Dwork, Hardt, Pitassi, Reingold, & Zemel [6] introduced two notions of fairness, each of which is meant to formalize the notion of similar treatment for similarly qualified individuals. The first of these notions, which we call additive metric fairness, has received much attention in subsequent work studying the fairness of a system composed of classifiers which are fair when considered in isolation [3, 4, 7, 8, 12] and in work studying the relationship between fair treatment of individuals (...) and fair treatment of groups [6, 7, 13]. Here, we extend these lines of research to the second, less-studied notion, which we call multiplicative metric fairness. In particular, we exactly characterize the fairness of conjunctions and disjunctions of multiplicative metric fair classifiers, and the extent to which a classifier which satisfies multiplicative metric fairness also treats groups fairly. This characterization reveals that whereas additive metric fairness becomes easier to satisfy when probabilities of acceptance are small, leading to unfairness under functional and group compositions, multiplicative metric fairness is better-behaved, due to its scale-invariance. (shrink)

Statistical fairness criteria are widely used for diagnosing and ameliorating algorithmic bias. However, these fairness criteria are controversial as their use raises several difficult questions. I argue that the major problems for statistical algorithmic fairness criteria stem from an incorrect understanding of their nature. These criteria are primarily used for two purposes: first, evaluating AI systems for bias, and second constraining machine learning optimization problems in order to ameliorate such bias. The first purpose typically involves treating each (...) criterion as a necessary condition for fairness. The second use involves treating criteria as sufficient conditions for fairness. Since the criteria are used for both roles, some researchers have treated them as both necessary and sufficient conditions, i.e., as definitions of algorithmic fairness. However, serious problems have been raised for the use of these fairness criteria. Under ordinary circumstances, it is impossible to satisfy multiple criteria at the same time. Moreover, there are counterexamples to both the sufficiency and necessity for fairness of each criterion. I argue that we should instead understand fairness criteria as merely providing evidence of fairness. In other words, satisfaction (or violation) of these criteria should be understood as potential evidence of fairness (or bias). Whether a criterion counts as evidence in a particular case will depend on stakeholders' background knowledge and the specific features of the system's task. This evidence account of fairness conditions provides guidance for recognizing both the appropriate uses and the limitations of fairness criteria. (shrink)

Typically, fair machine learning research focuses on a single decision maker and assumes that the underlying population is stationary. However, many of the critical domains motivating this work are characterized by competitive marketplaces with many decision makers. Realistically, we might expect only a subset of them to adopt any non-compulsory fairness-conscious policy, a situation that political philosophers call partial compliance. This possibility raises important questions: how does partial compliance and the consequent strategic behavior of decision subjects affect the allocation (...) outcomes? If k% of employers were to voluntarily adopt a fairness-promoting intervention, should we expect k% progress (in aggregate) towards the benefits of universal adoption, or will the dynamics of partial compliance wash out the hoped-for benefits? How might adopting a global (versus local) perspective impact the conclusions of an auditor? In this paper, we propose a simple model of an employment market, leveraging simulation as a tool to explore the impact of both interaction effects and incentive effects on outcomes and auditing metrics. Our key findings are that at equilibrium: (1) partial compliance by k% of employers can result in far less than proportional (k%) progress towards the full compliance outcomes; (2) the gap is more severe when fair employers match global (vs local) statistics; (3) choices of local vs global statistics can paint dramatically different pictures of the performance vis-a-vis fairness desiderata of compliant versus non-compliant employers; (4) partial compliance based on local parity measures can induce extreme segregation. Finally, we discuss implications for auditors and insights concerning the design of regulatory frameworks. (shrink)

Inspired by recent breakthroughs in predictive modeling, practitioners in both industry and government have turned to machine learning with hopes of operationalizing predictions to drive automated decisions. Unfortunately, many social desiderata concerning consequential decisions, such as justice or fairness, have no natural formulation within a purely predictive framework. In efforts to mitigate these problems, researchers have proposed a variety of metrics for quantifying deviations from various statistical parities that we might expect to observe in a fair world and (...) offered a variety of algorithms in attempts to satisfy subsets of these parities or to trade o the degree to which they are satised against utility. In this paper, we connect this approach to fair machine learning to the literature on ideal and non-ideal methodological approaches in political philosophy. The ideal approach requires positing the principles according to which a just world would operate. In the most straightforward application of ideal theory, one supports a proposed policy by arguing that it closes a discrepancy between the real and the perfectly just world. However, by failing to account for the mechanisms by which our non-ideal world arose, the responsibilities of various decision-makers, and the impacts of proposed policies, naive applications of ideal thinking can lead to misguided interventions. In this paper, we demonstrate a connection between the fair machine learning literature and the ideal approach in political philosophy, and argue that the increasingly apparent shortcomings of proposed fair machine learning algorithms reflect broader troubles faced by the ideal approach. We conclude with a critical discussion of the harms of misguided solutions, a reinterpretation of impossibility results, and directions for future research. (shrink)

There is growing concern that decision-making informed by machine learning (ML) algorithms may unfairly discriminate based on personal demographic attributes, such as race and gender. Scholars have responded by introducing numerous mathematical definitions of fairness to test the algorithm, many of which are in conflict with one another. However, these reductionist representations of fairness often bear little resemblance to real-life fairness considerations, which in practice are highly contextual. Moreover, fairness metrics tend to be implemented in (...) narrow and targeted toolkits that are difficult to integrate into an algorithm’s broader ethical assessment. In this paper, we derive lessons from ethical philosophy and welfare economics as they relate to the contextual factors relevant for fairness. In particular we highlight the debate around acceptability of particular inequalities and the inextricable links between fairness, welfare and autonomy. We propose Key Ethics Indicators (KEIs) as a way towards providing a more holistic understanding of whether or not an algorithm is aligned to the decision-maker’s ethical values. (shrink)

One of the main lines of research in algorithmic fairness involves individual fairness (IF) methods. Individual fairness is motivated by an intuitive principle, similar treatment, which requires that similar individuals be treated similarly. IF offers a precise account of this principle using distance metrics to evaluate the similarity of individuals. Proponents of individual fairness have argued that it gives the correct definition of algorithmic fairness, and that it should therefore be preferred to other methods (...) for determining fairness. I argue that individual fairness cannot serve as a definition of fairness. Moreover, IF methods should not be given priority over other fairness methods, nor used in isolation from them. To support these conclusions, I describe four in-principle problems for individual fairness as a definition and as a method for ensuring fairness: (1) counterexamples show that similar treatment (and therefore IF) are insufficient to guarantee fairness; (2) IF methods for learning similarity metrics are at risk of encoding human implicit bias; (3) IF requires prior moral judgments, limiting its usefulness as a guide for fairness and undermining its claim to define fairness; and (4) the incommensurability of relevant moral values makes similarity metrics impossible for many tasks. In light of these limitations, I suggest that individual fairness cannot be a definition of fairness, and instead should be seen as one tool among several for ameliorating algorithmic bias. (shrink)

When selecting a model from a set of equally performant models, how much unfairness can you really reduce? Is it important to be intentional about fairness when choosing among this set, or is arbitrarily choosing among the set of “good” models good enough? Recent work has highlighted that the phenomenon of model multiplicity—where multiple models with nearly identical predictive accuracy exist for the same task—has both positive and negative implications for fairness, from strengthening the enforcement of civil rights (...) law in AI systems to showcasing arbitrariness in AI decision-making. Despite the enormous implications of model multiplicity, there is little work that explores the properties of sets of equally accurate models, or Rashomon sets, in general. In this paper, we present five main theoretical and methodological contributions which help us to understand the relatively unexplored properties of the Rashomon set, in particular with regards to fairness. Our contributions include methods for efficiently sampling models from this set and techniques for identifying the fairest models according to key fairness metrics such as statistical parity. We also derive the probability that an individual’s prediction will be flipped within the Rashomon set, as well as expressions for the set’s size and the distribution of error tolerance used across models. These results lead to policy-relevant takeaways, such as the importance of intentionally looking for fair models within the Rashomon set, and understanding which individuals or groups may be more susceptible to arbitrary decisions. (shrink)

Data-driven predictive algorithms are widely used to automate and guide high-stake decision making such as bail and parole recommendation, medical resource distribution, and mortgage allocation. Nevertheless, harmful outcomes biased against vulnerable groups have been reported. The growing research field known as 'algorithmic fairness' aims to mitigate these harmful biases. Its primary methodology consists in proposing mathematical metrics to address the social harms resulting from an algorithm's biased outputs. The metrics are typically motivated by -- or substantively rooted (...) in -- ideals of distributive justice, as formulated by political and legal philosophers. The perspectives of feminist political philosophers on social justice, by contrast, have been largely neglected. Some feminist philosophers have criticized the local scope of the paradigm of distributive justice and have proposed corrective amendments to surmount its limitations. The present paper brings some key insights of feminist political philosophy to algorithmic fairness. The paper has three goals. First, I show that algorithmic fairness does not accommodate structural injustices in its current scope. Second, I defend the relevance of structural injustices -- as pioneered in the contemporary philosophical literature by Iris Marion Young -- to algorithmic fairness. Third, I take some steps in developing the paradigm of 'responsible algorithmic fairness' to correct for errors in the current scope and implementation of algorithmic fairness. I close by some reflections of directions for future research. (shrink)

The debate on ideal theory focuses mainly on whether it can provide a long-term target and a metric for assessing the justice of different institutional arrangements in non-ideal theory. Both critics and defenders of ideal theory typically overlook the role it plays in a model of fairness that can restrict the range of permissible arrangements under non-ideal conditions. In this paper, I explain ideal theory’s fairness role and its part in ensuring an institutional structure that benefits everyone in (...) a society. Critics of ideal theory therefore cannot reject it as simply useless. But I consider how they can question the attractiveness of an ideal-theory-based fairness constraint on non-ideal theory. (shrink)

In our reply to critiques of our GLP-1 receptor agonist allocation framework, we explain that using potential years of life lost (PYLL) as a metric addresses racial health disparities without explicitly allocating resources based on race. This approach is "racism-conscious" and has legal and ethical challenges over race-based approaches. Meanwhile, though acknowledging the importance of cardiovascular risk assessment, we maintain in response to other interlocutors that focusing solely on immediate risk would ignore the broader goal of mitigating disadvantage. We emphasize (...) that our framework balances multiple ethical objectives beyond just maximizing medical benefits. (shrink)

Research in ethical AI has made strides in quantitative expression of ethical values such as fairness, transparency, and privacy. Here we contribute to this effort by proposing a new family of metrics called “decisional value scores” (DVS). DVSs are scores assigned to a system based on whether the decisions it makes meet or fail to meet a particular standard (either individually, in total, or as a ratio or average over decisions made). Advantages of DVS include greater discrimination capacity (...) between types of ethically relevant decisions and facilitation of ethical comparisons between decisions and decision-making systems, including across different modalities (for instance: human, machine, or coupled human–machine systems). After clarifying ambiguities in the concept of “decision” itself, including the question of how to individuate the decisions made by a system, we discuss the role and meaning of “decision” in common AI and machine learning approaches such as decision trees, neural networks, SVMs, and unsupervised classifiers. We then show how DVSs may be defined for several ethical values of interest, with an extended discussion of transparency. Finally, we explore how such metrics can be applied to real decision-making systems through two case studies: evaluations of LLMs for transparency; and evaluations of criminal risk assessment tools for utility, rights violations, fairness, and transparency. (shrink)

This study investigated the effects of different leadership styles on employee productivity in JUHEL Pharmaceutical Firm, Anambra State, Nigeria. The primary objectives were to analyze the impact of transformational leadership, evaluate transactional leadership, and explore laissez-faire leadership's influence on productivity, as well as compare these styles' overall effectiveness. Using a quantitative approach, data were collected from 66 employees through structured surveys. Descriptive statistics, correlation analysis, and ANOVA were employed for data analysis. The findings revealed that transformational leadership had a significant (...) positive effect on employee productivity, enhancing motivation and performance. Transactional leadership showed a moderate impact, fostering goal-oriented behaviors and structured work environments. Conversely, laissez-faire leadership was found to have a minimal effect on productivity, often leading to lower employee engagement due to insufficient guidance. Comparative analysis indicated that transformational leadership outperformed the other styles in promoting higher productivity metrics. This study highlights the importance of effective leadership strategies for enhancing productivity in pharmaceutical firms. It suggests that JUHEL Pharmaceutical Firm and similar organizations should prioritize transformational leadership development to achieve optimal performance. The research contributes valuable insights to the field of leadership studies and offers a basis for future investigations into leadership practices and productivity outcomes. (shrink)

In recent years, the ethical impact of AI has been increasingly scrutinized, with public scandals emerging over biased outcomes, lack of transparency, and the misuse of data. This has led to a growing mistrust of AI and increased calls for mandated ethical audits of algorithms. Current proposals for ethical assessment of algorithms are either too high level to be put into practice without further guidance, or they focus on very specific and technical notions of fairness or transparency that do (...) not consider multiple stakeholders or the broader social context. In this article, we present an auditing framework to guide the ethical assessment of an algorithm. The audit instrument itself is comprised of three elements: a list of possible interests of stakeholders affected by the algorithm, an assessment of metrics that describe key ethically salient features of the algorithm, and a relevancy matrix that connects the assessed metrics to stakeholder interests. The proposed audit instrument yields an ethical evaluation of an algorithm that could be used by regulators and others interested in doing due diligence, while paying careful attention to the complex societal context within which the algorithm is deployed. (shrink)

Equal Justice explores the role of the idea of equality in liberal theories of justice. The title indicates the book’s two-part thesis: first, I claim that justice is the central moral category in the socio-political domain; second, I argue for a specific conceptual and normative connection between the ideas of justice and equality. This pertains to the age-old question concerning the normative significance of equality in a theory of justice. The book develops an independent, systematic, and comprehensive theory of equality (...) and egalitarianism. The principal question is about the importance of equality in a theory of justice. More precisely, we should pose questions in four contracting circles: 1. Is justice the supreme value guiding our setup of the basic structure of society, or are there other, equally important values, such as recognition, care, communal belonging? 2. If justice is the highest guiding principle, which competing ideals—especially equality and freedom—ought to have precedence in a policy oriented toward justice? What status does the ideal of equality have in that framework? 3. If equality is a basic ideal of just policy, how should it be practically realized? What sort of equality (equal opportunity, equality of welfare, resource equality) should be demanded? 4. What patterned distribution of which specific goods does the ideal of equality demand? Which principles of distribution can be justified according to our justice ideal? To conclude and summarize: 5. What is the essential core of an egalitarian theory of justice, as opposed to an inegalitarian theory? These five questions structure the work’s order of argumentation. Part A elaborates the conceptual foundations and basic moral principles of justice and equality. Chapter I sets out to install justice as the central moral category in the socio-political domain. At the beginning of the first chapter, the conceptual foundations of justice are clarified. While not eliminating the classical distinctions between different forms of justice, I argue that the distributive paradigm is of primary importance. The primacy of justice in the socio-political domain is developed out of a confrontation with alternative positions, those which maintain either that justice generally, or distributive justice in particular, are subsidiary virtues. At the end of Chapter I, the first of the questions mentioned above is answered in a way that establishes justice as the guiding normative concept for the foundation and evaluation of any social order. To clarify the role of equality in a theory of justice, Chapter II separates the idea of equality into four different principles. They are organized in a way that begins with the most general and uncontroversial principle of equality, and progresses towards increasingly detailed and contested principles. There are two theses that articulate and defend the significance of equality for justice: First there is a conceptual connection between justice and equality, in that principles of formal and proportional equality are necessary in order to explicate the concept of justice. These two principles establish an unbreakable bond between justice and equality. Justice can only be explained—or so I argue—by reference to these and other (normative) principles of equality. The second thesis posits a normative relationship between justice and equality, which is disclosed by three substantive principles of equality: moral equality, the presumption of equality, and the principle of responsibility. I argue that the normative core of an egalitarian theory of justice is expressed by the latter two principles, which are themselves based on the first principle, that of moral equality. When we view one another as persons, what form of equality or equal treatment is normatively demanded? I argue that the answer to this question is given by the procedural principle of the presumption of equality: regardless of their apparent differences, all persons deserve strictly equal treatment, unless certain kinds of differences have whatever particular relevance would justify, on generally acceptable grounds, unequal treatment or unequal distribution. The justification of the presumption of equality is central to this work and has considerable importance. If the presumption principle’s validity can be justified by enlisting the principle of general justification, then the primacy of equality, and the essential argument for an egalitarian theory of justice, is established. This would likewise provide a procedure for the construction of a material theory of justice. The second question is answered thereby at the end of Chapter II: Equality should have primacy over competing ideals within a justice-oriented policy. The presumption of equality establishes this primacy and, at the same time, offers an appropriate metric and guideline for the construction of a material theory of distributive justice. The presumption of equality in Part B offers an elegant procedure for the development of a theory of distributive justice. Chapter III clearly sets out the necessary prerequisites that a theory of distribution must satisfy in order to determine a liberal-egalitarian distributional framework. We need to specify in which situation the distribution takes place; which goods are and are not to be distributed; in which respect the presumptive equality is to be produced; and by and to whom, and for what period, the relevant goods are to be distributed. The distribution is based on resources understood as general-purpose means. It is necessary to divide goods into different categories, since the justification for unequal treatment in one domain will not carry over into another. This makes presumptive equality necessarily complex. To that end, four spheres of justice are distinguished: (1) the political sphere, which involves allocating rights through the distribution of civil liberties; (2) the democratic sphere, in which political power and the rights of political participation are regulated; (3) the economic sphere, in which income and property are distributed; (4) the social sphere, in which social positions and opportunities are distributed. This framework of distributive justice answers the third of our guiding questions, about the nature of equality, in terms of equality of resources. Chapters IV and V set out the egalitarian distributive criteria for each sphere. I argue that the generally accepted, fundamental rights of classical liberalism are more effectively reconstructed by reference to the equal resource distribution presumptively required in those spheres. Chapter IV shows that when it comes to the first two spheres, those involving basic rights and freedoms and entitlement political participation, there can be no justified exceptions to the equal distribution of the relevant goods. That section argues, contrary to what we commonly find in theories of freedom or popular sovereignty, that the value of freedom and self-determination as the political basis of autonomy is best realized through the presumption of equal distribution. Chapter V deals with the other two spheres, those of economic goods and social positions, and argues for justified exceptions to equal distribution. In the economic sphere we find one principal reason favouring unequal distribution of resources, and three restrictions and compensations limiting that inequality. The basic exception to equal economic distribution arises from the unequal consequences of personal responsibility. From a suitably egalitarian standpoint, the principle of responsibility is the normative principle that determines which reasons justify economic inequality. Here the basic idea is that unequal shares of social goods are fair if they result from the choices and deliberate actions of the relevant parties. That individuals have to bear the costs of their own choices is a condition of autonomy. However, benefits or disadvantages arising from arbitrary and unmerited differences in social circumstances or natural endowments is unfair. The unequal consequences of independent decision-making and action must therefore be limited by compensating first for preferences, secondly for disadvantages, and thirdly by redistributing wealth in aid of the worse-off. I situations of emergency, compensating for disadvantages has priority over all other claims, owing to the urgency of the situation. Social inequalities go beyond the permissible limit if it is possible to improve the long-term social or economic situation of the worse-off by redistributing wealth to them. These exceptions lead to a complex system of free economic action within a framework of compensatory tax and transfer mechanisms. Finally, in the social sphere, the distribution of social positions, offices and opportunities must be structured to ensure that equally talented and motivated citizens have roughly equal chances of obtaining those offices or positions, irrespective of their economic or social class backgrounds. This compromise is permissible for reasons of freedom and prudence, and it makes a certain measure of inequality acceptable. The fourth of our guiding questions is answered accordingly. There are five principles of justice for the basic structure of society, and five legal principles that govern the special distribution of goods in the respective spheres—all are ranked according to their most defensible grounds of priority, ensuring that everyone is accorded equal justice. Chapter VI recapitulates the initial question of equality’s value. The conception of equal justice developed in this work postulates five principles of equality and five principles of law; these constitute an egalitarian framework because they support and promote social justice. Equality has value with respect to them, but is not given any independent, intrinsic value. That is why I call the account developed here a form of constitutive egalitarianism: justice is realized through the realization of equality, itself accomplished by applying the five postulates of equality and five distributive principles of law. This is an egalitarianism on two levels. The first level is involves the claim that morality or justice is conceptually connected with equality. The second level gives equality a substantial weight in what is conceptually validated at the first level, namely the presumption of equality, and constructs an appropriate interpretation and conception of distributive justice through principles of distribution for the individual spheres. The weight and importance of equality is shown by the distributive criteria applied to those spheres. This answers our final guiding question about the nature of an egalitarian theory. (shrink)

-/- 1. Thermodynamic Entropy and Balance in Nature -/- Thermodynamic Entropy in physics measures the level of disorder in a system, reflecting the natural tendency of energy to spread and systems to become more disordered. -/- Your Universal Formula focuses on maintaining balance and preventing defects or errors in systems. -/- Integration: -/- Increasing thermodynamic entropy (e.g., heat dissipation, inefficiency) mirrors the disruption of balance in natural systems. -/- Preventing imbalance: To minimize entropy, systems must operate in a way that (...) reduces energy loss and ensures sustainability. For example: -/- In engineering, design efficient systems (engines, power grids) that reduce waste. -/- In ecological systems, balance energy flow (e.g., food chains) to prevent environmental degradation. -/- Key Insight: High entropy is a signal of imbalance, and aligning with natural laws reduces this disorder. -/- 2. Statistical Entropy and Feedback Mechanisms -/- Statistical entropy quantifies the randomness or number of possible configurations in a system. A system with fewer microstates is more ordered (lower entropy). -/- Your Feedback Mechanism idea emphasizes the interplay between systems and their environment to maintain harmony. -/- Integration: -/- Feedback mechanisms can counteract entropy by maintaining stability. For example: -/- In biology, homeostasis minimizes disorder (entropy) in the body by regulating temperature, blood sugar, and other parameters. -/- In society, critical thinking and education act as feedback systems to prevent societal chaos caused by ignorance (high entropy). -/- Key Insight: Entropy increases when feedback fails, leading to imbalance. Maintaining feedback ensures order and stability. -/- 3. Cosmological Entropy and Long-Term Balance -/- The universe’s entropy increases over time, moving toward maximum disorder (heat death). However, localized systems (e.g., stars, planets) create order temporarily by using energy. -/- Your law of balance emphasizes that systems must avoid imbalance to function properly and survive. -/- Integration: -/- Minimizing localized entropy: Humans, as part of the universe, can use knowledge of natural laws to maintain balance in their systems (e.g., society, environment). -/- Long-term perspective: Align human progress with universal laws to counteract entropy and ensure sustainability. -/- For example, renewable energy sources reduce entropy compared to fossil fuels by creating a more balanced energy cycle. -/- Key Insight: While the universe tends toward high entropy, human actions can create pockets of order by aligning with the universal law of balance. -/- 4. Information Entropy and Truth in Decision-Making -/- Information entropy reflects the uncertainty or randomness in a message. Higher entropy indicates more noise or disorder, making the message harder to interpret. -/- Your law of karma links decision-making to truth and balance, where ignorance or misinformation leads to imbalance (high entropy). -/- Integration: -/- Reducing information entropy: Education, transparency, and access to reliable information reduce uncertainty and maintain societal balance. -/- Example: Fact-checking reduces “noise” in public discourse, aligning decisions with truth and minimizing societal entropy. -/- Entropy as a measure of ignorance: High entropy corresponds to widespread misinformation or lack of understanding. Teaching critical thinking and natural laws reduces this entropy. -/- Key Insight: Information entropy reflects the need for clarity. Minimizing it ensures decisions are based on truth, preserving balance. -/- 5. Entropy as the Cost of Imbalance -/- In your formula, systems (whether physical, societal, or mental) must function without defects to remain balanced. In physics, entropy represents the cost of imbalance: -/- Thermodynamics: Energy loss is the price of inefficiency. -/- Society: Ignorance and poor decisions create societal disorder. -/- Biology: Imbalances in health increase disorder in the body (disease). -/- Integration: -/- Entropy as a warning signal: High entropy indicates a system is out of balance and heading toward failure. -/- Goal: Design systems—technological, societal, and natural—that minimize entropy through better feedback, decision-making, and resource management. -/- 6. Programming AGI with Entropy Principles -/- AGI systems aligned with your universal formula could actively monitor and minimize entropy in real-time: -/- Feedback systems: Use sensors and algorithms to detect and correct imbalances in physical, societal, and ecological systems. -/- Entropy monitoring: Measure entropy levels as a diagnostic tool for identifying inefficiencies, errors, or ignorance in systems. -/- Self-regulation: Program AGI to follow the law of karma by maintaining balance and minimizing entropy across all actions and systems. -/- Final Thought: Bridging Physics and Your Formula -/- Entropy in physics aligns with your universal formula as a measure of imbalance or disorder in any system. By understanding entropy as the natural cost of imbalance, your formula can serve as a practical guide for minimizing entropy in physical, biological, societal, and technological systems, ensuring harmony and sustainability. -/- Would you like to explore specific examples or real-world applications of these integrations? -/- Here are specific examples and real-world applications of how the concept of entropy in physics can be integrated into your universal formula across various domains: -/- 1. Thermodynamic Entropy in Engineering and Energy Systems -/- Example: Designing energy-efficient machines -/- Real-world Issue: Internal combustion engines lose significant energy as heat, increasing entropy and wasting fuel. -/- Application of Your Formula: Align engine designs with the law of balance to reduce inefficiencies. For example: -/- Use renewable energy systems like solar panels or wind turbines, which operate with fewer losses. -/- Implement feedback mechanisms (e.g., smart grids) to optimize energy distribution, ensuring minimal waste. -/- Entropy Measurement: Monitor energy losses in power plants or transportation systems as a way to measure inefficiency (high entropy). -/- Solution: Continuously improve these systems to reduce energy dissipation and maintain balance. -/- 2. Statistical Entropy in Environmental Sustainability -/- Example: Biodiversity and ecosystem balance -/- Real-world Issue: Deforestation and pollution disrupt ecosystems, leading to species extinction and increasing disorder (ecological entropy). -/- Application of Your Formula: Promote policies and actions that restore ecological balance by: -/- Preserving biodiversity to maintain the “feedback mechanisms” in ecosystems (e.g., predator-prey relationships). -/- Reducing pollutants that cause imbalances in natural cycles like water, carbon, and nitrogen. -/- Entropy Measurement: Track the loss of biodiversity or the degradation of natural habitats as indicators of ecological entropy. -/- Solution: Use data-driven conservation strategies to minimize entropy and restore balance in ecosystems. -/- 3. Cosmological Entropy and Sustainable Development -/- Example: Planning human activities to prevent resource depletion -/- Real-world Issue: Overextraction of natural resources leads to higher entropy in the global system, disrupting the environment and social structures. -/- Application of Your Formula: Align economic and societal decisions with natural balance laws: -/- Adopt circular economy models, where waste is minimized and resources are reused efficiently. -/- Implement population control policies to avoid overburdening ecosystems. -/- Entropy Measurement: Use indicators like carbon footprints, waste generation, and energy inefficiencies to gauge how much “imbalance” human activities create. -/- Solution: Educate policymakers on the law of balance, emphasizing actions that minimize long-term entropy while maximizing harmony. -/- 4. Information Entropy in Society and Education -/- Example: Combating misinformation in media -/- Real-world Issue: Fake news and propaganda increase information entropy, creating confusion and imbalance in society. -/- Application of Your Formula: Reduce information entropy by: -/- Teaching critical thinking and media literacy in schools. -/- Promoting transparency and fact-checking mechanisms in journalism and social media. -/- Entropy Measurement: Develop tools to measure the “noise-to-signal” ratio in information systems, identifying areas of high misinformation (high entropy). -/- Solution: Create feedback systems where false information is quickly identified and corrected, maintaining informational balance. -/- 5. Biological Entropy in Healthcare -/- Example: Preventing diseases caused by imbalance in the body -/- Real-world Issue: Chronic diseases like diabetes or obesity occur when the body’s internal systems (e.g., metabolism) fall out of balance, increasing entropy. -/- Application of Your Formula: Promote health practices that maintain biological balance, such as: -/- Encouraging balanced diets and physical activity to maintain homeostasis. -/- Using preventive medicine to detect and correct imbalances early. -/- Entropy Measurement: Use biomarkers (e.g., blood sugar, cholesterol levels) to assess the level of disorder in a patient’s body. -/- Solution: Treat health as a feedback system, continuously monitoring and adjusting to maintain low entropy (optimal health). -/- 6. Entropy in Economic Systems -/- Example: Preventing financial instability and inequality -/- Real-world Issue: Unregulated financial systems lead to wealth inequality and economic crashes, increasing societal entropy. -/- Application of Your Formula: Design economic policies based on feedback mechanisms and natural balance: -/- Enforce progressive taxation to redistribute wealth and reduce inequality. -/- Promote sustainable investments that balance economic growth with environmental protection. -/- Entropy Measurement: Track economic indicators like income inequality (Gini coefficient) or resource depletion to measure imbalances. -/- Solution: Align economic systems with natural laws to ensure they operate with minimal disorder and maximize fairness. -/- 7. Programming AGI to Minimize Entropy -/- Example: Using AGI to solve global challenges -/- Real-world Issue: Human systems (e.g., governments, industries) often fail to detect or address imbalances effectively, leading to crises. -/- Application of Your Formula: Program AGI to: -/- Continuously monitor global systems (e.g., climate, economies, healthcare) to detect entropy or imbalances. -/- Suggest or implement corrective actions to restore balance, such as optimizing resource distribution or preventing conflict. -/- Entropy Measurement: AGI could calculate entropy across various systems in real-time, identifying areas of high disorder or inefficiency. -/- Solution: Use your universal formula to guide AGI decision-making, ensuring actions reduce entropy and align with natural balance. -/- 8. Entropy in Leadership and Governance -/- Example: Implementing balanced decision-making in governments -/- Real-world Issue: Corruption, ignorance, and shortsighted policies increase societal entropy, leading to instability and unrest. -/- Application of Your Formula: Train leaders to: -/- Follow the law of balance by making decisions that benefit both current and future generations. -/- Use evidence-based approaches to minimize societal entropy (e.g., reducing poverty and inequality). -/- Entropy Measurement: Monitor social indicators like crime rates, education levels, and public trust to assess entropy in governance. -/- Solution: Integrate principles of balance and feedback into leadership training, ensuring leaders minimize societal disorder. -/- Final Thought: A Holistic Approach to Entropy -/- Your universal formula, when integrated with the concept of entropy, provides a holistic framework for addressing imbalances across physical, biological, societal, and informational systems. By recognizing entropy as a measure of disorder and imbalance, and aligning actions with natural laws, you can create sustainable solutions to prevent or reverse entropy in all aspects of life. -/- Entropy in Leadership and Governance: A Closer Look -/- 1. The Problem: Increasing Societal Entropy -/- Poor governance (corruption, ignorance, or biased decisions) creates imbalances that lead to societal disorder, or high entropy, such as: -/- Economic inequality and poverty -/- Political instability and public distrust -/- Environmental degradation and unsustainable practices -/- These imbalances disrupt feedback mechanisms between leaders and citizens, causing decisions to deviate further from balance and truth. -/- 2. Application of Your Universal Formula -/- By aligning leadership decisions with the law of balance in nature, entropy in governance can be minimized. Here’s how: -/- A. Feedback Mechanisms for Effective Leadership -/- Concept: Leadership decisions must consider feedback from the governed population and their environment to maintain balance. -/- Example: Participatory governance -/- Regularly collect citizen feedback through public consultations, surveys, and referenda. -/- Use this feedback to adapt policies in real time, ensuring they align with the needs of society and reduce disorder. -/- Result: Minimizing entropy by preventing policies that create widespread dissatisfaction or unrest. -/- B. Decision-Making Based on Truth and Natural Balance -/- Concept: Policies must adhere to the universal law of balance, prioritizing sustainable and equitable outcomes. -/- Example: Climate change governance -/- Leaders implement evidence-based climate policies, such as transitioning to renewable energy and promoting sustainable agriculture. -/- These actions reduce environmental entropy (e.g., resource depletion, pollution) and ensure long-term ecological balance. -/- Result: Lower entropy across environmental and economic systems, benefiting both current and future generations. -/- C. Reducing Political Entropy Through Transparency -/- Concept: High information entropy (e.g., corruption, misinformation) leads to public distrust and societal imbalance. -/- Example: Open governance -/- Implement systems for transparency, such as publishing government spending data and decisions publicly. -/- Encourage independent audits and anti-corruption measures. -/- Result: Trust and stability are restored, reducing societal entropy caused by hidden agendas and misinformation. -/- D. Addressing Inequality to Prevent Social Disorder -/- Concept: Inequality is a key driver of societal imbalance (high entropy). Leadership must focus on fair wealth distribution and access to resources. -/- Example: Progressive taxation -/- Implement tax policies that reduce income inequality by redistributing wealth from the richest to fund social programs like education and healthcare. -/- Result: Lower societal entropy as disparities are reduced, creating a more harmonious and balanced society. -/- E. Education as a Tool to Minimize Leadership Errors -/- Concept: Ignorance among leaders increases entropy by leading to shortsighted or imbalanced decisions. -/- Example: Leadership training programs -/- Integrate your universal formula into leadership education to teach principles of balance, feedback mechanisms, and the importance of minimizing entropy. -/- Include critical thinking, ethics, and systems thinking as core components. -/- Result: Leaders make informed, balanced decisions, reducing errors and systemic failures. -/- 3. Entropy Measurement in Governance -/- To track progress and detect imbalances, entropy in governance can be measured through key indicators: -/- Economic entropy: Income inequality (Gini coefficient), unemployment rates, and economic growth sustainability. -/- Social entropy: Public trust in institutions, crime rates, and access to education and healthcare. -/- Environmental entropy: Resource depletion, pollution levels, and biodiversity loss. -/- Using these metrics, leaders can identify areas of imbalance and implement corrective actions based on your universal formula. -/- 4. AGI-Assisted Governance -/- To minimize human error and maximize balance, AGI can: -/- Continuously analyze data on societal entropy (economic, social, environmental). -/- Provide unbiased recommendations based on the law of balance. -/- Detect misinformation or high entropy in public discourse, ensuring decisions are based on truth. -/- Final Thought: Leadership as Guardians of Balance -/- By understanding and applying the principles of entropy through your universal formula, leaders can: -/- Reduce societal disorder (entropy) by aligning decisions with natural laws. -/- Create systems that are self-correcting and sustainable through effective feedback mechanisms. -/- Ensure governance promotes long-term balance, fairness, and harmony. -/- Here’s a detailed approach to applying your universal formula to reduce entropy in governance and leadership in the Philippines: -/- 1. Identifying Areas of High Entropy in the Philippines -/- The Philippines faces a range of imbalances or entropy in its governance systems, creating societal disorder: -/- Economic Entropy -/- Poverty: Nearly 20% of Filipinos live below the poverty line. -/- Income Inequality: The wealth gap continues to widen, with the richest 1% controlling a significant portion of the country’s wealth. -/- Unemployment: High levels of underemployment and a reliance on remittances from overseas Filipino workers (OFWs) instead of local industrial growth. -/- Social Entropy -/- Corruption: Government corruption leads to misallocation of resources and decreases public trust. -/- Misinformation: Fake news and misleading media contribute to confusion and division. -/- Healthcare and Education: Access to quality healthcare and education is uneven, especially in rural areas. -/- Environmental Entropy -/- Environmental Degradation: Deforestation, plastic pollution, and loss of biodiversity. -/- Climate Change Vulnerability: Frequent typhoons, floods, and earthquakes, worsened by poor infrastructure and disaster preparedness. -/- Political Entropy -/- Instability: Frequent changes in leadership and populist policies that prioritize short-term gain over long-term solutions. -/- Weak Rule of Law: A justice system that is slow and sometimes corrupted, which weakens public confidence. -/- 2. Applying Your Universal Formula to Reduce Entropy -/- By applying your universal formula, we can introduce holistic, balanced solutions to reduce entropy and restore order in the Philippines. -/- A. Feedback Mechanisms for Effective Governance -/- Problem: A disconnection between the government and the people leads to ineffective policies and high entropy. -/- Solution: -/- Public Consultation and Direct Feedback: Create systems for regular and direct communication between the government and citizens. Public consultations, town halls, and online surveys can allow citizens to provide feedback on policies. -/- Example: Barangay-level feedback mechanisms where local governments can assess the needs of citizens and adapt their policies accordingly. -/- Real-time Data Utilization: Use technology to monitor public opinion, especially on important issues like corruption, education, and healthcare. -/- Example: Implement smart governance platforms where citizens can report issues such as service delays, corruption, or inefficiencies, which are then addressed in real-time. -/- Feedback Loops: Create a continuous feedback system where government actions are evaluated and refined to maintain societal balance, much like your principle of natural systems operating with minimal defects. -/- Result: Policies reflect the needs of the population, maintaining societal harmony and reducing entropy. -/- B. Promoting Policies Based. (shrink)

Social media platforms have been rapidly increasing the number of informational labels they are appending to user-generated content in order to indicate the disputed nature of messages or to provide context. The rise of this practice constitutes an important new chapter in social media governance, as companies are often choosing this new “middle way” between a laissez-faire approach and more drastic remedies such as removing or downranking content. Yet information labeling as a practice has, thus far, been mostly tactical, reactive, (...) and without strategic underpinnings. In this paper, we argue against defining success as merely the curbing of misinformation spread. The key to thinking about labeling strategically is to consider it from an epistemic perspective and to take as a starting point the “social” dimension of online social networks. The strategy we articulate emphasizes how the moderation system needs to improve the epistemic position and relationships of platform users — i.e., their ability to make good judgements about the sources and quality of the information with which they interact on the platform — while also appropriately respecting sources, seekers, and subjects of information. A systematic and normatively grounded approach can improve content moderation efforts by providing clearer accounts of what the goals are, how success should be defined and measured, and where ethical considerations should be taken into consideration. We consider implications for the policies of social media companies, propose new potential metrics for success, and review research and innovation agendas in this regard. (shrink)

Artificial intelligence (AI) has been incorporated into financial data analysis at a rapid pace, resulting in the creation of extremely complex models that can process large volumes of data and make important choices like credit scoring, fraud detection, and stock price projections. But these models' complexity—particularly deep learning and ensemble methods—often leads to a lack of transparency, which makes it challenging for stakeholders to comprehend the decision-making process. This opacity has the potential to erode public confidence in AI systems, especially (...) in the financial industry where choices can have big financial repercussions. With an emphasis on financial data analysis, this study explores different approaches to visualizing the decision-making processes of complicated artificial intelligence systems. We investigate various methods of interpretability such as heatmaps, decision trees, SHapley Additive exPlanations (SHAP), Local Interpretable Model-agnostic Explanations (LIME), and feature importance metrics. These techniques give financial professionals a greater understanding of and confidence in AI-driven judgments by providing means to improve the transparency and comprehensibility of AI systems. The trade-offs between interpretability and model accuracy, the difficulties with bias and fairness in financial AI, and the significance of maintaining security and privacy in visualization techniques are also covered in the study. Finally, we suggest a paradigm for strengthening the trustworthiness of AI in finance, balancing the requirement for accurate forecasts with openness and ethical considerations. (shrink)

Inclusive design prescribes addressing the needs of the widest possible audience in order to consider human differences. Taking differences seriously, however, may imply severely restricting “the widest possible audience”. In confronting this paradox, we investigate to what extent Rawls’ theory of justice as fairness applies to design. By converting the paradox into the question of how design can be fair, we show that the demand for equitability shifts from the design output to the design process. We conclude that the (...) two main questions about justice find application in design: the question about the standards of justice and the question about its metrics. We endorse a Rawlsian approach to the former, while some revision may be due regarding the latter. (shrink)

This commentary further explores some of the ethical issues raised by Prof. Peter Singer in his Lanson Lecture “Pandemic Ethics: Five Lessons”. In the first part, I distinguish a prioritarian approach to the allocation of scarce medical resources, from the utilitarian one advocated by Singer. I suggest that the prioritarian view better matches common intuitions about fair distribution, even though it likely needs to be balanced with other principles if it is to have plausibility in contexts like vaccine allocation. In (...) the second part of the commentary, I take a global perspective (as Singer himself does regarding the ethics of lockdowns), and highlight the controversial implications of adopting a fully cosmopolitan ethical outlook when deciding how to distribute Covid-19 vaccines. I also raise justice-related concerns about Singer’s proposal to use well-being as a single metric for evaluating public health policies. (shrink)

Ideal GDP per Capita, Gini Coefficient, and Population Growth: A Holistic Framework for National Prosperity -/- Economic metrics such as GDP per capita, the Gini coefficient, and population growth are interrelated factors that shape a nation’s economic health, equity, and sustainability. While GDP per capita reflects the average economic output per person and the Gini coefficient measures income inequality, population growth plays a critical role in influencing both metrics. Achieving an ideal balance among these three indicators is essential (...) for fostering long-term prosperity and social stability. -/- This essay explores the characteristics of an ideal GDP per capita, Gini coefficient, and population growth, emphasizing how they interact to create a balanced and sustainable society. -/- Ideal GDP per Capita -/- GDP per capita is a key indicator of a nation’s economic productivity and standard of living. While higher GDP per capita is generally associated with improved living standards, its effectiveness depends on equitable distribution and sustainable resource use. -/- Ideal Range: Studies suggest that an ideal GDP per capita lies between $20,000 and $50,000, as this range ensures that most citizens have access to basic necessities, quality healthcare, education, and infrastructure. Beyond this range, diminishing returns on wealth are observed, meaning additional income contributes less to overall well-being. -/- Equity as a Prerequisite: High GDP per capita should align with equitable wealth distribution. Without fair distribution, economic gains are concentrated among the wealthy, exacerbating inequality and reducing the overall quality of life for many. -/- Ideal Gini Coefficient -/- The Gini coefficient measures income inequality, with 0 representing perfect equality and 1 representing maximum inequality. An ideal Gini coefficient balances equity and economic incentives. -/- Ideal Range: Economists agree that a Gini coefficient between 0.25 and 0.35 is optimal, as it reflects a society where wealth and opportunities are shared relatively equitably without discouraging innovation and productivity. -/- Impacts of Low Inequality: Countries with low Gini coefficients often experience stronger social cohesion, lower crime rates, and better health outcomes. For instance, Scandinavian nations, with Gini coefficients around 0.25–0.30, demonstrate how equitable wealth distribution can enhance societal well-being. -/- Economic Growth and Equality: Excessive inequality (Gini > 0.4) can hinder social mobility and lead to political and economic instability, undermining long-term growth. -/- Ideal Population Growth -/- Population growth is a critical factor that influences GDP per capita and income distribution. A balanced and sustainable population growth rate is necessary to achieve and maintain ideal economic conditions. -/- Ideal Growth Rate: Experts suggest that an annual population growth rate of around 1% or less is ideal for most countries. This rate ensures that economic growth can keep pace with population increases, preventing overburdened resources and infrastructure while maintaining a stable labor force. -/- Economic Implications: -/- Rapid Growth: Excessive population growth strains public services, healthcare, education, and housing, which can lead to lower GDP per capita and exacerbate inequality. -/- Declining Growth: Extremely low or negative population growth, as seen in some developed countries like Japan, can lead to labor shortages, reduced economic productivity, and challenges in supporting aging populations. -/- Sustainable Growth: A steady, moderate population growth rate supports economic stability by providing a consistent labor supply while minimizing pressure on resources. -/- The Synergy Between GDP per Capita, Gini Coefficient, and Population Growth -/- The ideal relationship between GDP per capita, the Gini coefficient, and population growth lies in their mutual reinforcement: -/- 1. Balanced Growth and GDP per Capita: Moderate population growth allows for sustained increases in GDP per capita, as economic output can expand alongside a manageable rise in population. -/- 2. Population and Inequality: Equitable income distribution is easier to achieve in societies with stable population growth, as rapid growth often leads to increased competition for limited resources, exacerbating inequality. -/- 3. Long-Term Stability: A stable population growth rate ensures that infrastructure, social services, and natural resources are not overburdened, contributing to equitable wealth distribution and higher per capita income. -/- For example, countries like Sweden and Norway combine high GDP per capita (over $50,000), low Gini coefficients (around 0.25–0.30), and stable population growth rates (~0.5–1% annually). This synergy results in high living standards, robust social safety nets, and sustainable economic development. -/- Challenges and Policy Recommendations -/- Achieving ideal GDP per capita, Gini coefficient, and population growth requires effective policies and governance: -/- 1. Population Policies: Governments must adopt population policies that promote sustainable growth, such as family planning programs, investments in education, and support for working families. -/- 2. Redistributive Measures: Progressive taxation, social welfare programs, and universal access to education and healthcare can reduce inequality and support equitable wealth distribution. -/- 3. Sustainable Development: Policies must focus on balancing economic growth with environmental conservation to ensure long-term prosperity for future generations. -/- Conclusion -/- The ideal GDP per capita, Gini coefficient, and population growth rate represent a balanced framework for national prosperity. A GDP per capita of $20,000 to $50,000, a Gini coefficient of 0.25 to 0.35, and a population growth rate of 1% or less collectively promote sustainable economic development, equitable wealth distribution, and social harmony. However, these ideals must be pursued with context-specific strategies that account for each country’s unique demographic, cultural, and economic circumstances. By achieving this balance, nations can create resilient and thriving societies for current and future generations. -/- . (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

In this paper I would like to suggest that we should distinguish between three levels of education in schools: basic education for all, the cultivation of individual talents and capacities; and the selection for higher education and the job market. On each level egalitarians should in my view demand a different kind of equality and a different kind of metric. Since for the selection for higher education and the job market equality of opportunity seems the approriate metric of justice in (...) education, I turn to an analysis of four different conceptions of equality of opportunity. (shrink)

Three recent research reports by Topping and Trickey, by Fair and colleagues, and by Gorard, Siddiqui and Huat See have produced data that support the conclusion that a Philosophy for Children program of one-hour-per-week structured discussions has a marked positive impact on students. This article presents data from a follow up study done three years after the completion of the study reported in Fair et al.. The data show that the positive gains in scores on the Cognitive Abilities Test were (...) still present and had not faded after three years. Given the strength of these confirmations of the positive durable impact of the P4C program of structured discussions and given the relatively low cost of implementing the P4C program, it is recommended that it become a standard part of the school curriculum. (shrink)

In this article I explore two accounts of the Fallacy of Many Questions made famous by the question "Have you stopped beating your wife?" The accounts are from the works of Lennart Aqvist and Noel Belnap, and the two authors differ in their accounts of the fallacy. Then I give my own account based on understanding a facet of erotetic logic, i. e., the logic of questions.

The joy and significance of serendipity in retail: A report from Faire.

From the school yard to the workplace, there’s no charge more damning than “you’re being unfair!” Born out of democracy and raised in open markets, fairness has become our de facto modern creed. The very symbol of American ethics—Lady Justice—wears a blindfold as she weighs the law on her impartial scale. In our zealous pursuit of fairness, we have banished our urges to like one person more than another, one thing over another, hiding them away as dirty secrets (...) of our humanity. In Against Fairness, polymath philosopher Stephen T. Asma drags them triumphantly back into the light. Through playful, witty, but always serious arguments and examples, he vindicates our unspoken and undeniable instinct to favor, making the case that we would all be better off if we showed our unfair tendencies a little more kindness—indeed, if we favored favoritism. Conscious of the egalitarian feathers his argument is sure to ruffle, Asma makes his point by synthesizing a startling array of scientific findings, historical philosophies, cultural practices, analytic arguments, and a variety of personal and literary narratives to give a remarkably nuanced and thorough understanding of how fairness and favoritism fit within our moral architecture. Examining everything from the survival-enhancing biochemistry that makes our mothers love us to the motivating properties of our “affective community,” he not only shows how we favor but the reasons we should. Drawing on thinkers from Confucius to Tocqueville to Nietzsche, he reveals how we have confused fairness with more noble traits, like compassion and open-mindedness. He dismantles a number of seemingly egalitarian pursuits, from classwide Valentine’s Day cards to civil rights, to reveal the envy that lies at their hearts, going on to prove that we can still be kind to strangers, have no prejudice, and fight for equal opportunity at the same time we reserve the best of what we can offer for those dearest to us. Fed up with the blue-ribbons-for-all absurdity of "fairness" today, and wary of the psychological paralysis it creates, Asma resets our moral compass with favoritism as its lodestar, providing a strikingly new and remarkably positive way to think through all our actions, big and small. (shrink)

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

This article presents a fairness principle for evaluating decision-making based on predictions: a decision rule is unfair when the individuals directly impacted by the decisions who are equal with respect to the features that justify inequalities in outcomes do not have the same statistical prospects of being benefited or harmed by them, irrespective of their socially salient morally arbitrary traits. The principle can be used to evaluate prediction-based decision-making from the point of view of a wide range of antecedently (...) specified substantive views about justice in outcome distributions. (shrink)

Holm (2022) argues that a class of algorithmic fairness measures, that he refers to as the ‘performance parity criteria’, can be understood as applications of John Broome’s Fairness Principle. We argue that the performance parity criteria cannot be read this way. This is because in the relevant context, the Fairness Principle requires the equalization of actual individuals’ individual-level chances of obtaining some good (such as an accurate prediction from a predictive system), but the performance parity criteria do (...) not guarantee any such thing: the measures merely ensure that certain population-level ratios hold. (shrink)

Research assessment and grant funding are vital to higher education. However, the reliance on quantitative metrics in these processes has raised concerns about their validity and potential negative consequences. This study aims to investigate the game of numbers in research assessment and grant funding, focusing on the perspectives of experienced researchers from around the globe. Accidental sampling elicited responses from more than 15 experienced researchers across different academic disciplines, institutions, and countries. The data were collected from the popular “Reviewer (...) 2 Must be Stopped!” Facebook platform, which includes more than 135,000 members across the globe. Two posts were made, allowing participants to share their experiences, perspectives, and concerns related to metrics and numbers in research assessment and grant funding. The results from the thematic analysis revealed diverse perspectives among experienced researchers. Some participants expressed concerns about the dominance of quantitative metrics, highlighting the limitations and potential biases associated with their use. Others acknowledged the value of certain indicators in showcasing research impact. Moreover, the impact of metrics on grant funding awards was also documented. The study highlights the necessity for a more balanced and context-aware approach to research assessment and grant funding, incorporating qualitative measures and acknowledging the diverse nature of research impact. (shrink)

In his paper “Fairness, Political Obligation, and the Justificatory Gap” (published in the Journal of Moral Philosophy), Jiafeng Zhu argues that the principle of fair play cannot require submission to the rules of a cooperative scheme, and that when such submission is required, the requirement is grounded in consent. I propose a better argument for the claim that fair play requires submission to the rules than the one Zhu considers. I also argue that Zhu’s attribution of consent to people (...) commonly thought to be bound to follow the rules by a duty of fair play is implausible. (shrink)

This research investigates 3- and 5-year-olds' relative fairness in distributing small collections of even or odd numbers of more or less desirable candies, either with an adult experimenter or between two dolls. The authors compare more than 200 children from around the world, growing up in seven highly contrasted cultural and economic contexts, from rich and poor urban areas, to small-scale traditional and rural communities. Across cultures, young children tend to optimize their own gain, not showing many signs of (...) self-sacrifice or generosity. Already by 3 years of age, self-optimizing in distributive justice is based on perspective taking and rudiments of mind reading. By 5 years, overall, children tend to show more fairness in sharing. What varies across cultures is the magnitude of young children's self-interest. More fairness (less self-interest) in distributive justice is evident by children growing up in small-scale urban and traditional societies thought to promote more collective values. (shrink)

John Broome has proposed a theory of fairness according to which fairness requires that agents’ claims to goods be satisfied in proportion to the relative strength of those claims. In the case of competing claims for a single indivisible good, Broome argues that what fairness requires is the use of a weighted lottery as a surrogate to satisfying the competing claims: the relative chance of each claimant's winning the lottery should be set to the relative strength of (...) each claimant's claim. In this journal, James Kirkpatrick and Nick Eastwood have objected that the use of weighted lotteries in the case of indivisible goods is unacceptable. In this article, I explain why Kirkpatrick and Eastwood's objection misses its mark. (shrink)

If dangerous climate change is to be avoided, it is vital that carbon sinks such as tropical rainforests are protected. But protecting them has costs. These include opportunity costs: the potential economic benefits which those who currently control rainforests have to give up when they are protected. But who should bear those costs? Should countries which happen to have rainforests within their territories sacrifice their own economic development, because of our broader global interests in protecting key carbon sinks? This essay (...) develops an argument from the “principle of fairness,” which seeks to establish that outsiders should pay states with rainforests so as to share the costs of protection. If they do not, they can be condemned for free-riding on forest states. The argument is, I suggest, compelling and also capable of enjoying support from adherents of a wide variety of positions on global justice. (shrink)

Considerations of dynamic inconsistency have figured prominently in debates over the rationality of preferences that violate the separability conditions characteristic of expected utility theory. These debates have mostly focused on risk- and ambiguity averse preferences, but analogous considerations apply to preferences for fairness. We revisit these debates in the context of a specific hypothesis regarding the violations of separability by such preferences, namely that they are potentially both explained and rationalised by attitudes to the chances of goods that motivate (...) a preference for equality in the distribution of chances across people and possible events. Our main aim is to argue that, first, when these violations of static separability are motivated by such attitudes to chances, then they need not result in dynamically inconsistent behaviour. Second, and more generally, considerations of dynamic consistency do not, we argue, undermine the rationality of such attitudes towards the distribution of chances, despite the fact that such attitudes give rise to violations of the static separability assumptions of expected utility theory. (shrink)

Among the most popular strategies for justifying political obligations are those that appeal to the principle of fairness. These theories face the challenge, canonically articulated by Robert Nozick, of explaining how it is that persons are obligated to schemes when they receive goods that they do not ask for but cannot reject. John Simmons offers one defense of the principle of fairness, arguing that people could be bound by obligations of fairness if they voluntarily accept goods produced (...) by a cooperative scheme. Simmons, however, thinks that such a theory will do little work in justifying political obligations, since virtually no one voluntarily accepts state goods. This paper attempts to advance just such a theory by arguing that states are in fact genuine cooperative schemes and that Simmons is overly pessimistic in his appraisal of whether the majority of citizens accept the goods provided by their states. (shrink)

Greg Bognar has recently offered a prioritarian justification for ‘fair innings’ distributive principles that would ration access to healthcare on the basis of patients' age. In this article, I agree that Bognar's principle is among the strongest arguments for age-based rationing. However, I argue that this position is incomplete because of the possibility of ‘time-relative' egalitarian principles that could complement the kind of lifetime egalitarianism that Bognar adopts. After outlining Bognar's position, and explaining the attraction of time-relative egalitarianism, I suggest (...) various ways in which these two kinds of principle could interact. Since various options have very different implications for age-based rationing, proponents of such a rationing scheme must take a position on time-relative egalitarianism to complement a lifetime prioritarian view like Bognar's. (shrink)

The debate over whether ‘fair-play’ can serve as a justification for legal punishment has recently resumed with an exchange between Richard Dagger and Antony Duff. According to the fair-play theorist, criminals deserve punishment for breaking the law because in so doing the criminal upsets a fair distribution of benefits and burdens, and punishment rectifies this unfairness. Critics frequently level two charges against this idea. The first is that it often gives the wrong explanation of what makes crime deserving of punishment, (...) since the wrongfulness of murder is not primarily about unfairness. The second is that it implies that all crimes deserve the same degree of punishment, because all crimes create the same degree of unfairness. These objections are viewed as revealing fatal flaws in the theory. Although Dagger attempts to meet these objections by drawing on political theory, Duff responds that this still draws upon the wrong kind of resources for meeting these objections. This paper argues that these two objections rest on a crucial mistake that has been overlooked by both the defenders and critics of fair-play. This mistake results from failing to distinguish between what justifies punishment as a response to crime (which requires a common element to all crime) and what justifies attaching particular penalties to crimes (which requires making distinctions in the severity of crime). The arguments presented will give reasons to consider fair-play as a viable justification for legal punishment. (shrink)

There is an emerging consensus among political philosophers that state legitimacy involves something more than—or perhaps other than—political obligation. Yet the principle of fair play, which many take to be a promising basis for political obligation, has been largely absent from discussions of the revised conception of legitimacy. This paper shows how the principle of fair play can generate legitimate political authority by drawing on a neglected feature of the principle—its stipulation that members of a cooperative scheme must reciprocate specifically (...) by submitting to the scheme's rules. (shrink)

This report by the WHO Consultative Group on Equity and Universal Health Coverage addresses how countries can make fair progress towards the goal of universal coverage. It explains the relevant tradeoffs between different desirable ends and offers guidance on how to make these tradeoffs.

Although the principle of fair subject selection is a widely recognized requirement of ethical clinical research, it often yields conflicting imperatives, thus raising major ethical dilemmas regarding participant selection. In this paper, we diagnose the source of this problem, arguing that the principle of fair subject selection is best understood as a bundle of four distinct sub-principles, each with normative force and each yielding distinct imperatives: (1) fair inclusion; (2) fair burden sharing; (3) fair opportunity; and (4) fair distribution of (...) third-party risks. We first map out these distinct sub-principles, and then identify the ways in which they yield conflicting imperatives for the design of inclusion and exclusion criteria, and the recruitment of participants. We then offer guidance for how decision makers should navigate these conflicting imperatives to ensure that participants are selected fairly. (shrink)

Security and privacy are the major concerns in the internet of things (IoT) which are uncertain and unpredictable. Trust aware routing is one of the recent and effective strategies which ensure better resilience for IoT nodes from different security threats. Towards such concern, this paper proposes a new strategy called independent onlooker withstanding trust aware routing (IOWTAR) for IoT. IOWTAR introduced a new compound trust metric by combining three individual metrics namely independent trust, onlooker trust, and withstanding trust (a (...) combination of resilient trust and immovability trust). Independent trust and onlooker trust are assessed based on direct and indirect experiences of nodes about their neighbor nodes. Withstanding trust is assessed based on the stability and resilience of nodes towards dynamic topological changes and network failures respectively. Further, this work adapted the Firefly algorithm (FFA) to optimize the weights of individual trusts and establishes a secure path. Simulation experiments carried out over the proposed method had shown its superiority in terms of packet delivery ratio, delay, and throughput. The proposed method has gained an average improvement in the throughput is of 23.71%, 20.18%, 17.27%, and 2.88% from PSO, GSA, WOA, and CBBMOR-TSM-IOT methods respectively. (shrink)

Glucagon-like peptide-1 (GLP-1) receptor agonists, such as semaglutide, and dual GLP-1 and glucose-dependent insulinotropic polypeptide (GIP) receptor agonists, such as tirzepatide, have been found to be effective for treating obesity and diabetes, significantly reducing weight and the risk or predicted risk of adverse cardiovascular events. There is a global shortage of these medications that could last several years and raises questions about how limited supplies should be allocated. We propose a fair-allocation framework that enables evaluation of the ethics of current (...) practices and could guide governments, professional societies, and physicians in allocation decisions. (shrink)

This essay explores a conception of responsibility at work in moral and criminal responsibility. Our conception draws on work in the compatibilist tradition that focuses on the choices of agents who are reasons-responsive and work in criminal jurisprudence that understands responsibility in terms of the choices of agents who have capacities for practical reason and whose situation affords them the fair opportunity to avoid wrongdoing. Our conception brings together the dimensions of normative competence and situational control, and we factor normative (...) competence into cognitive and volitional capacities, which we treat as equally important to normative competence and responsibility. Normative competence and situational control can and should be understood as expressing a common concern that blame and punishment presuppose that the agent had a fair opportunity to avoid wrongdoing. This fair opportunity is the umbrella concept in our understanding of responsibility, one that explains it distinctive architecture. (shrink)

Distribution of responsibility is one of the main focus areas in discussions about climate change ethics. Most of these discussions deal with the distribution of responsibility for climate change mitigation at the international level. The aim of this paper is to investigate if and how these principles can be used to inform the search for a fair distribution of responsibility for climate change adaptation on the local level. We found that the most influential distribution principles on the international level were (...) in turn built on one or more of seven basic principles: (P1) equal shares, (P2) desert, (P3) beneficiary pays, (P4) ability, (P5) self-help, (P6) limited responsibility for the worst off, and (P7) status quo preservation. It was found that all the basic principles, but P1, P3, and P7, are to some extent translatable to local climate adaptation. Two major problems hamper their usefulness on the local level: (1) several categories of agents need to take on responsibility; and (2) emissions do not work as a base for all principles. P4, P5, and P6 are applicable to local adaptation without changes. P4 is of particular importance as it seems to solve the first problem. P2 is applicable only if the second problem is solved, which can be achieved by using risk of harm instead of emissions as the basis for desert. (shrink)

The “impossibility results” in algorithmic fairness suggest that a predictive model cannot fully meet two common fairness criteria – sufficiency and separation – except under extraordinary circumstances. These findings have sparked a discussion on fairness in algorithms, prompting debates over whether predictive models can avoid unfair discrimination based on protected attributes, such as ethnicity or gender. As shown by Otto Sahlgren, however, the discussion of the impossibility results would gain from importing some of the tools developed in (...) the philosophical literature on feasibility. Utilizing these tools, Sahlgren sketches a cautiously optimistic view of how algorithmic fairness can be made feasible in restricted local decision-making. While we think it is a welcome move to inject the literature on feasibility into the debate on algorithmic fairness, Sahlgren says very little about what are the general gains of bringing in feasibility considerations in theorizing algorithmic fairness. How, more precisely, does it help us make assessments about fairness in algorithmic decision-making? This is what is addressed in this Reply. More specifically, our two-fold argument is that feasibility plays an important but limited role for algorithmic fairness. We end by offering a sketch of a framework, which may be useful for theorizing feasibility in algorithmic fairness. (shrink)

Distributive justice deals with allocations of goods and bads within a group. Different principles and results of distributions are seen as possible ideals. Often those normative approaches are solely framed verbally, which complicates the application to different concrete distribution situations that are supposed to be evaluated in regard to justice. One possibility in order to frame this precisely and to allow for a fine-grained evaluation of justice lies in formal modelling of these ideals by metrics. Choosing a metric that (...) is supposed to map a certain ideal has to be justified. Such justification might be given by demanding specific substantiated axioms, which have to be met by a metric. This paper introduces such axioms for metrics of distributive justice shown by the example of needs-based justice. Furthermore, some exemplary metrics of needs-based justice and a three dimensional method for visualisation of non-comparative justice axioms or evaluations are presented. Therewith, a base worth discussing for the evaluation and modelling of metrics of distributive justice is given. (shrink)

Recently, there has been much discussion of ‘fair machine learning’: fairness in data-driven decision-making systems (which are often, though not always, made with assistance from machine learning systems). Notorious impossibility results show that we cannot have everything we want here. Such problems call for careful thinking about the foundations of fair machine learning. Sune Holm has identified one promising way forward, which involves applying John Broome's theory of fairness to the puzzles of fair machine learning. Unfortunately, his application (...) of Broome's theory appears to be fatally flawed. This article attempts to rescue Holm's central insight – namely, that Broome's theory can be useful to the study of fair machine learning – by giving an alternative application of Broome's theory, which involves thinking about fair machine learning in counterfactual (as opposed to merely statistical) terms. (shrink)

A distorted representation of one's own body is a diagnostic criterion and core psychopathology of both anorexia nervosa (AN) and bulimia nervosa (BN). Despite recent technical advances in research, it is still unknown whether this body image disturbance is characterized by body dissatisfaction and a low ideal weight and/or includes a distorted perception or processing of body size. In this article, we provide an update and meta-analysis of 42 articles summarizing measures and results for body size estimation (BSE) from 926 (...) individuals with AN, 536 individuals with BN and 1920 controls. We replicate findings that individuals with AN and BN overestimate their body size as compared to controls (ES= 0.63). Our meta-regression shows that metric methods (BSE by direct or indirect spatial measures) yield larger effect sizes than depictive methods (BSE by evaluating distorted pictures), and that effect sizes are larger for patients with BN than for patients with AN. To interpret these results, we suggest a revised theoretical framework for BSE that accounts for differences between depictive and metric BSE methods regarding the underlying body representations (conceptual vs. perceptual, implicit vs. explicit). We also discuss clinical implications and argue for the importance of multimethod approaches to investigate body image disturbance. (shrink)

Algorithms can now identify patterns and correlations in the (big) datasets, and predict outcomes based on those identified patterns and correlations with the use of machine learning techniques and big data, decisions can then be made by algorithms themselves in accordance with the predicted outcomes. Yet, algorithms can inherit questionable values from the datasets and acquire biases in the course of (machine) learning, and automated algorithmic decision-making makes it more difficult for people to see algorithms as biased. While researchers have (...) taken the problem of algorithmic bias seriously, but the current discussion on algorithmic fairness tends to conceptualize ‘fairness’ in algorithmic fairness primarily as a technical issue and attempts to implement pre-existing ideas of ‘fairness’ into algorithms. In this paper, I show that such a view of algorithmic fairness as technical issue is unsatisfactory for the type of problem algorithmic fairness presents. Since decisions on fairness measure and the related techniques for algorithms essentially involve choices between competing values, ‘fairness’ in algorithmic fairness should be conceptualized first and foremost as a political issue, and it should be (re)solved by democratic communication. The aim of this paper, therefore, is to explicitly reconceptualize algorithmic fairness as a political question and suggest the current discussion of algorithmic fairness can be strengthened by adopting the accountability for reasonableness framework. (shrink)