicit bias, we have (...) good reason to doubt their veracity. In this paper we explore a novel way to come to terms with the epistemological problem as it manifests itself in ranking situations, i.e. how we can know that the way in which we have ranked a group of people for a certain position, reflects their actual competence. On our approach, rather than attempting to make people less biased, we suggest that biased behavior can sometimes be corrected after the fact. In particular, the veracity of rankings can sometimes be improved by modifying the rankings directly. We investigate three methods that modify biased rankings, and argue that the last of these solves the epistemological problem that we are concerned with. (shrink)

This chapter addresses the problem of ranking available drugs in guideline development to support clinicians in their work. Based on a pragmatic approach to the notion of evidence and a hierarchical view on different kinds of evidence this chapter introduces a decision aid, HiDAD, which draws on the multi criteria decision making literature. This decision aid implements the wide-spread intuition that there are different kinds of evidence with varying degrees of importance by relying on a strict ordinal ordering (...) of kinds of evidence. In order to construct a ranking every pair of drugs is first compared separately on all kinds of evidence. Next, these quantitative comparisons are then aggregated into an overall comparison between drugs based on all the available evidence in a way which avoids that evidence of less importance is trumped by evidence of the higher levels. Finally, these overall comparisons are used to determine the final ranking of drugs which then informs the process of guideline writing. Properties, modifications and applicability of the decision aid HiDAD are discussed and assessed. (shrink)

What is the level of John Rawls? There is a problem I have, which may be from my specific perspective. I have written a lot on John Rawls and Milan Kundera, and they seem to belong to the same class, especially they get past certain kinds of checks. If you raise a concern, you are more or less ignored by the many fans/admirers. "This definition doesn't work." Goes back to Kundera/Rawls. But here is the problem: Milan Kundera is (...) not respected like Rawls is. If I were forced to get involved in ranking within a class, I would say Kundera is fractionally better. 1/100th better. (shrink)

Expertise in the field of pedagogy began to be more thoroughly researched at the end of the last and the beginning of this century. It has been observed that expert teachers possess a range of characteristics that enhance the quality of educational system. Flexibility, analytical thinking, a strong understanding of abstract concepts, attention to detail, and better problem solving and decision-making strategies are among the traits of expert teachers. Through continuous work on their own professional development, teachers achieve excellence (...) in their field and become experts, demonstrating their expertise, among other ways, through advancement to higher professional ranks. The aim of this research was to explore the experiences of expert teachers regarding professional advancement and their role within the educational system. A qualitative study was conducted using a focus group. Data were collected through semi-structured interviews with eight female teachers who had attained the titles of teacher advisor or teacher excellent advisor. The findings indicate that there are numerous challenges in the process of professional advancement into higher ranks for teachers and that expert teachers often represent an underutilized potential within the educational system. (shrink)

Scientific explanationScientific explanations cannot take place outside a context and each context has its own hierarchy among competing explanations. The lexicographic ordering among explanations help us rank the relevance of each possible explanation not with respect to a certain set of value judgments but with respect to the available evidence; the more relevant an explanation is, the higher is placed in the ordering. The notion of explanatory indexicals is introduced and is described as a set that involves terms which are (...) unique under each context. The informationInformation these terms carry can be used to help us construct the lexicographic hierarchy. This approach captures many episodes of scientific explanationScientific explanations including explanations induced by false propositions as well as non-causalNon-causal explanations. It furthermore evades problems that probabilistic theories of explanatory virtues face such as the lottery paradoxLottery paradoxes and is not laid open to certain downsides of the well-known “inference to the best explanation” such as the commitment to consider only true propositions as possible explanations. (shrink)

Data-driven algorithms are currently deployed in several fields, leading to a rapid increase in the importance algorithms have in decision-making processes. Over the last years, several instances of discrimination by algorithms were observed. A new branch of research emerged to examine the concept of “algorithmic fairness.” No consensus currently exists on a single operationalization of fairness, although causal-based definitions are arguably more aligned with the human conception of fairness. The aim of this article is to investigate the degree of this (...) alignment in a case study inspired by a recent ruling of an Italian court on the reputational-ranking algorithm used by a food delivery platform. I relied on the documentation of the legal dispute to discuss the applicability, intuitiveness and appropriateness of causal models in evaluating fairness, with a specific focus on a causal-based fairness definition called “counterfactual fairness.” I first describe the details of the dispute and the arguments presented to the court, as well as the court’s final decision, to establish the context of the case study. Then, I translate the dispute into a formal simplified problem using a causal diagram, which represents the main aspects of the data generation process in the case study. I identify the criteria used by the court in ruling that the algorithm was unfair and compare them with the counterfactual fairness definition. The definition of counterfactual fairness was found to be well aligned with the human conception of fairness in this case study, using the court order rationale as a gold standard. (shrink)

Let $\operatorname {TFAb}_r$ be the class of torsion-free abelian groups of rank r, and let $\operatorname {FD}_r$ be the class of fields of characteristic $0$ and transcendence degree r. We compare these classes using various notions. Considering the Scott complexity of the structures in the classes and the complexity of the isomorphism relations on the classes, the classes seem very similar. Hjorth and Thomas showed that the $\operatorname {TFAb}_r$ are strictly increasing under Borel reducibility. This is not so for the (...) classes $\operatorname {FD}_r$. Thomas and Velickovic showed that for sufficiently large r, the classes $\operatorname {FD}_r$ are equivalent under Borel reducibility. We try to compare the groups with the fields, using Borel reducibility, and also using some effective variants. We give functorial Turing computable embeddings of $\operatorname {TFAb}_r$ in $\operatorname {FD}_r$, and of $\operatorname {FD}_r$ in $\operatorname {FD}_{r+1}$. We show that under computable countable reducibility, $\operatorname {TFAb}_1$ lies on top among the classes we are considering. In fact, under computable countable reducibility, isomorphism on $\operatorname {TFAb}_1$ lies on top among equivalence relations that are effective $\Sigma _3$. (shrink)

The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

This chapter examines the practice of frank speech or candid criticism, the principal educational method of late Epicurean schools and a major tool of moral and psychological therapy. The chapter is divided into four sections, corresponding to the following topics: first, the nature, scope, kinds, and circumstances of application of _parrhēsia_; second, the characters of the students and their positive or negative reactions to parrhesiastic criticism; third, the dispositions of the teachers and the ways in which these dispositions affect the (...) use of frank speech; and fourth, the confessional and corrective practices applied at every level of hierarchy of the Epicurean school, and especially among the sages. Philodemus' discussion of these topics presents both historical and theoretical interest. It gives a fairly detailed idea of life in an Epicurean school in Zeno's and Philodemus' times, the interchange between teachers and students, and the methods used for the assimilation of the Epicurean values and way of life. _On Frank Speech_ also advances challenging views about central problems of philosophical psychology and the philosophy of education. (shrink)