I discuss a stochastic model of language learning and change. During a syntactic change, each speaker makes use of constructions from two different idealized grammars at variable rates. The model incorporates regularization in that speakers have a slight preference for using the dominant idealized grammar. It also includes incrementation: The population is divided into two interacting generations. Children can detect correlations between age and speech. They then predict where the population’s language is moving and speak according to that prediction, (...) which represents a social force encouraging children not to sound out-dated. Both regularization and incrementation turn out to be necessary for spontaneous language change to occur on a reasonable time scale and run to completion monotonically. Chance correlation between age and speech may be amplified by these social forces, eventually leading to a syntactic change through prediction-driven instability. (shrink)

Current mathematical models are notoriously unreliable in describing the time evolution of unexpected social phenomena, from financial crashes to revolution. Can such events be forecast? Can we compute probabilities about them? Can we model them? This book investigates and attempts to answer these questions through GOdel's two incompleteness theorems, and in doing so demonstrates how influential GOdel is in modern logical and mathematical thinking. Many mathematical models are applied to economics and social theory, (...) while GOdel's theorems are able to predict their limitations for more accurate analysis and understanding of national and international events. This unique discussion is written for graduate level mathematicians applying their research to the social sciences, including economics, social studies and philosophy, and also for formal logicians and philosophers of science. (shrink)

Ever since the early decades of this century, there have emerged a number of competing schools of ecology that have attempted to weave the concepts underlying natural resource management and natural-historical traditions into a formal theoretical framework. It was widely believed that the discovery of the fundamental mechanisms underlying ecological phenomena would allow ecologists to articulate mathematically rigorous statements whose validity was not predicated on contingent factors. The formulation of such statements would elevate ecology to the standing of a rigorous (...) scientific discipline on a par with physics. However, there was no agreement as to the fundamental units of ecology. Systems ecologists sought to identify the fundamental organization that tied the physical and biological components of ecosystems into an irreducible unit: the ecosystem was their fundamental unit. Population ecologists sought, instead, to identify the biological mechanisms regulating the abundance and distribution of plant and animal species: to these ecologists, the individual organism was the fundamental unit of ecology, and the physical environment was nothing more than a stage upon which the play of individuals in perennial competition took place. As Joel Hagen has pointed out, the two schools were thus dividied by fundamentally different and irreconcilable assumptions about the nature of ecosystems.Notwithstanding these divisive efforts to elevate the image of ecology, the discipline remained in the shadows of American academia until the mid-1960s, when systems ecologists succeeded in projecting ecology onto the national scene. They did so by seeking closer involvement with practical problems: they argued before Congress that their approach to the theoretical problems of ecology was uniquely suited to the solution of the impending “environmental crisis.” With the establishment of the International Biological Program, they succeeded in attracting unprecedented levels of funding for systems ecology research. Theoretical population ecologists, on the other hand, found themselves consigned to the outer regions of this new institutional landscape. The systems ecologists' successful capture of the limelight and the purse brought the divisions between them and population ecologists into sharper relief — hence the hardening of the division of ecology observed by Hagen.45I have argued that the population biologist Richard Levins, prompted by these institutional developments, sought to challenge the social position of systems ecology, and to assert the intellectual priority of theoretical population ecology. He attempted to do so by articulating a nontrivial and rather carefully thought out classification of ecological models that led to the disqualification of systems analysis as a legitimate approach to the study of ecological phenomena. I have suggested that — ultimately —Levins's case against systems analysis in ecology rested on the view that an aspiration to realism and prediction was incompatible with an interest in theoretical issues, a concern that he equated with the search for generality. He sought to reinforce this argument by exploiting the fact that systems ecologists had staked their future on the provision of technical solutions to the problems of the “environmental crisis”: he associated systems ecologists' aspiration to realism and precision with a concern for practical issues, trading on the widely accepted view that practical imperatives are incompatible with the aims of scientific inquiry.46 These are plausible, but nonetheless questionable, claims which have now become an integral part of ecological knowledge. And finally, I hope to have shown how even the most abstract levels of scientific argument are shaped by political considerations, and how discussions of the conceptual development of modern ecology might benefit from a greater consideration of its historical and social dimensions.47. (shrink)

Predictive policing has become a new panacea for crime prevention. However, we still know too little about the performance of computational methods in the context of predictive policing. The paper provides a detailed analysis of existing approaches to algorithmic crime forecasting. First, it is explained how predictive policing makes use of predictive models to generate crime forecasts. Afterwards, three epistemologies of predictive policing are distinguished: mathematical social science, social physics and machine learning. Finally, it is shown (...) that these epistemologies have significant implications for the constitution of predictive knowledge in terms of its genesis, scope, intelligibility and accessibility. It is the different ways future crimes are rendered knowledgeable in order to act upon them that reaffirm or reconfigure the status of criminological knowledge within the criminal justice system, direct the attention of law enforcement agencies to particular types of crimes and criminals and blank out others, satisfy the claim for the meaningfulness of predictions or break with it and allow professionals to understand the algorithmic systems they shall rely on or turn them into a black box. By distinguishing epistemologies and analysing their implications, this analysis provides insight into the techno-scientific foundations of predictive policing and enables us to critically engage with the socio-technical practices of algorithmic crime forecasting. (shrink)

Physics has for a long time been regarded as the most mature of all sciences due to strict mathematically formulated laws of physics and success of theories in applications, for which it has been taken as the example of scientificity which other sciences should strive towards. Just what aspect of physics it is that is regarded as the cause of its success and hence the yardstick of scientificity – this question has given rise to differing opinions. In his book Making (...) Social Sciences More Scientific. The Need For Predictive Models Rein Taagepera criticises the opinion that physics is a rigorous science ‘merely’ due to the use of mathematical operations and numerical accuracy of results. He shows that the strictness of physics consists instead in its method that allows to set numbers and mathematical formalism into correspondence with real phenomena in a way that enables application (first of all prediction), and to unite physical theories into uniform, integral systems. At the same time he teaches how it would be possible to reach the same in social sciences. In the first part of my review I will give an overview of the book’s chapters, describing in more detail Taagepera’s general understanding of science and scientific method. In the second part of the review I analyse the positions presented in the book from the point of view of philosophy of science (particularly that of constructive realism), providing examples from social sciences. With my critique I show that the society cannot be handled with strict theories similar to those of physics, and that in order to raise the applicational strength of social sciences, other means often suit better than rendering them similar to physics by developing mathematical formalism. (shrink)

Question order effects are commonly observed in self-report measures of judgment and attitude. This article develops a quantum question order model (the QQ model) to account for four types of question order effects observed in literature. First, the postulates of the QQ model are presented. Second, an a priori, parameter-free, and precise prediction, called the QQ equality, is derived from these mathematical principles, and six empirical data sets are used to test the prediction. Third, a new index (...) is derived from the model to measure similarity between questions. Fourth, we show that in contrast to the QQ model, Bayesian and Markov models do not generally satisfy the QQ equality and thus cannot account for the reported empirical data that support this equality. Finally, we describe the conditions under which order effects are predicted to occur, and we review a broader range of findings that are encompassed by these very same quantum principles. We conclude that quantum probability theory, initially invented to explain order effects on measurements in physics, appears to be a powerful natural explanation for order effects of self-report measures in social and behavioral sciences, too. (shrink)

I examine the role that mathematics plays in understanding and modelling finance, especially stock markets, and how philosophy affects it. To this end, I explore how mathematics penetrates finance via physics, constructing a ‘financial physics’, and I outline the philosophical backgrounds of this process, in particular the ‘philosophy of equilibrium’ and that of critical points or ‘out-of-equilibrium’. I discuss the main characteristics and a few weaknesses of these mathematizations of financial systems, notably econometrics and econophysics, and I compare the two (...) ways, top-down and bottom-up, of building mathematical approaches to finance. The top-down approach is the most used and the most conservative. I argue that it guarantees a mathematical account, but it is less effective than the more difficult bottom-up approach, which is more appropriate and which may end up without a mathematical account of financial phenomena. I then consider two important issues raised by a mathematical approach to finance, that is, the performative and the reversing side of mathematics, and an ethics of mathematics. In the first case I argue that mathematics not only can be a performative device, but it also enables ‘reversing’ dynamics, that is, a mathematical model may become not a representational tool, but a device of social engineering—a mathematical way of investigating what are the initial conditions and processes needed to obtain an intended result. In the second case I argue that this specific relation between mathematical modelling and prediction raises an ethical question in finance, namely, a responsible construction and use of the mathematical models provided by a financial physics. (shrink)

This essay proposes that mathematical biology can be used as a fruitful exemplar for the introduction of scientific principles to history. After reviewing the antecedents of the application of mathematics to biology, in particular evolutionary biology, I describe in detail a mathematical model of cultural diffusion based on an analogy with population genetics. Subsequently, as a case study, this model is used to investigate the dynamics of the early modern European witch-crazes in Bavaria, England, Hungary and Finland. In (...) the second part of the article, I sketch the methodological significance of this type of 'scientific history' and, in particular, I identify three lessons that mathematical biology can contribute to historiography. The first lesson is on the fundamental distinction between agent's purposes and structural social processes. I argue that mathematical modeling can be fruitfully applied to describe social processes, while agents' purposes ought to be addressed following an hermeneutic tradition. The second lesson is on the aim of mathematical modeling. Here I argue that the object of modeling, rather than being the prediction or retrodiction of events , is the understanding of the factors involved in the dynamics of social processes . Finally, the third lesson is on the new understanding of science after the collapse of the standard view. In summary, while mathematical modeling can provide an extremely powerful approach to clarify the dynamics of certain macro-historical processes, scientific methods ought to be regarded as a complement, not a substitute, to classical historiography. (shrink)

We consider a situation in which individuals search for accurate decisions without direct feedback on their accuracy, but with information about the decisions made by peers in their group. The “wisdom of crowds” hypothesis states that the average judgment of many individuals can give a good estimate of, for example, the outcomes of sporting events and the answers to trivia questions. Two conditions for the application of wisdom of crowds are that estimates should be independent and unbiased. Here, we study (...) how individuals integrate social information when answering trivia questions with answers that range between 0% and 100%. We find that, consistent with the wisdom of crowds hypothesis, average performance improves with group size. However, individuals show a consistent bias to produce estimates that are insufficiently extreme. We find that social information provides significant, albeit small, improvement to group performance. Outliers with answers far from the correct answer move toward the position of the group mean. Given that these outliers also tend to be nearer to 50% than do the answers of other group members, this move creates group polarization away from 50%. By looking at individual performance over different questions we find that some people are more likely to be affected by social influence than others. There is also evidence that people differ in their competence in answering questions, but lack of competence is not significantly correlated with willingness to change guesses. We develop a mathematical model based on these results that postulates a cognitive process in which people first decide whether to take into account peer guesses, and if so, to move in the direction of these guesses. The size of the move is proportional to the distance between their own guess and the average guess of the group. This model closely approximates the distribution of guess movements and shows how outlying incorrect opinions can be systematically removed from a group resulting, in some situations, in improved group performance. However, improvement is only predicted for cases in which the initial guesses of individuals in the group are biased. (shrink)

Herbert A. Simon's reply (Inquiry, Vol. 25, No. 3) to my criticism of his 1954 paper is not to the point. He fails to respond to some of my arguments and misconceives others. One of his misconceptions is that any mathematical deduction from empirical premises which are formulated mathematically will necessarily lead to empirically valid conclusions. This claim is particularly unwarrantable in Simon's case since his mathematical premise, the continuity of the reaction function, is empirically meaningless.

Recent finance literature attributes the development of derivative instruments to technological advances, and improved mathematical models for predicting option prices. This paper explores the role of social ethics in the acceptance of financial derivatives. The relationship between utilitarian ethical principles and the demise of turn-of-the-century bucket shops is contrasted with modern tolerance of financial derivatives based upon libertarian ethical precepts. Our conclusion is that a change in social ethics also facilitated the growth in trading in modern (...) financial derivatives. (shrink)

It is certainly well accepted that formal models play a key role in scientific job. Its use goes from natural sciences like physics and even to social sciences like economics and politics. Using mathematics allows the researcher to consider more complicated scenarios involving several variables. Some models are developed to make predictions, others to describe a phenomena, or just to improve the explanation of events in the world. But what has all this to do with philosophy? The (...) aim of the present paper is to investigate debates on the role of formal models in a specific philosophical subject, precisely, the epistemology of rationality. Are we able to explain why models are needed in epistemological work? This answer will be addressed on the assumptions that epistemological theorizing is committed with normative statements. More specifically, epistemologists are concerned with normative questions about what rationality requires from epistemic agents. The first goal is to discuss some assumptions about the role of mathematical models in formal epistemology undertaking. And secondly, I will argue for the following two claims: formal models are useful tools for predicting consequences of normative assumption about what is intuitively required by rationality; and insofar rationality theory is normative in virtue of being instrumentalist and aiming at truth, formal models are means-end tools, therefore, for rationality, mathematical models are devices for maximizing truth in doxastic states. (shrink)

This paper presents a simple mathematical model that shows how economic inequality between social groups can arise and be maintained even when the only adaptive learning process driving cultural evolution increases individuals’ economic gains. The key assumptions are that human populations are structured into groups and that cultural learning is more likely to occur within than between groups. Then, if groups are sufficiently isolated and there are potential gains from specialization and exchange, stable stratification can sometimes result. This (...) model predicts that stratification is favored, ceteris paribus, by (1) greater surplus production, (2) more equitable divisions of the surplus among specialists, (3) greater cultural isolation among subpopulations within a society, and (4) more weight given to economic success by cultural learners. (shrink)

In this paper, we analyse higher-order risky choices by the representative cumulative prospect theory (CPT) decision maker from three alternative reference points. These are the status quo, average payout and maxmin. The choice tasks we consider in our analysis include binary risks, and are the ones employed in the experimental literature on higher order risk preferences. We demonstrate that the choices made by the representative subject depend on the reference point. If the reference point is the status quo and the (...) lottery choices exhibit symmetric risk, we demonstrate that there is no third order reflection effect of lottery choices but there is a fourth order reflection effect. When the average payout is the reference point, we demonstrate that any third or fourth order lottery choice is possible dependent upon the lottery payoffs. However, under the assumption of maxmin reference point, the risky choices are prudent and temperate. In addition to these results, our analysis reveals that the representative CPT subject can choose combinations of second with third and fourth order risky options that differ from those in other major models of decision under risk. We contrast our theoretical predictions with the empirical results reported in the literature on higher order risk preferences and are able to reconcile some conflicting experimental evidence. (shrink)

In recent years, the green aviation technology draws more attention, and more hybrid power units have been applied to the aerial vehicles. To achieve the high performance and long lifetime of components during varied working conditions, the effective regulation of the energy management is necessary for the vehicles with hybrid power unit. In this paper, power prediction-based model predictive control for energy management strategy is proposed for the vehicle equipped with HPU based on turboshaft engine in order to maintain (...) proper battery’s state of charge and decrease turboshaft engine’s exhaust gas temperature. First, a modeling approach based on data-driven method is adopted to obtain the mathematical model of turboshaft engine considering time delay and inertial of states. An integrated power predictor consisting of the classification of input status and the subpredictors are developed based on the deep learning method to improve the accuracy of the prediction model of the model predictive control. Subsequently, an EMS based on MPC using the proposed power predictor is introduced to regulate the SOC of battery and the EGT of turboshaft engine. The comparison with experimental results shows the high accuracy of mathematical model of turboshaft engine. The simulation results show the effectiveness of the proposed EMS for the vehicle, and the effects of different weight coefficients of objective function on the proposed EMS are discussed. (shrink)

In settler-colonial Canada, the state does not receive Indigenous testimony as credible evidence. While the state often accepts Indigenous testimony in formal hearings, the state fundamentally rejects Indigenous evidence as a description of the world as it is, as an onto-epistemology. In other words, the Indigenous worldview formation, while it functions as a knowledge system that knows and predicts life, is not admitted to regulatory discussions about effects of resource extraction projects on life. Particularly in such resource-extraction review hearings, partly (...) for obvious reasons of ecological ethics, there is no space for Indigenous relational-ontology. I theorize that beyond racism, white supremacy, and greed, settler-colonial onto-epistemological structures are structured to systematically eliminate the potential for relational-ontologies. This exclusion is complementary to resource-extractivist and legal positivist procedures and is biased against Indigenous knowledge and knowledge-sharing procedures; it is a crisis of state integrity and is philosophically unsound. In my analysis of Canadian National Energy Board documents, I ferret out some of these structures that de facto discredit Indigenous onto-epistemologies; I propose this fundamental problem of the Canadian settler-colonial state must be recognized and changed if the calls of Canada’s Truth and Reconciliation commission are to be met. (shrink)

This article contributes to the revision of the procedure of robustness analysis of mathematical models in epistemic democracy using the systematic review method. It identifies the drawbacks of robustness analysis in epistemic democracy in terms of sample universality and inference from samples with the same results. To exemplify the effectiveness of systematic review, this article conducted a pilot review of diversity trumps ability theorem models, which are mathematical models of deliberation often cited by epistemic democrats. (...) A review of nine models extracted from 352 papers exemplifies the effectiveness of robustness analysis supplemented by systematic review in epistemic democracy. (shrink)

Most studies of corporate social responsiveness (CSR) focus on the relationship between CSR and profit. Here, we use three perspectives (institutional theory, economic theory and agency theory) to explain CSR. Industry norms, market share and indicators of management reputation predict variance in CSR. The combined perspectives improve understanding of both CSR and the CSR-profit relationship in two ways. First, they suggest that CSR levels and their relationship with profit will vary by industry. Second, they suggest that stock market measures (...) and accounting measures will respond differently to CSR measures. Stock market measures lead, while accounting measures lag, CSR. (shrink)

Idealization is a necessity. Stripping away levels of complexity makes questions tractable, focuses our attention, and lets us develop comprehensible, testable models. Applying such models, however, requires care and attention to how the idealizations incorporated into their development affect their predictions. In epistemology, we tend to focus on idealizations concerning individual agents' capacities, such as memory, mathematical ability, and so on, when addressing this concern. By contrast, this dissertation focuses on social idealizations, particularly those pertaining to (...) salient social categories like race, sex, and gender. In Chapter II, Privilege and Superiority, we begin with standpoint epistemology, one of the earliest efforts to grapple with the ways that social structures affect our epistemic lives. I argue that, if we interpret standpoint epistemologists' claims as hypotheses about the ways that our social positions affect access to evidence, we can fruitfully employ recent developments in evidence logic to study the consequences. I lay the groundwork for this project, developing a model based on neighborhood semantics for modal logic. Adapting this framework to standpoint epistemology helps to clarify the meaning of terms like "epistemic privilege" and "superior knowledge" and to elucidate the differences between various accounts of standpoint epistemology. I also address a longstanding criticism of these views: Longino's (1990) bias paradox, which suggests that there is no objective position from which to judge the goodness of a particular standpoint. Chapter III, Evidence in a Non-Ideal World, turns to the broader social context, looking at how ideology affects the availability of evidence. Throughout the chapter, I take the formation, justification, and maintenance of racist, sexist, and otherwise oppressive beliefs as a central case. I argue that these beliefs are, at least sometimes, formed as a result of evidential distortion, a structural feature of our epistemic contexts that skews readily available evidence in favor of dominant ideologies. Because they are formed this way, such beliefs will appear justified on prominent accounts of justification, both internalist and externalist. As a result, epistemic norms that fail to account for such non-ideal conditions will deliver verdicts that are not only counter-intuitive, but also morally unpalatable. This, I argue, reveals a kind of structural epistemic injustice, especially where oppressive ideology is involved and suggests the need for epistemic norms that are sensitive to agents' social contexts. Much of the discussion in Chapters II and III depends on social categories like race and gender, arguing that they have a distinctive influence on our epistemic lives. In Chapter IV, I Know You Are, But What Am I?, my co-author and I focus on social categories themselves, distinguishing between self-identity, social identity, and social role. We self-identify as gay or straight, men or women, couch-potatoes or gym rats. Sometimes, these identities affect our social roles---the way we are perceived and treated by others---and sometimes they do not. This relationship between our internal identities and our preferred public perceptions begs for explanation. On our account, this relationship is captured by what we refer to as 'social identity'---roughly, internal identities made available to others. We argue that this account of social identity plays an illuminating role in structural explanation of discrimination and individual behavior, dissolves puzzles surrounding the phenomenon of 'passing', and explains certain moral and political obligations toward individuals. (shrink)

Despite its importance, the linkage between genetic and cultural evolution has until now been little explored. An understanding of this linkage is needed to extend evolutionary theory so that it can deal for the first time with the phenomena of mind and human social history. We characterize the process of gene-culture coevolution, in which culture is shaped by biological imperatives while biological traits are simultaneously altered by genetic evolution in response to cultural history. A case is made from both (...) theory and evidence that genetic and cultural evolution are inseverable, and that the human mind has tended to evolve so as to bias individuals toward certain patterns of cognition and choice rather than others. With the aid of mathematical models we trace the coevolutionary circuit: The genes prescribe structure in developmental pathways that lay down endocrine and neural systems, imposing regularities in the development of cognition and behavior; these regularities translate upward into holistic patterns of culture, which can be predicted in the form of probability density distributions ; natural selection acts within human history to favor certain epigenetic rules over others; and the selection alters the frequencies of the underlying genes. The effects of genetic and cultural changes reverberate throughout the circuit and are consequently tested with the passage of each life cycle. In addition to modeling gene-culture coevolution, we apply methods from island biogeography and information theory to examine the cultural capacity of the genes, the factors determining the magnitude of cultural diversity, and the possible reasons for the uniqueness of the human achievement. (shrink)

Most models of the formation of political coalitions use either Euclidean spaces or rely purely on game theory. This limits their applicability. In this article, a single model is presented which is more broadly applicable. In principle any kind of set can be used as a policy space. The model is also able to incorporate different kinds of party motivations: both rent-seeking and idealism. The model uses party preferences and power to identify stable coalitions and predict government policy as (...) well as to indicate which member of the opposition will be able to break up the governing coalition if no stable coalition exists. In the latter case it will also indicate on which issue the government is likely to split. Parties may have preferences over issues such as the composition of cabinet and/or the governing coalition as well as the more traditional issues of government formation. The model also provides a rationale for log-rolling. (shrink)

The widespread and long-lived failings of academic economics are due to an over-reliance on largely inappropriate mathematical methods of analysis. This is an assessment I have long maintained. Many heterodox economists, however, appear to hold instead that the central problem is a form of political-economic ideology. Specifically, it is widely contended in heterodox circles that the discipline goes astray just because so many economists are committed to a portrayal of the market economy as a smoothly or efficiently functioning system (...) or some such, a portrayal that, whether sincerely held or otherwise, is inconsistent with the workings of social reality. Here I critically examine the contention that a form of political-economic ideology of this sort is the primary problem and assess its explanatory power. I conclude that the contention does not fare very well. I do not, though, deny that ideology of some sort has a major impact on the output of the modern economics academy. However it is of a different nature to the form typically discussed, and works in somewhat indirect and complex ways. Having raised the question of the impact of ideology I take the opportunity to explore its play in the economics academy more generally. (shrink)

To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality, personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement about ‘truth’, but (...) the assignment of mathematics to informal reality is not itself formally analysable, and it is dependent on social and personal construction processes. On these levels, absolute agreement cannot be expected. Starting from this point of view, repercussion of mathematical on social and personal reality, the historical development of mathematical modelling, and the role, use and interpretation of mathematical models in scientific practice are discussed. (shrink)

We propose simple nonlinear mathematical models for the legal concept of balancing of interests. Our aim is to bridge the gap between an abstract formalisation of a balancing decision while assuring consistency and ultimately legal certainty across cases. We focus on the conflict between the rights to privacy and to the protection of personal data in Art. 7 and Art. 8 of the EU Charter of Fundamental Rights (EUCh) against the right of access to information derived from Art. (...) 11 EUCh. These competing rights are denoted by ( \(i_1\) ) _right to privacy _ and ( \(i_2\) ) _access to information_; mathematically, their indices are respectively assigned by \(u_1\in [0,1]\) and \(u_2\in [0,1]\) subject to the constraint \(u_1+u_2=1\). This constraint allows us to use one single index _u_ to resolve the conflict through balancing. The outcome will be concluded by comparing the index _u_ with a prior given threshold \(u_0\). For simplicity, we assume that the balancing depends on only selected legal criteria such as the social status of affected person, and the sphere from which the information originated, which are represented as inputs of the models, called legal parameters. Additionally, we take “time” into consideration as a legal criterion, building on the European Court of Justice’s ruling on the right to be forgotten: by considering time as a legal parameter, we model how the outcome of the balancing changes over the passage of time. To catch the dependence of the outcome _u_ by these criteria as legal parameters, data were created by a fully-qualified lawyer. By comparison to other approaches based on machine learning, especially neural networks, this approach requires significantly less data. This might come at the price of higher abstraction and simplification, but also provides for higher transparency and explainability. Two mathematical models for _u_, a time-independent model and a time-dependent model, are proposed, that are fitted by using the data. (shrink)

The predictive processing framework includes a broad set of ideas, which might be articulated and developed in a variety of ways, concerning how the brain may leverage predictive models when implementing perception, cognition, decision-making, and motor control. This article provides an up-to-date introduction to the two most influential theories within this framework: predictive coding and active inference. The first half of the paper (Sections 2–5) reviews the evolution of predictive coding, from early ideas about efficient coding in the visual (...) system to a more general model encompassing perception, cognition, and motor control. The theory is characterized in terms of the claims it makes at Marr's computational, algorithmic, and implementation levels of description, and the conceptual and mathematical connections between predictive coding, Bayesian inference, and variational free energy (a quantity jointly evaluating model accuracy and complexity) are explored. The second half of the paper (Sections 6–8) turns to recent theories of active inference. Like predictive coding, active inference models assume that perceptual and learning processes minimize variational free energy as a means of approximating Bayesian inference in a biologically plausible manner. However, these models focus primarily on planning and decision-making processes that predictive coding models were not developed to address. Under active inference, an agent evaluates potential plans (action sequences) based on their expected free energy (a quantity that combines anticipated reward and information gain). The agent is assumed to represent the world as a partially observable Markov decision process with discrete time and discrete states. Current research applications of active inference models are described, including a range of simulation work, as well as studies fitting models to empirical data. The paper concludes by considering future research directions that will be important for further development of both models. (shrink)

Current understanding of the development of quantity representations is based primarily on performance in the number‐line task. We posit that the data from number‐line tasks reflect the observer's underlying representation of quantity, together with the cognitive strategies and skills required to equate line length and quantity. Here, we specify a unified theory linking the underlying psychological representation of quantity and the associated strategies in four variations of the number‐line task: the production and estimation variations of the bounded and unbounded number‐line (...) tasks. Comparison of performance in the bounded and unbounded number‐line tasks provides a unique and direct way to assess the role of strategy in number‐line completion. Each task produces a distinct pattern of data, yet each pattern is hypothesized to arise, at least in part, from the same underlying psychological representation of quantity. Our model predicts that the estimated biases from each task should be equivalent if the different completion strategies are modeled appropriately and no other influences are at play. We test this equivalence hypothesis in two experiments. The data reveal all variations of the number‐line task produce equivalent biases except for one: the estimation variation of the bounded number‐line task. We discuss the important implications of these findings. (shrink)

The predictive inadequacy of the social sciences is well documented, and philosophers have sought to diagnose it. This paper examines Brian Epstein’s recent diagnosis. He argues that the social sciences treat the social world as entirely composed of individual people. Instead, social scientists should recognize that material, non-individualistic entities determine the social world, as well. First, I argue that Epstein’s argument both begs the question against his opponents and is not sufficiently charitable. Second, I present (...) doubts that his proposal will improve predictive success for the social sciences, which I support with Edith Penrose’s resource-based theory of the firm. (shrink)

Despite its importance, the linkage between genetic and cultural evolution has until now been little explored. An understanding of this linkage is needed to extend evolutionary theory so that it can deal for the first time with the phenomena of mind and human social history. We characterize the process of gene-culture coevolution, in which culture is shaped by biological imperatives while biological traits are simultaneously altered by genetic evolution in response to cultural history. A case is made from both (...) theory and evidence that genetic and cultural evolution are inseverable, and that the human mind has tended to evolve so as to bias individuals toward certain patterns of cognition and choice rather than others. With the aid of mathematical models we trace the coevolutionary circuit: The genes prescribe structure in developmental pathways that lay down endocrine and neural systems, imposing regularities in the development of cognition and behavior; these regularities translate upward into holistic patterns of culture, which can be predicted in the form of probability density distributions ; natural selection acts within human history to favor certain epigenetic rules over others; and the selection alters the frequencies of the underlying genes. The effects of genetic and cultural changes reverberate throughout the circuit and are consequently tested with the passage of each life cycle. In addition to modeling gene-culture coevolution, we apply methods from island biogeography and information theory to examine the cultural capacity of the genes, the factors determining the magnitude of cultural diversity, and the possible reasons for the uniqueness of the human achievement. (shrink)

I reflect on challenges to the validation of theoretical models from the perspective of a critical rationalist seeking to develop true Explanation of empirical phenomena. I illustrate my arguments with examples from the rich literature on social-influence models, a field that has profited from contributions from various disciplines such as physics, and mathematics. While this field is characterized by a large number of competing formal models, it has been criticized for having failed to generate reliable explanations (...) and predictions, because of a lack of empirical research validating models. I list five challenges to model validation in the social sciences: First, social-scientific theories are based on many obscure concepts. Second, many social-scientific concepts are latent. Third, the Representation of time is unclear in many models. Forth, in most social settings, various processes influence dynamics in parallel. Fifth, context dependencies limit the development of general models. (shrink)

Search and switching costs are two market frictions that are well known in the literature for preventing people from switching to a new and cheaper provider. Previous experimental literature has studied these two frictions in isolation. However, field evidence shows that these two frictions frequently occur together. Recently, a theoretical framework has been developed (Wilson in Eur Econ Rev 56(6):1070–1086) which studies the interplay between these two costs. We report on an experiment testing this theory to see if individual behaviour (...) with search and switching costs is in line with the theoretical predictions derived from the optimal choice rule of Wilson. The results show the crucial role of the search strategy: not only, according to Wilson model, the search cost has a greater deterrent impact on search than the switching costs, but also the sub-optimality of the search strategy is the major source of sub-optimality in the switching behaviour. (shrink)

Machine learning (ML) models recently led to major breakthroughs in predictive tasks in the natural sciences. Yet their benefits for the social sciences are less evident, as even high-profile studies on the prediction of life trajectories have shown to be largely unsuccessful – at least when measured in traditional criteria of scientific success. This paper tries to shed light on this remarkable performance gap. Comparing two social science case studies to a paradigm example from the natural (...) sciences, we argue that, in addition to explanation, prediction is an important goal of social science – and we identify constraints that impede pure ML prediction from being successful in that field. As a remedy, we outline elements of an integrative modelling approach that combines explanatory models and predictive ML models. (shrink)

Quantitative assessments of when infectious disease outbreaks end are crucial, as resources targeted towards outbreak responses typically remain in place until outbreaks are declared over. Recent improvements and innovations in mathematical approaches for determining when outbreaks end provide public health authorities with more confidence when making end-of-outbreak declarations. Although quantitative analyses of outbreaks have a long history, more complex mathematical and statistical methodologies for analysing outbreak data were developed early in the 20th century and continue to be refined. (...) Historically, such methodologies focused primarily on factors affecting the early and middle phases of an outbreak, with less attention given to determining how and when outbreaks end. This review discusses mathematical modelling methods from the last 20 years that have been developed for determining the ends of infectious disease outbreaks, and considers factors that affect the accuracy of such determinations. When disease surveillance systems provide timely and representative data to inform models, the timings of end-of-outbreak declarations can be fine-tuned to allow outbreaks to be declared over quickly and with a low risk of being incorrect. Premature declarations that outbreaks are over can undermine earlier achievements in disease control and may result in a resurgence of cases, but unnecessary delays in declaring outbreaks over can cause significant economic and social harm. Appropriate declarations that balance the benefits of relaxing control measures against the risk of a surge in cases allow public health resources to be conserved (and economic and social pressures to be reduced) while limiting the potential for additional transmission. (shrink)

This volume represents a magnum opus by Wolfgang Weidlich, summarizing his long work in the area of sociodynamics. It lays out the origins and development of his ideas on this topic, presents a variety of applications drawn from his previous work, and offers some new insights and suggestions. For those acquainted with Professor Weidlich’s work it is a satisfying summing up. For those unacquainted with it, the book provides a good overview and discussion of what is involved in it, both (...) its weaknesses and its strengths. It has a definite predecessor, Weidlich’s 1983 book with his frequent coauthor, Günter Haag, Concepts and Models of a Quantitative Sociology, but goes well beyond the arguments and models presented in that volume. (shrink)

This paper develops a synthesis of three basic societal dimensions. These three qualify as basic dimensions by virtue of being collectively inclusive, mutually exclusive to a higher degree than any alternative dimensions we have explored, and universally applicable, i.e., to all social situations. We take the six transact dimensions to be such a set. Of these six we here develop a synthesis of three (acts, people, and time) which we take to be most basic, not in the sense of (...) relative importance to human life and welfare, but in the sense of being completely mutually exclusive, of being explicitly as well as implicitly necessary in the modelling of a very large proportion of social situations, and of being not at all elusive when observed as here in all-or-none units for the acts, “noses counted” for the people, and discrete units of time. For these reasons we consider this set of dimensions especially suitable for first attempts at synthesized rational and predictive models (as distinct from purely analytical, empirical and descriptive models). It is anticipated, however, that as initial efforts increase our scientific skill, essentially the same modelbuilding techniques will be applicable when the “trickiest” or most compounded of the transact dimensions, namely values and circumstances, are also dealt with. Other systems of synthesized, predictive models which we are exploring are described briefly in a later note. (shrink)

Theory of Mind (ToM) is the term used for our ability to predict and explain the behaviour of ourselves and others. Accounts of this theory have so far fallen into two competing types: Simulation Theory and 'Theory Theory'. In contrast with Theory Theory, Simulation Theory argues that we predict behaviour not by employing a model of people, but by replicating others' thoughts and feelings. This book presents a novel defence of Simulation Theory, reviewing the major challenges against it and positing (...) the theory as the most effective method for exploring how we know each other and ourselves. Drawing on key research in the field, chapters reopen the debates surrounding Theory of Mind and cover a variety of topics including schizophrenia with implications for experimental social psychology. In the past, one of the greatest criticisms against Simulation Theory is that it cannot explain systematic error in Theory of Mind. This book explores the rapidly developing heuristics and biases programme, pioneered by Kahneman and Tversky, to suggest that a novel bias mismatch defence available to Simulation Theory explains these systematic errors. Simulation Theory: A psychological and philosophical consideration will appeal to a range of researchers and academics, including psychologists from the fields of cognitive, social and developmental psychology, as well as philosophers, psychotherapists and practitioners looking for further research on Theory of Mind. The book will also be of relevance to those interested in autism, since it offers a new approach to Theory of Mind which explains central symptoms in autistic subjects. (shrink)

This cross-sectional study aimed to assess the applicability of social cognitive determinants among the Chinese adolescents and examine whether the predictability of the social cognitive theory model on physical activity differs across gender and urbanization. A total of 3,000 Chinese adolescents ranging between the ages of 12–15 years were randomly selected to complete a set of questionnaires. Structural equation modeling was applied to investigate the relationships between social cognitive variables and PA in the urbanization and gender subgroups. (...) The overall model explained 38.9% of the variance in PA. Fit indices indicated that the structural model of SCT was good: root mean square error of approximation = 0.047, RMR = 0.028, goodness of fit index = 0.974, adjusted goodness of fit index = 0.960, Tucker–Lewis coefficient = 0.971, and comparative fit index = 0.978. Regarding the subgroup analysis, social support had a more substantial impact on the PA of adolescents in suburban areas than that in urban areas, whereas self-regulation had a more substantial impact on the PA of adolescents in urban areas than in suburban areas. The results indicate that the SCT model predicts the PA of Chinese adolescents substantially. An SCT model could apply over a range of subgroups to predict the PA behavior and should be considered comprehensively when designing interventions. These findings would benefit PA among the Chinese adolescents, especially across genders and urbanization. (shrink)

Mathematical models are potentially as useful for culture as for evolution, but cultural models must have different designs from genetic models. Social sciences must borrow from biology the idea of modeling, rather than the structure of models, because copying the product is fundamentally different from copying the design. Transfer of most cultural information from brains to artificial media increases the differences between cultural and biological information. (Published Online November 9 2006).

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students’ level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of four years as a variable. The sampled students were (...) initially assessed by means of an Early Numeracy Test (ENT), and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence (TILE). The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 to 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain. (shrink)

Socialist buildings in the city of Kruja (Albania) date back after the Second World War between the years 1945-1990. These buildings were built during the time of the socialist Albanian dictatorship and the totalitarian communist regime. A questionnaire with 30 questions was conducted and 14 people were interviewed. The interviewed residents belong to a certain area of the city of Kruja. Based on the results obtained, diagrams have been conceived and mathematical regression models have been developed which will (...) serve as a base for drawing conclusions. The purpose of this study is to find a relationship that specifies the role of the inhabitants, the role of the dwellings, the physical-mechanical characteristics, and their energy efficiency, in order to improve the living conditions of the inhabitants. The independent variables interact with each other assuming positive or negative values depending on the probabilistic mathematical regression, giving different results based on the calculated data. The variables that co-exist among them are living space, quality of life, time spent at home, social interaction of residents, dwelling humidity level, dwelling orientation, satisfaction level of the inhabitants, dwelling improvements demand, and monthly electricity bills. (shrink)

This chapter contains sections titled: Why Use Mathematical Models? Theory‐based Models Data‐based Modeling Computational Approaches Conclusions Notes.

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal (...) result to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

Projections of future climate change cannot rely on a single model. It has become common to rely on multiple simulations generated by Multi-Model Ensembles (MMEs), especially to quantify the uncertainty about what would constitute an adequate model structure. But, as Parker points out (2018), one of the remaining philosophically interesting questions is: “How can ensemble studies be designed so that they probe uncertainty in desired ways?” This paper offers two interpretations of what General Circulation Models (GCMs) are and how (...) MMEs made of GCMs should be designed. In the first interpretation, models are combinations of modules and parameterisations; an MME is obtained by “plugging and playing” with interchangeable modules and parameterisations. In the second interpretation, models are aggregations of expert judgements that result from a history of epistemic decisions made by scientists about the choice of representations; an MME is a sampling of expert judgements from modelling teams. We argue that, while the two interpretations involve distinct domains from philosophy of science and social epistemology, they both could be used in a complementary manner in order to explore ways of designing better MMEs. (shrink)

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological (...) models, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically. (shrink)

The development of Information and Communication Technologies has favored access to technological resources in adolescents. These tools provide access to information that can promote learning. However, they can also have a negative effect against people, as they can be used with other functionality, in which cyberbullying situations are caused during the interactions that arise when using social networks. The objective of this study was to determine the predictive value of the role of cyberbullying victims based on variables related to (...) other roles involved in cyberbullying and bullying, as well as personal characteristics, contextual characteristics and positive teamwork habits.. Information was collected from 227 students of the educational stages of Primary Education and Secondary Education, aged between 11 and 15 years, in a city with a high index of cultural diversity. The step-by-step technique was used to build the regression model. The results indicate that the model has a good goodness of fit coefficient. The role of cyberbully is the most important predictive variable of the role of the victim in cyberbullying and, to a lesser extent, the role of the witness in cyberbullying, the role of the witness in bullying, and the role of the victim of bullying. The role of the bullying aggressor and the variables sex, age, type of educational center, and teamwork habits are excluded in the predictive model. (shrink)

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A,O and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and (...) combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence and parental aspirations when comparing children with and without MLD. In addition, A, O and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided. (shrink)

Some basic mathematical facts pertaining to " Catastrophe Theory" are sketched. The alleged applications to the social sciences are studied. Three representative models, due to E.C. Zeeman, are described in detail, and critically analyzed. The models are found to be vaguely formulated, to be based on false hypotheses, to lead to few nontrivial predictions. Moreover, most of those predictions do not agree with reality. Finally, the only nontrivial mathematical result used in these models - (...) Thom 's theorem - is found to be incorrectly applied. It is concluded that no justification exists for the claim that Catastrophe Theory can be applied to the social sciences. (shrink)