Fairness emerges as a vital concern to decision makers as crucial as efficiency, if not more important. Fair operations decisions are aimed at distributive justice in various scenarios. In this dissertation, we study two examples of distributively fair decision making in operations research, a dynamic fair allocation problem and a subpopulational robustness assessment problem for machine learning models. We first study a dynamic allocation problem in which 𝑇 sequentially arriving divisible resources are to be allocated to a number of agents with concave utilities. The joint utility functions of each resource to the agents are drawn stochastically from a known joint distribution, independently and identically across time, and the central planner makes immediate and irrevocable allocation decisions. Most works on dynamic resource allocation aim to maximize the utilitarian welfare, i.e., the efficiency of the allocation, which may result in unfair concentration of resources on certain high-utility agents while leaving others' demands under-fulfilled. In this work, aiming at balancing efficiency and fairness, we instead consider a broad collection of welfare metrics, the Hölder means, which includes the Nash social welfare and the egalitarian welfare. To this end, we first study a fluid-based policy derived from a deterministic surrogate to the underlying problem and show that for all smooth Hölder mean welfare metrics it attains an 𝑂 (1) regret over the time horizon length 𝑇 against the hindsight optimum, i.e., the optimal welfare if all utilities were known in advance of deciding on allocations. However, when evaluated under the non-smooth egalitarian welfare, the fluid-based policy attains a regret of order 𝛩 (√𝑇). We then propose a new policy built thereupon, called Backward Infrequent Re-solving (𝖡𝖨𝖱), which consists of re-solving the deterministic surrogate problem at most 𝑂 (log 𝑇) times. We show under a mild regularity condition that it attains a regret against the hindsight optimal egalitarian welfare of order 𝑂 (1) when all agents have linear utilities and 𝑂 (log 𝑇) otherwise. We further propose the Backward Infrequent Re-solving with Thresholding (𝖡𝖨𝖱𝖳) policy, which enhances the (𝖡𝖨𝖱𝖳) policy by thresholding adjustments and performs similarly without any assumption whatsoever. More specifically, we prove the (𝖡𝖨𝖱𝖳) policy attains an 𝑂 (1) regret independently of the horizon length 𝑇 when all agents have linear utilities and 𝑂 (log²⁺^𝜀) otherwise. We conclude by presenting numerical experiments to corroborate our theoretical claims and to illustrate the significant performance improvement against several benchmark policies. The performance of ML models degrades when the training population is different from that seen under operation. Towards assessing distributional robustness, we study the worst-case performance of a model over 𝒂𝒍𝒍 subpopulations of a given size, defined with respect to core attributes 𝑍. This notion of robustness can consider arbitrary (continuous) attributes 𝑍, and automatically accounts for complex intersectionality in disadvantaged groups. We develop a scalable yet principled two-stage estimation procedure that can evaluate the robustness of state-of-the-art models. We prove that our procedure enjoys several finite-sample convergence guarantees, including 𝒅𝒊𝒎𝒆𝒏𝒔𝒊𝒐𝒏-𝒇𝒓𝒆𝒆 convergence. Instead of overly conservative notions based on Rademacher complexities, our evaluation error depends on the dimension of 𝑍 only through the out-of-sample error in estimating the performance conditional on 𝑍. On real datasets, we demonstrate that our method certifies the robustness of a model and prevents deployment of unreliable models.

<p dir="ltr">Despite the recent advancement and exponential growth in the utility of deep learning models across various fields and tasks, we are confronted with emerging challenges. Among them, one prevalent issue is the biases inherent in deep models, which often mimic stereotypical or subjective behavior observed in data, potentially resulting in negative societal impact or disadvantaging certain subpopulations based on race, gender, etc. This dissertation addresses the critical problem of fairness and bias in machine learning from diverse perspectives, encompassing both data biases and model biases.</p><p dir="ltr">First, we study the multifaceted nature of data biases to comprehensively address the challenges. Specifically, the proposed approaches include the development of a generative model for balancing data distribution with counterfactual samples to address data skewness. In addition, we introduce a novel feature selection method aimed at eliminating sensitive-relevant features that could potentially convey sensitive information, e.g., race, considering the interrelationship between features. Moreover, we present a scalable thresholding method to appropriately binarize model outputs or regression data considering fairness constraints for fairer decision-making, extending fairness beyond categorical data.</p><p dir="ltr">However, addressing fairness problem solely by correcting data bias often encounters several challenges. Particularly, establishing fairness-curated data demands substantial resources and may be restricted by regal constraints, while explicitly identifying the biases is non-trivial due to their intertwined nature. Further, it is important to recognize that models may interpret data differently by their architectures or downstream tasks. In response, we propose a line of methods to address model bias, on top of addressing the data bias mentioned above, by learning fair latent representations. These methods include fair disentanglement learning, which projects latent subspace independent of sensitive information by employing conditional mutual information, and a debiased contrastive learning method for fair self-supervised learning without sensitive attribute annotations. Lastly, we introduce a novel approach to debias the multimodal embedding of pretrained vision-language models (VLMs) without requiring downstream annotated datasets, retraining, or fine-tuning of the large model considering the constrained resource of research labs.</p>

Recently, there has been a massive growth in the number of mobile users and their traffic. The data traffic volume almost doubles every year. Mobile users are currently running multiple applications that require higher bandwidth which makes users so limited to the service providers' resources. Increasing the utilization of the existing spectrum can significantly improve network capacity, data rates and user experience. Spectrum sharing enables wireless systems to harvest under-utilized swathes of spectrum, which would vastly increase the efficiency of spectrum usage. Making more spectrum available can provide significant gain in mobile broadband capacity only if those resources can be aggregated efficiently with the existing commercial mobile system resources. Carrier aggregation (CA) is one of the most distinct features of 4G systems including Long Term Evolution Advanced (LTE-Advanced). In this dissertation, a resource allocation with carrier aggregation framework is proposed to allocate multiple carriers resources optimally among users with elastic and inelastic traffic in cellular networks. We use utility proportional fairness allocation policy, where the fairness among users is in utility percentage of the application running on the user equipment (UE). A resource allocation (RA) with CA is proposed to allocate single or multiple carriers resources optimally among users subscribing for mobile services. Each user is guaranteed a minimum quality of service (QoS) that varies based on the user's application type. In addition, a resource allocation with user discrimination framework is proposed to allocate single or multiple carriers resources among users running multiple applications. Furthermore, an application-aware resource block (RB) scheduling with CA is proposed to assign RBs of multiple component carriers to users' applications based on a utility proportional fairness scheduling policy. We believe that secure spectrum auctions can revolutionize the spectrum utilization of cellular networks and satisfy the ever increasing demand for resources. Therefore, a framework for multi-tier dynamic spectrum sharing system is proposed to provide an efficient sharing of spectrum with commercial wireless system providers (WSPs) with an emphasis on federal spectrum sharing. The proposed spectrum sharing system (SSS) provides an efficient usage of spectrum resources, manages intra-WSP and inter-WSP interference and provides essential level of security, privacy, and obfuscation to enable the most efficient and reliable usage of the shared spectrum. It features an intermediate spectrum auctioneer responsible for allocating resources to commercial WSPs' base stations (BS)s by running secure spectrum auctions. In order to insure truthfulness in the proposed spectrum auction, an optimal bidding mechanism is proposed to enable BSs (bidders) to determine their true bidding values. We also present a resource allocation based on CA approach to determine the BS's optimal aggregated rate allocated to each UE from both the BS's permanent resources and winning auctioned spectrum resources. / Ph. D.

Fairneß (d.h. faire Konfliktlösung), Randomisierung (d.h. Münzwürfe) und partielle Synchronie sind verschiedene Konzepte, die häufig zur Lösung zentraler Synchronisations- und Koordinationsprobleme in verteilten Systemen verwendet werden. Beispiele für solche Probleme sind das Problem des wechselseitigen Ausschlusses (kurz: Mutex-Problem) sowie das Konsens-Problem. Für einige solcher Probleme wurde bewiesen, daß ohne die oben genannten Konzepte keine Lösung für das betrachtete Problem existiert. Unmöglichkeitsresultate dieser Art verbessern unser Verständnis der Wirkungsweise verteilter Algorithmen sowie das Verständnis des Trade-offs zwischen einem leicht analysierbaren und einem ausdrucksstarken Modell für verteiltes Rechnen. In dieser Arbeit stellen wir zwei neue Unmöglichkeitsresultate vor. Darüberhinaus beleuchten wir ihre Hintergründe. Wir betrachten dabei Modelle, die Randomisierung einbeziehen, da bisher wenig über die Grenzen der Ausdrucksstärke von Randomisierung bekannt ist. Mit einer Lösung eines Problems durch Randomisierung meinen wir, daß das betrachtete Problem mit Wahrscheinlichkeit 1 gelöst wird. Im ersten Teil der Arbeit untersuchen wir die Beziehung von Fairneß und Randomisierung. Einerseits ist bekannt, daß einige Probleme (z.B. das Konsens- Problem) durch Randomisierung nicht aber durch Fairneß lösbar sind. Wir zeigen nun, daß es andererseits auch Probleme gibt (nämlich das Mutex-Problem), die durch Fairneß, nicht aber durch Randomisierung lösbar sind. Daraus folgt, daß Fairneß nicht durch Randomisierung implementiert werden kann. Im zweiten Teil der Arbeit verwenden wir ein Modell, das Fairneß und Randomisierung vereint. Ein solches Modell ist relativ ausdrucksstark: Es erlaubt Lösungen für das Mutex-Problem, das Konsens-Problem, sowie eine Lösung für das allgemeine Mutex-Problem. Beim allgemeinen Mutex-Problem (auch bekannt als Problem der speisenden Philosophen) ist eine Nachbarschaftsrelation auf den Agenten gegeben und ein Algorithmus gesucht, der das Mutex-Problem für jedes Paar von Nachbarn simultan löst. Schließlich betrachten wir das ausfalltolerante allgemeine Mutex-Problem -- eine Variante des allgemeinen Mutex-Problems, bei der Agenten ausfallen können. Wir zeigen, daß sogar die Verbindung von Fairneß und Randomisierung nicht genügt, um eine Lösung für das ausfalltolerante allgemeine Mutex-Problem zu konstruieren. Ein Hintergrund für dieses Unmöglichkeitsresultat ist ein unerwünschtes Phänomen, für das in der Literatur der Begriff Konspiration geprägt wurde. Konspiration wurde bisher nicht adäquat charakterisiert. Wir charakterisieren Konspiration auf der Grundlage nicht-sequentieller Abläufe. Desweiteren zeigen wir, daß Konspiration für eine große Klasse von Systemen durch die zusätzliche Annahme von partieller Synchronie verhindert werden kann, d.h. ein konspirationsbehaftetes System kann zu einem randomisierten System verfeinert werden, das unter Fairneß und partieller Synchronie mit Wahrscheinlichkeit 1 konspirationsfrei ist. Partielle Synchronie fordert, daß alle relativen Geschwindigkeiten im System durch eine Konstante beschränkt sind, die jedoch den Agenten nicht bekannt ist. Die Darstellung der Unmöglichkeitsresultate und die Charakterisierung von Konspiration wird erst durch die Verwendung nicht-sequentieller Abläufe möglich. Ein nicht-sequentieller Ablauf repräsentiert im Gegensatz zu einem sequentiellen Ablauf kausale Ordnung und nicht zeitliche Ordnung von Ereignissen. Wir entwickeln in dieser Arbeit eine nicht-sequentielle Semantik für randomisierte verteilte Algorithmen, da es bisher keine in der Literatur gibt. In dieser Semantik wird kausale Unabhängigkeit durch stochastische Unabhängigkeit widergespiegelt. / Concepts such as fairness (i.e., fair conflict resolution), randomization (i.e., coin flips), and partial synchrony are frequently used to solve fundamental synchronization- and coordination-problems in distributed systems such as the mutual exclusion problem (mutex problem for short) and the consensus problem. For some problems it is proven that, without such concepts, no solution to the particular problem exists. Impossibilty results of that kind improve our understanding of the way distributed algorithms work. They also improve our understanding of the trade-off between a tractable model and a powerful model of distributed computation. In this thesis, we prove two new impossibility results and we investigate their reasons. We are in particular concerned with models for randomized distributed algorithms since little is yet known about the limitations of randomization with respect to the solvability of problems in distributed systems. By a solution through randomization we mean that the problem under consideration is solved with probability 1. In the first part of the thesis, we investigate the relationship between fairness and randomization. On the one hand, it is known that to some problems (e.g. to the consensus problem), randomization admits a solution where fairness does not admit a solution. On the other hand, we show that there are problems (viz. the mutex problem) to which randomization does not admit a solution where fairness does admit a solution. These results imply that fairness cannot be implemented by coin flips. In the second part of the thesis, we consider a model which combines fairness and randomization. Such a model is quite powerful, allowing solutions to the mutex problem, the consensus problem, and a solution to the generalized mutex problem. In the generalized mutex problem (a.k.a. the dining philosophers problem), a neighborhood relation is given and mutual exclusion must be achieved for each pair of neighbors. We finally consider the crash-tolerant generalized mutex problem where every hungry agent eventually becomes critical provided that neither itself nor one of its neighbors crashes. We prove that even the combination of fairness and randomization does not admit a solution to the crash-tolerant generalized mutex problem. We argue that the reason for this impossibility is the inherent occurrence of an undesirable phenomenon known as conspiracy. Conspiracy was not yet properly characterized. We characterize conspiracy on the basis of non-sequential runs, and we show that conspiracy can be prevented by help of the additional assumption of partial synchrony, i.e., we show that every conspiracy-prone system can be refined to a randomized system which is, with probability 1, conspiracy-free under the assumptions of partial synchrony and fairness. Partial synchrony means that each event consumes a bounded amount of time where, however, the bound is not known. We use a non-sequential semantics for distributed algorithms which is essential to some parts of the thesis. In particular, we develop a non-sequential semantics for randomized distributed algorithms since there is no such semantics in the literature. In this non-sequential semantics, causal independence is reflected by stochastic independence.

The thesis analyses the concept ‘fairness’ in consumer contracts regulated by the Consumer Protection Act 68 of 2008, mainly from the perspective of a freedom and fairness orientation. It discusses the evolution of ‘fairness’ as background to a more detailed discussion of the classification of fairness into substantive and procedural fairness. The thesis examines dimensions of fairness, factors which play a role in the determination of fairness, and fairness- oriented approaches in an attempt to formulate a framework for fairness in consumer contracts. The main aspects that should be taken into account to justify a finding of fairness, or to determine whether a contract is fair, are identified. This analysis addresses, too, the extent to which the fairness provisions of the Consumer Protection Act are appropriate (with reference to the law of South Africa, Europe, and England). / Mercantile Law / LL.D.

The dissertation examines the applicability of procedural fairness to actions by members of the South African National Defence Forces (SANDF). The research focuses on and uses the South African Defence Force Union v The Minister of South African National Defence Force (SANDU 2010 judgment) to illustrate how procedural fairness should find application in the SANDF, given the sui generis nature of the defence forces. This judgment presented an opportunity to investigate whether the legislative framework that is available in the SANDF is adequate to protect the right to procedural fairness of the members of the SANDF encapsulated in section 33 of the Constitution, 1996. The dissertation examines the relevant sections of the Defence Act, Military Discipline Supplementary Measures Act, Labour Relations Act (LRA), and the Promotion of Administrative Justice Act (PAJA) read with sections 23 and 33 of the Constitution to determine whether there is a gap that exists in so far as the protection of the right to procedural fairness of members of the defence forces is concerned. It also examines the Military Discipline Code and the rules and regulations of the Defence Forces. The analysis of the SANDU 2010 judgment demonstrates that PAJA could find application in dismissal or employment related disputes within the SANDF. The scenario that is evidenced from the analysis of the defence force legislative framework is that the legislative framework that is available within the SANDF is inadequate to protect and deal with disputes which arise from allegations of infringement of the right to procedural fairness. This scenario is compounded by the fact that the LRA which is the empowering legislation that was promulgated to give effect to the right to section 23 of the Constitution and to deal with dismissal and employment related disputes, does not apply to members of the SANDF. / Public, Constitutional, and International Law / LL. M.

The thesis analyses the concept ‘fairness’ in consumer contracts regulated by the Consumer Protection Act 68 of 2008, mainly from the perspective of a freedom and fairness orientation. It discusses the evolution of ‘fairness’ as background to a more detailed discussion of the classification of fairness into substantive and procedural fairness. The thesis examines dimensions of fairness, factors which play a role in the determination of fairness, and fairness- oriented approaches in an attempt to formulate a framework for fairness in consumer contracts. The main aspects that should be taken into account to justify a finding of fairness, or to determine whether a contract is fair, are identified. This analysis addresses, too, the extent to which the fairness provisions of the Consumer Protection Act are appropriate (with reference to the law of South Africa, Europe, and England). / Mercantile Law / LL.D.

This study focuses on the impact of legal representation in general as well as on CCMA proceedings involving unfair dismissals relating to conduction on capacity. The study also touches on the common law position before the enactment of Labour Relations Act 28 of 1956 and Labour Relations Act 66 of 1995. Rule 25 of CCMA rules which makes provision that legal representation at CCMA arbitration proceedings relating to fairness of dismissal and party has alleged that the reason for dismissal relates to the employees conduct on capacity, the party is not entitled to be represented by a legal practitioner. The dissertation analyses the effect of this provision on the Constitutional rights to legal representations well as rights relating to fair procedure. Refusal of legal representation in certain instances is justified in the right of legislative requirements on obligation placed particularly on the arbitrator legislative measures which, justifies refusal of legal representation at CCMA that cannot be imposed without giving consideration to the Constitution. The study will highlight the South African case on position with regards to legal representation at CCMA. A literature study will be done using current and researched sources such as textbooks, law journals, and legislation, case law, conferences papers and internet sources. Different rights will be weighed up through literature sources. / LLM (Labour Law), North-West University, Potchefstroom Campus, 2015

This study focuses on the impact of legal representation in general as well as on CCMA proceedings involving unfair dismissals relating to conduction on capacity. The study also touches on the common law position before the enactment of Labour Relations Act 28 of 1956 and Labour Relations Act 66 of 1995. Rule 25 of CCMA rules which makes provision that legal representation at CCMA arbitration proceedings relating to fairness of dismissal and party has alleged that the reason for dismissal relates to the employees conduct on capacity, the party is not entitled to be represented by a legal practitioner. The dissertation analyses the effect of this provision on the Constitutional rights to legal representations well as rights relating to fair procedure. Refusal of legal representation in certain instances is justified in the right of legislative requirements on obligation placed particularly on the arbitrator legislative measures which, justifies refusal of legal representation at CCMA that cannot be imposed without giving consideration to the Constitution. The study will highlight the South African case on position with regards to legal representation at CCMA. A literature study will be done using current and researched sources such as textbooks, law journals, and legislation, case law, conferences papers and internet sources. Different rights will be weighed up through literature sources. / LLM (Labour Law), North-West University, Potchefstroom Campus, 2015

The aim of this study was to determine employees' perceptions of the fairness of employment equity practices. It was conducted in an organisation in the Health Services industry, using a Diversity Questionnaire. The sample size was 520 and 245 responses were received, constituting a 47% response rate. Employees' responses were measured along 10 dimensions of employment equity. The unit of analysis was the group according to gender, race, age and job level. Independent t-tests and analysis of variance techniques were used to determine any statistically significant differences in perceptions between groups. Statistically significant differences were found between race groups and job levels. Gender and age did not significantly affect employees' responses. The research concluded that compliance with organisational justice requirements is as important as compliance with legislative requirements. Ultimately, every organisation should adapt its employment equity strategy according to its specific demographic and environmental context. / Industrial and Organisational Psychology / M. Admin.